Stats
Stats are primarily modified through the gear your character has equipped. Weapons/utilities only modify your character while held. For example, holding a Main-Hand and Off-Hand weapon in the first weapon slot will give each other weapon their stats, but neither will benefit from the stats of the weapon(s) in the second slot. Similarly, the bonuses from a Flute are only granted while wielding the Flute. Stats from these sources will not be reflected in the Lobby.
Stats may also be modified by perks, buffs, and debuffs. Stats from perks will be reflected in the Lobby only if those stats are applied unconditionally. Stats from conditional perks (as well as buffs and debuffs) will not be viewable from the Lobby.
Charts
Charts are created using the data points directly taken from the game. Therefore, if there is a mismatch between chart and the in game display, it is better to look at chart info.
For example, even though the formula might give 32.5, in game the display might get rounded to 33.
Attributes
Main stats that affect multiple other stats. Each class has varying base attributes, but they sum up to 105 for each class. Can be found as primary stats (stats which are always present on an item of the same name regardless of rarity or instance such as Strength on a Padded Tunic) as well as enchantments.
Strength
Physical Power
Physical Power governs your Physical Power Bonus.
Strength governs your Physical Power.
0 Strength starts at 0 Physical Power.
- 0 -> 0
- 0 to 100 = 1 each, up to 100
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LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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P_{hysicalPower}(S_{trength})=\left\{0 \le S_{trength}<100:0+1\left|S_{trength}-0\right|\right\}
See Example for how to use.
Physical Power Bonus
Also known as Physical Damage Bonus, Physical Power Bonus governs the potency of your physical damage dealing weapons, utility items, and abilities.
Physical Power governs your Physical Power Bonus.
0 Physical Power starts at -80% Physical Power Bonus.
- 0 -> -80%
- 0 to 5 = 10% each, up to -30%
- 5 to 7 = 5% each, up to -20%
- 7 to 11 = 3% each, up to -8%
- 11 to 15 = 2% each, up to 0%
- 15 to 50 = 1% each, up to 35%
- 50 to 60 = 0.5% each, up to 40%
- 60 to 100 = 0.25% each, up to 50%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
P_{hysicalPowerBonus}(P_{hysicalPower})=\left\{0 \le P_{hysicalPower}<5:-0.8+0.1\left|P_{hysicalPower}-0\right|,5 \le P_{hysicalPower}<7:-0.3+0.05\left|P_{hysicalPower}-5\right|,7 \le P_{hysicalPower}<11:-0.2+0.03\left|P_{hysicalPower}-7\right|,11 \le P_{hysicalPower}<15:-0.08+0.02\left|P_{hysicalPower}-11\right|,15 \le P_{hysicalPower}<50:0+0.01\left|P_{hysicalPower}-15\right|,50 \le P_{hysicalPower}<60:0.35+0.005\left|P_{hysicalPower}-50\right|,60 \le P_{hysicalPower}<100:0.4+0.002\left|P_{hysicalPower}-60\right|\right\}
See Example for how to use.
Lower limit of -100%.
Base Health from Strength
Base Health determines your characters maximum Health.
See the Hybrid stat Base Health for more.
Vigor
Base Health from Vigor
Base Health determines your characters maximum Health.
See the Hybrid stat Base Health for more.
Health Recovery
Affects the rate at which you restore health when Resting, but not when using Bandages.
Health Recovered per tick = Base Recovery * (1 + Health Recovery Bonus)
For example, a Barbarian resting with 95% Health Recovery Bonus will recover
Health Recovered every 2s = 1 * (1 + .95) = 1.95 Health
Can't be found on gear aside from in the form of its governing attribute.
Vigor governs your Health Recovery.
0 Vigor starts at -55% Health Recovery.
- 0 -> -55%
- 0 to 5 = 5% each, up to -30%
- 5 to 15 = 3% each, up to 0%
- 15 to 25 = 7% each, up to 70%
- 25 to 35 = 5% each, up to 120%
- 35 to 84 = 2% each, up to 218%
- 84 to 85 = 1% each, up to 219%
- 85 to 86 = 3% each, up to 222%
- 86 to 100 = 2% each, up to 250%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
H_{ealthRecovery}(V_{igor})=\left\{0 \le V_{igor}<5:-0.55+0.05\left|V_{igor}-0\right|,5 \le V_{igor}<15:-0.3+0.03\left|V_{igor}-5\right|,15 \le V_{igor}<25:0+0.07\left|V_{igor}-15\right|,25 \le V_{igor}<35:0.7+0.05\left|V_{igor}-25\right|,35 \le V_{igor}<84:1.2+0.02\left|V_{igor}-35\right|,84 \le V_{igor}<85:2.18+0.01\left|V_{igor}-84\right|,85 \le V_{igor}<86:2.19+0.03\left|V_{igor}-85\right|,86 \le V_{igor}<100:2.22+0.02\left|V_{igor}-86\right|\right\}
See Example for how to use.
Agility
Action Speed from Agility
Action Speed governs the speed at which you interact with your weapons, meaning stowing, swapping, reloading or attacking with weapons, as well as the speed of usage of consumables.
See the Hybrid stat Action Speed for more.
Move Speed
Move Speed governs the speed at which your character runs or walks. Every 3 points in Move Speed is equal to 1% movement speed. There are many factors which can affect Move Speed, see Movement Speed for details.
To calculate total Move Speed, add the baseline 300 Move Speed to the appropriate value below.
Agility governs your Move Speed.
0 Agility starts at -10 Move Speed.
- 0 -> -10
- 0 to 10 = 0.5 each, up to -5
- 10 to 15 = 1 each, up to 0
- 15 to 75 = 0.75 each, up to 45
- 75 to 100 = 0.5 each, up to 57.5
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
M_{oveSpeed}(A_{gility})=\left\{0 \le A_{gility}<10:-10+0.5\left|A_{gility}-0\right|,10 \le A_{gility}<15:-5+1\left|A_{gility}-10\right|,15 \le A_{gility}<75:0+0.75\left|A_{gility}-15\right|,75 \le A_{gility}<100:45+0.5\left|A_{gility}-75\right|\right\}
See Example for how to use.
Hard capped to 330 Move Speed
Regular Interaction Speed from Agility
Regular Interaction Speed governs the speed at which you interact with objects/mechanisms in the dungeon.
See the Hybrid stat Regular Interaction Speed for more.
Dexterity
Action Speed from Dexterity
Action Speed governs the speed at which you interact with your weapons, meaning stowing, swapping, reloading or attacking with weapons, as well as the speed of usage of consumables.
See the Hybrid stat Action Speed for more.
Manual Dexterity
Manual Dexterity determines how quickly Bard plays an instrument.
Can't be found on gear aside from in the form of its governing attribute.
Dexterity governs your Manual Dexterity.
0 Dexterity starts at -15% Manual Dexterity.
- 0 -> -15%
- 0 to 15 = 1% each, up to 0%
- 15 to 23 = 3% each, up to 24%
- 23 to 31 = 2% each, up to 40%
- 31 to 37 = 1% each, up to 46%
- 37 to 45 = 0.5% each, up to 50%
- 45 to 95 = 0.1% each, up to 55%
- 95 to 100 = 0% each, up to 55%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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M_{anualDexterity}(D_{exterity})=\left\{0 \le D_{exterity}<15:-0.15+0.01\left|D_{exterity}-0\right|,15 \le D_{exterity}<23:0+0.03\left|D_{exterity}-15\right|,23 \le D_{exterity}<31:0.24+0.02\left|D_{exterity}-23\right|,31 \le D_{exterity}<37:0.4+0.01\left|D_{exterity}-31\right|,37 \le D_{exterity}<45:0.46+0.005\left|D_{exterity}-37\right|,45 \le D_{exterity}<95:0.5+0.001\left|D_{exterity}-45\right|,95 \le D_{exterity}<100:0.55+0\left|D_{exterity}-95\right|\right\}
See Example for how to use.
Capped to 50%.
Item Equip Speed
Item Equip Speed adjusts the speed at which you equip all Armors, Ranged Weapons, and Throwable/Percussion/"explosive Light Source" Utility items.
All other items such as Jewelry, Melee Weapons, Shields, and Consumable/Drink/"non-exploding Light Source" Utility items are instantly equipped.
Can't be found on gear aside from in the form of its governing attribute.
Dexterity governs your Item Equip Speed.
0 Dexterity starts at -95% Item Equip Speed.
- 0 -> -95%
- 0 to 1 = 0% each, up to -95%
- 1 to 2 = 4% each, up to -91%
- 2 to 15 = 7% each, up to 0%
- 15 to 35 = 5% each, up to 100%
- 35 to 70 = 2% each, up to 170%
- 70 to 100 = 1% each, up to 200%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
I_{temEquipSpeed}(D_{exterity})=\left\{0 \le D_{exterity}<1:-0.95+0\left|D_{exterity}-0\right|,1 \le D_{exterity}<2:-0.95+0.04\left|D_{exterity}-1\right|,2 \le D_{exterity}<15:-0.91+0.07\left|D_{exterity}-2\right|,15 \le D_{exterity}<35:0+0.05\left|D_{exterity}-15\right|,35 \le D_{exterity}<70:1+0.02\left|D_{exterity}-35\right|,70 \le D_{exterity}<100:1.7+0.01\left|D_{exterity}-70\right|\right\}
See Example for how to use.
Will
Magical Power
Also known as Magic Power, Magical Power governs your Magic Power Bonus.
Will governs your Magical Power.
0 Will starts at 0 Magical Power.
- 0 -> 0
- 0 to 100 = 1 each, up to 100
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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M_{agicalPower}(W_{ill})=\left\{0 \le W_{ill}<100:0+1\left|W_{ill}-0\right|\right\}
See Example for how to use.
Magic Power Bonus
Also known as Magical Damage Bonus, though contrary to this alternative name, it affects Healing too.
Magic Power bonus governs the potency of your magical spells, magical damage dealing abilities and magical healing abilities.
Magical Power governs your Magical Power Bonus.
0 Magical Power starts at -80% Magical Power Bonus.
- 0 -> -80%
- 0 to 5 = 10% each, up to -30%
- 5 to 7 = 5% each, up to -20%
- 7 to 11 = 3% each, up to -8%
- 11 to 15 = 2% each, up to 0%
- 15 to 50 = 1% each, up to 35%
- 50 to 60 = 0.5% each, up to 40%
- 60 to 100 = 0.25% each, up to 50%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
M_{agicalPowerBonus}(M_{agicalPower})=\left\{0 \le M_{agicalPower}<5:-0.8+0.1\left|M_{agicalPower}-0\right|,5 \le M_{agicalPower}<7:-0.3+0.05\left|M_{agicalPower}-5\right|,7 \le M_{agicalPower}<11:-0.2+0.03\left|M_{agicalPower}-7\right|,11 \le M_{agicalPower}<15:-0.08+0.02\left|M_{agicalPower}-11\right|,15 \le M_{agicalPower}<50:0+0.01\left|M_{agicalPower}-15\right|,50 \le M_{agicalPower}<60:0.35+0.005\left|M_{agicalPower}-50\right|,60 \le M_{agicalPower}<100:0.4+0.002\left|M_{agicalPower}-60\right|\right\}
See Example for how to use.
Magical Resistance
Magic Resistance governs your Magical Damage Reduction.
Will governs your Magic Resistance.
0 Will starts at -20 Magic Resistance.
- 0 -> -20
- 0 to 5 = 4 each, up to 0
- 5 to 15 = 3 each, up to 30
- 15 to 33 = 4 each, up to 102
- 33 to 48 = 3 each, up to 147
- 48 to 58 = 2 each, up to 167
- 58 to 100 = 1 each, up to 209
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
M_{agicResistance}(W_{ill})=\left\{0 \le W_{ill}<5:-20+4\left|W_{ill}-0\right|,5 \le W_{ill}<15:0+3\left|W_{ill}-5\right|,15 \le W_{ill}<33:30+4\left|W_{ill}-15\right|,33 \le W_{ill}<48:102+3\left|W_{ill}-33\right|,48 \le W_{ill}<58:147+2\left|W_{ill}-48\right|,58 \le W_{ill}<100:167+1\left|W_{ill}-58\right|\right\}
See Example for how to use.
Magical Damage Reduction
Magical Damage Reduction governs your resistance to magical damage dealing weapons, spells and projectiles.
Magic Resistance governs your Magical Damage Reduction.
-300 Magic Resistance starts at -595% Magical Damage Reduction.
- -300 -> -595%
- -300 to -15 = 2% each, up to -25%
- -15 to 8 = 1% each, up to -2%
- 8 to 18 = 0.5% each, up to 3%
- 18 to 33 = 0.4% each, up to 9%
- 33 to 53 = 0.3% each, up to 15%
- 53 to 85 = 0.25% each, up to 23%
- 85 to 280 = 0.2% each, up to 62%
- 280 to 340 = 0.15% each, up to 71%
- 340 to 430 = 0.1% each, up to 80%
- 430 to 500 = 0.05% each, up to 83.5%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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M_{agicalDamageReduction}(M_{agicResistance})=\left\{-300 \le M_{agicResistance}<-15:-5.95+0.02\left|M_{agicResistance}--300\right|,-15 \le M_{agicResistance}<8:-0.25+0.01\left|M_{agicResistance}--15\right|,8 \le M_{agicResistance}<18:-0.02+0.005\left|M_{agicResistance}-8\right|,18 \le M_{agicResistance}<33:0.03+0.004\left|M_{agicResistance}-18\right|,33 \le M_{agicResistance}<53:0.09+0.003\left|M_{agicResistance}-33\right|,53 \le M_{agicResistance}<85:0.15+0.003\left|M_{agicResistance}-53\right|,85 \le M_{agicResistance}<280:0.23+0.002\left|M_{agicResistance}-85\right|,280 \le M_{agicResistance}<340:0.62+0.001\left|M_{agicResistance}-280\right|,340 \le M_{agicResistance}<430:0.71+0.001\left|M_{agicResistance}-340\right|,430 \le M_{agicResistance}<500:0.8+0\left|M_{agicResistance}-430\right|\right\}
See Example for how to use.
Magical Damage Reduction is capped to 65%
Buff Duration
Buff Duration modifies the duration of any temporary beneficial status effects you have.
Buff Duration does not modify buffs you apply to others.
Will governs your Buff Duration.
0 Will starts at -80% Buff Duration.
- 0 -> -80%
- 0 to 5 = 10% each, up to -30%
- 5 to 7 = 5% each, up to -20%
- 7 to 11 = 3% each, up to -8%
- 11 to 15 = 2% each, up to 0%
- 15 to 50 = 1% each, up to 35%
- 50 to 100 = 0.5% each, up to 60%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
B_{uffDuration}(W_{ill})=\left\{0 \le W_{ill}<5:-0.8+0.1\left|W_{ill}-0\right|,5 \le W_{ill}<7:-0.3+0.05\left|W_{ill}-5\right|,7 \le W_{ill}<11:-0.2+0.03\left|W_{ill}-7\right|,11 \le W_{ill}<15:-0.08+0.02\left|W_{ill}-11\right|,15 \le W_{ill}<50:0+0.01\left|W_{ill}-15\right|,50 \le W_{ill}<100:0.35+0.005\left|W_{ill}-50\right|\right\}
See Example for how to use.
Debuff Duration
Debuff Duration modifies the duration of temporary negative status effects; a negative value will shorten the duration, which is beneficial, and vise versa.
Debuff Duration does not modify debuffs you apply to others.
Will governs your Debuff Duration.
0 Will starts at 400% Debuff Duration.
- 0 -> 400%
- 0 to 1 = -166.7% each, up to 233.3%
- 1 to 2 = -83.3% each, up to 150%
- 2 to 3 = -50% each, up to 100%
- 3 to 4 = -33.3% each, up to 66.7%
- 4 to 5 = -23.8% each, up to 42.9%
- 5 to 6 = -9.6% each, up to 33.3%
- 6 to 7 = -8.3% each, up to 25%
- 7 to 8 = -4.5% each, up to 20.5%
- 8 to 9 = -4.2% each, up to 16.3%
- 9 to 10 = -3.9% each, up to 12.4%
- 10 to 11 = -3.7% each, up to 8.7%
- 11 to 12 = -2.3% each, up to 6.4%
- 12 to 14 = -2.2% each, up to 2%
- 14 to 15 = -2% each, up to 0%
- 15 to 17 = -1% each, up to -2%
- 17 to 19 = -0.9% each, up to -3.8%
- 19 to 20 = -1% each, up to -4.8%
- 20 to 21 = -0.9% each, up to -5.7%
- 21 to 22 = -0.8% each, up to -6.5%
- 22 to 24 = -0.9% each, up to -8.3%
- 24 to 29 = -0.8% each, up to -12.3%
- 29 to 30 = -0.7% each, up to -13%
- 30 to 31 = -0.8% each, up to -13.8%
- 31 to 32 = -0.7% each, up to -14.5%
- 32 to 33 = -0.8% each, up to -15.3%
- 33 to 36 = -0.7% each, up to -17.4%
- 36 to 37 = -0.6% each, up to -18%
- 37 to 39 = -0.7% each, up to -19.4%
- 39 to 41 = -0.6% each, up to -20.6%
- 41 to 42 = -0.7% each, up to -21.3%
- 42 to 46 = -0.6% each, up to -23.7%
- 46 to 47 = -0.5% each, up to -24.2%
- 47 to 49 = -0.6% each, up to -25.4%
- 49 to 50 = -0.5% each, up to -25.9%
- 50 to 52 = -0.3% each, up to -26.5%
- 52 to 53 = -0.2% each, up to -26.7%
- 53 to 55 = -0.3% each, up to -27.3%
- 55 to 56 = -0.2% each, up to -27.5%
- 56 to 58 = -0.3% each, up to -28.1%
- 58 to 59 = -0.2% each, up to -28.3%
- 59 to 60 = -0.3% each, up to -28.6%
- 60 to 61 = -0.2% each, up to -28.8%
- 61 to 62 = -0.3% each, up to -29.1%
- 62 to 63 = -0.2% each, up to -29.3%
- 63 to 64 = -0.3% each, up to -29.6%
- 64 to 65 = -0.2% each, up to -29.8%
- 65 to 66 = -0.3% each, up to -30.1%
- 66 to 67 = -0.2% each, up to -30.3%
- 67 to 68 = -0.3% each, up to -30.6%
- 68 to 70 = -0.2% each, up to -31%
- 70 to 71 = -0.3% each, up to -31.3%
- 71 to 73 = -0.2% each, up to -31.7%
- 73 to 74 = -0.3% each, up to -32%
- 74 to 76 = -0.2% each, up to -32.4%
- 76 to 77 = -0.3% each, up to -32.7%
- 77 to 80 = -0.2% each, up to -33.3%
- 80 to 81 = -0.3% each, up to -33.6%
- 81 to 86 = -0.2% each, up to -34.6%
- 86 to 87 = -0.3% each, up to -34.9%
- 87 to 100 = -0.2% each, up to -37.5%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
D_{ebuffDuration}(W_{ill})=\left\{0 \le W_{ill}<1:4+-1.667\left|W_{ill}-0\right|,1 \le W_{ill}<2:2.333+-0.833\left|W_{ill}-1\right|,2 \le W_{ill}<3:1.5+-0.5\left|W_{ill}-2\right|,3 \le W_{ill}<4:1+-0.333\left|W_{ill}-3\right|,4 \le W_{ill}<5:0.667+-0.238\left|W_{ill}-4\right|,5 \le W_{ill}<6:0.429+-0.096\left|W_{ill}-5\right|,6 \le W_{ill}<7:0.333+-0.083\left|W_{ill}-6\right|,7 \le W_{ill}<8:0.25+-0.045\left|W_{ill}-7\right|,8 \le W_{ill}<9:0.205+-0.042\left|W_{ill}-8\right|,9 \le W_{ill}<10:0.163+-0.039\left|W_{ill}-9\right|,10 \le W_{ill}<11:0.124+-0.037\left|W_{ill}-10\right|,11 \le W_{ill}<12:0.087+-0.023\left|W_{ill}-11\right|,12 \le W_{ill}<14:0.064+-0.022\left|W_{ill}-12\right|,14 \le W_{ill}<15:0.02+-0.02\left|W_{ill}-14\right|,15 \le W_{ill}<17:0+-0.01\left|W_{ill}-15\right|,17 \le W_{ill}<19:-0.02+-0.009\left|W_{ill}-17\right|,19 \le W_{ill}<20:-0.038+-0.01\left|W_{ill}-19\right|,20 \le W_{ill}<21:-0.048+-0.009\left|W_{ill}-20\right|,21 \le W_{ill}<22:-0.057+-0.008\left|W_{ill}-21\right|,22 \le W_{ill}<24:-0.065+-0.009\left|W_{ill}-22\right|,24 \le W_{ill}<29:-0.083+-0.008\left|W_{ill}-24\right|,29 \le W_{ill}<30:-0.123+-0.007\left|W_{ill}-29\right|,30 \le W_{ill}<31:-0.13+-0.008\left|W_{ill}-30\right|,31 \le W_{ill}<32:-0.138+-0.007\left|W_{ill}-31\right|,32 \le W_{ill}<33:-0.145+-0.008\left|W_{ill}-32\right|,33 \le W_{ill}<36:-0.153+-0.007\left|W_{ill}-33\right|,36 \le W_{ill}<37:-0.174+-0.006\left|W_{ill}-36\right|,37 \le W_{ill}<39:-0.18+-0.007\left|W_{ill}-37\right|,39 \le W_{ill}<41:-0.194+-0.006\left|W_{ill}-39\right|,41 \le W_{ill}<42:-0.206+-0.007\left|W_{ill}-41\right|,42 \le W_{ill}<46:-0.213+-0.006\left|W_{ill}-42\right|,46 \le W_{ill}<47:-0.237+-0.005\left|W_{ill}-46\right|,47 \le W_{ill}<49:-0.242+-0.006\left|W_{ill}-47\right|,49 \le W_{ill}<50:-0.254+-0.005\left|W_{ill}-49\right|,50 \le W_{ill}<52:-0.259+-0.003\left|W_{ill}-50\right|,52 \le W_{ill}<53:-0.265+-0.002\left|W_{ill}-52\right|,53 \le W_{ill}<55:-0.267+-0.003\left|W_{ill}-53\right|,55 \le W_{ill}<56:-0.273+-0.002\left|W_{ill}-55\right|,56 \le W_{ill}<58:-0.275+-0.003\left|W_{ill}-56\right|,58 \le W_{ill}<59:-0.281+-0.002\left|W_{ill}-58\right|,59 \le W_{ill}<60:-0.283+-0.003\left|W_{ill}-59\right|,60 \le W_{ill}<61:-0.286+-0.002\left|W_{ill}-60\right|,61 \le W_{ill}<62:-0.288+-0.003\left|W_{ill}-61\right|,62 \le W_{ill}<63:-0.291+-0.002\left|W_{ill}-62\right|,63 \le W_{ill}<64:-0.293+-0.003\left|W_{ill}-63\right|,64 \le W_{ill}<65:-0.296+-0.002\left|W_{ill}-64\right|,65 \le W_{ill}<66:-0.298+-0.003\left|W_{ill}-65\right|,66 \le W_{ill}<67:-0.301+-0.002\left|W_{ill}-66\right|,67 \le W_{ill}<68:-0.303+-0.003\left|W_{ill}-67\right|,68 \le W_{ill}<70:-0.306+-0.002\left|W_{ill}-68\right|,70 \le W_{ill}<71:-0.31+-0.003\left|W_{ill}-70\right|,71 \le W_{ill}<73:-0.313+-0.002\left|W_{ill}-71\right|,73 \le W_{ill}<74:-0.317+-0.003\left|W_{ill}-73\right|,74 \le W_{ill}<76:-0.32+-0.002\left|W_{ill}-74\right|,76 \le W_{ill}<77:-0.324+-0.003\left|W_{ill}-76\right|,77 \le W_{ill}<80:-0.327+-0.002\left|W_{ill}-77\right|,80 \le W_{ill}<81:-0.333+-0.003\left|W_{ill}-80\right|,81 \le W_{ill}<86:-0.336+-0.002\left|W_{ill}-81\right|,86 \le W_{ill}<87:-0.346+-0.003\left|W_{ill}-86\right|,87 \le W_{ill}<100:-0.349+-0.002\left|W_{ill}-87\right|\right\}
See Example for how to use.
Debuff Duration has a lower cap of -95%, meaning at minimum a debuff can last 1/20th of its base duration.
Magical Interaction Speed
Magical Interaction Speed affects the speed with which the player interacts with magical objects, such as Shrines and Portals. See Action/Interaction/Cast_Speed for more.
Will governs your Magical Interaction Speed.
0 Will starts at -75% Magical Interaction Speed.
- 0 -> -75%
- 0 to 15 = 5% each, up to 0%
- 15 to 25 = 7% each, up to 70%
- 25 to 35 = 5% each, up to 120%
- 35 to 84 = 2% each, up to 218%
- 84 to 85 = 1% each, up to 219%
- 85 to 86 = 3% each, up to 222%
- 86 to 100 = 2% each, up to 250%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
M_{agicalInteractionSpeed}(W_{ill})=\left\{0 \le W_{ill}<15:-0.75+0.05\left|W_{ill}-0\right|,15 \le W_{ill}<25:0+0.07\left|W_{ill}-15\right|,25 \le W_{ill}<35:0.7+0.05\left|W_{ill}-25\right|,35 \le W_{ill}<84:1.2+0.02\left|W_{ill}-35\right|,84 \le W_{ill}<85:2.18+0.01\left|W_{ill}-84\right|,85 \le W_{ill}<86:2.19+0.03\left|W_{ill}-85\right|,86 \le W_{ill}<100:2.22+0.02\left|W_{ill}-86\right|\right\}
See Example for how to use.
Note that the Debuff Duration Bonus enchant converts into a negative Debuff Duration, decreasing the duration of debuffs on you.
Durations are not rounded and last their exact amount. However, actions that are performed in intervals, like Damage/Healing [time], are rounded down to the nearest integer, resulting in thresholds that players may want to take advantage of.
Knowledge
Spell Casting Speed
Spell Casting Speed governs the speed at which you cast magical spells. See Action/Interaction/Cast_Speed for more.
Knowledge governs your Spell Casting Speed.
0 Knowledge starts at -60% Spell Casting Speed.
- 0 -> -60%
- 0 to 5 = 5% each, up to -35%
- 5 to 10 = 4% each, up to -15%
- 10 to 20 = 3% each, up to 15%
- 20 to 50 = 2.5% each, up to 90%
- 50 to 80 = 2% each, up to 150%
- 80 to 100 = 1.5% each, up to 180%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
S_{pellCastingSpeed}(K_{nowledge})=\left\{0 \le K_{nowledge}<5:-0.6+0.05\left|K_{nowledge}-0\right|,5 \le K_{nowledge}<10:-0.35+0.04\left|K_{nowledge}-5\right|,10 \le K_{nowledge}<20:-0.15+0.03\left|K_{nowledge}-10\right|,20 \le K_{nowledge}<50:0.15+0.025\left|K_{nowledge}-20\right|,50 \le K_{nowledge}<80:0.9+0.02\left|K_{nowledge}-50\right|,80 \le K_{nowledge}<100:1.5+0.015\left|K_{nowledge}-80\right|\right\}
See Example for how to use.
Spell Casting Time = (Base Casting Time)/(1 + Spell Casting Speed)
- A Spell Casting Speed of 50% results in the casting time lasting for only 67% of the base casting time.
- A Spell Casting Speed of 100% results in the casting time lasting for only 50% of the base casting time.
Memory Capacity
Memory Capacity govern your spell/song cost cap, meaning equipping spells/songs that exceed this cap will not be usable.
Knowledge governs your Memory Capacity.
0 Knowledge starts at 0 Memory Capacity.
- 0 -> 0
- 0 to 6 = 0 each, up to 0
- 6 to 100 = 1 each, up to 94
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
M_{emoryCapacity}(K_{nowledge})=\left\{0 \le K_{nowledge}<6:0+0\left|K_{nowledge}-0\right|,6 \le K_{nowledge}<100:0+1\left|K_{nowledge}-6\right|\right\}
See Example for how to use.
Total Memory Capacity = ceil(Memory Cap from Knowledge * (1 + Memory Cap Bonus%)) + Add Memory Cap
Memory Cap Bonus% and Add Memory Cap are two different Enchantments.
For example, with 12 Memory Cap from 18 knowledge, 7.7% Memory Cap Bonus, and +8 Add Memory Cap, the final Memory Capacity will be
ceil(12 * 1.077) + 8 = 21 Memory Capacity
Knowledge vs Memory Capacity Bonus
Expand
Classes |
Knowledge (-6) |
(+1) |
(+2) |
(+3) |
(+4) |
(+5) |
(+6) |
(+7) |
(+8) |
(+9) |
(+10) |
(+11) |
(+12)
|
Warlock |
15 (9) |
5.6% |
16.7% |
27.8% |
38.9% |
50.0% |
61.2% |
|
|
|
|
|
|
|
16 (10) |
5.0% |
15.0% |
25.0% |
35.0% |
45.0% |
55.0% |
65.0% |
|
|
|
N/A |
|
|
17 (11) |
4.6% |
13.7% |
22.8% |
31.9% |
41.0% |
50.0%
|
59.1% |
68.2% |
|
|
|
|
|
18 (12) |
4.2% |
12.5% |
20.9% |
29.2% |
37.5% |
45.9% |
54.2% |
62.5% |
|
|
|
|
|
19 (13) |
3.9% |
11.6% |
19.3% |
27.0% |
34.7% |
42.4% |
50.0% |
57.7% |
65.4% |
|
|
|
Bard/Cleric/Druid |
20 (14) |
3.6% |
10.8% |
17.9% |
25.0% |
32.2% |
39.3% |
46.5% |
53.6% |
60.8% |
67.9% |
|
|
|
21 (15) |
3.4% |
10.0% |
16.7% |
23.4% |
30.0% |
36.7% |
43.4% |
50.0% |
56.7% |
63.4% |
70.0% |
|
|
22 (16) |
3.2% |
9.4% |
15.7% |
21.9% |
28.2% |
34.4% |
40.7% |
46.9% |
53.2% |
59.4% |
65.7% |
|
|
23 (17) |
3.0% |
8.9% |
14.8% |
20.6% |
26.5% |
32.4% |
38.3% |
44.2% |
50.0% |
55.9% |
61.8% |
67.7%
|
|
24 (18) |
2.8% |
8.4% |
13.9% |
19.5% |
25.0% |
30.6% |
36.2% |
41.7% |
47.3% |
52.8% |
58.4% |
63.9%
|
Wizard |
25 (19) |
2.7% |
7.9% |
13.2% |
18.5% |
23.7% |
29.0% |
34.3% |
39.5% |
44.8% |
50.0% |
55.3% |
60.6%
|
|
26 (20) |
2.5% |
7.5% |
12.5% |
17.5% |
22.5% |
27.5% |
32.5% |
37.5% |
42.5% |
47.5% |
52.5% |
57.5%
|
|
27 (21) |
2.4% |
7.2% |
12.0% |
16.7% |
21.5% |
26.2% |
31.0% |
35.8% |
40.5% |
45.3% |
50.0% |
54.8%
|
|
28 (22) |
2.3% |
6.9% |
12.5% |
16.0% |
20.5% |
25.0% |
29.6% |
34.1% |
38.7% |
43.2% |
47.8% |
52.3%
|
|
29 (23) |
2.2% |
6.6% |
10.9% |
15.3% |
19.6% |
24.0% |
28.3% |
32.7% |
37.0% |
41.4% |
45.7% |
50.0%
|
|
30 (24) |
2.1% |
6.3% |
10.5% |
14.6% |
18.8% |
23.0% |
27.1% |
31.3% |
35.5% |
39.6% |
43.8% |
48.0%
|
|
31 (25) |
2.0% |
6.0% |
10.0% |
14.0% |
18.0% |
22.0% |
26.0% |
30.0% |
34.0% |
38.0% |
42.0% |
46.0%
|
|
32 (26) |
2.0% |
5.8% |
9.7% |
13.5% |
17.4% |
21.2% |
25.0% |
28.9% |
32.7% |
36.6% |
40.4% |
44.3%
|
|
33 (27) |
1.9% |
5.6% |
9.3% |
13.0% |
16.7% |
20.4% |
24.1% |
27.8% |
31.5% |
35.2% |
38.9% |
42.6%
|
|
34 (28) |
1.8% |
5.4% |
9.0% |
12.5% |
16.1% |
19.7% |
23.3% |
26.8% |
30.4% |
34.0% |
37.5% |
41.1%
|
|
35 (29) |
1.8% |
5.2% |
8.7% |
12.1% |
15.6% |
19.0% |
22.5% |
25.9% |
29.4% |
32.8% |
36.3% |
39.7%
|
|
36 (30) |
1.7% |
5.0% |
8.4% |
11.7% |
15.0% |
18.4% |
21.7% |
25.0%
|
28.4% |
31.7% |
35.0% |
38.4%
|
Memory Recovery
Increases the amount of Spell/(Skill?) Points (SP) you restore per tick.
Despite also being referred to as Spell Recovery Bonus, this also applies to Bard songs.
Can't be found on gear aside from in the form of its governing attribute.
Knowledge governs your Memory Recovery.
0 Knowledge starts at 43% Memory Recovery.
- 0 -> 43%
- 0 to 28 = 1.5% each, up to 85%
- 28 to 35 = 5% each, up to 120%
- 35 to 84 = 2% each, up to 218%
- 84 to 85 = 1% each, up to 219%
- 85 to 86 = 3% each, up to 222%
- 86 to 100 = 2% each, up to 250%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
M_{emoryRecovery}(K_{nowledge})=\left\{0 \le K_{nowledge}<28:0.43+0.015\left|K_{nowledge}-0\right|,28 \le K_{nowledge}<35:0.85+0.05\left|K_{nowledge}-28\right|,35 \le K_{nowledge}<84:1.2+0.02\left|K_{nowledge}-35\right|,84 \le K_{nowledge}<85:2.18+0.01\left|K_{nowledge}-84\right|,85 \le K_{nowledge}<86:2.19+0.03\left|K_{nowledge}-85\right|,86 \le K_{nowledge}<100:2.22+0.02\left|K_{nowledge}-86\right|\right\}
See Example for how to use.
SP Recharge per tick (SP/tick) = Base Recharge * (1 + Memory Recovery Bonus)
Resourcefulness
Regular Interaction Speed from Resourcefulness
Regular Interaction Speed governs the speed at which you interact with objects/mechanisms in the dungeon.
See the Hybrid stat Regular Interaction Speed for more.
Cooldown Reduction
Cooldown Reduction reduces the cooldowns of skills/perks, this includes spells such as Sorcerer spells.
Reduced cooldown length = Base Cooldown * (1 - Cooldown Reduction)
Note that perk cooldowns are in the form of a debuff and are additionally affected by Buff/Debuff Duration.
Reduced cooldown length = Post buff/debuff duration cooldown * (1 - Cooldown Reduction)
Can't be found on gear aside from in the form of its governing attribute.
Resourcefulness governs your Cooldown Reduction.
0 Resourcefulness starts at -30% Cooldown Reduction.
- 0 -> -30%
- 0 to 20 = 2% each, up to 10%
- 20 to 50 = 1% each, up to 40%
- 50 to 100 = 0.5% each, up to 65%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
C_{ooldownReduction}(R_{esourcefulness})=\left\{0 \le R_{esourcefulness}<20:-0.3+0.02\left|R_{esourcefulness}-0\right|,20 \le R_{esourcefulness}<50:0.1+0.01\left|R_{esourcefulness}-20\right|,50 \le R_{esourcefulness}<100:0.4+0.005\left|R_{esourcefulness}-50\right|\right\}
See Example for how to use.
Persuasiveness
Persuasiveness determines the duration of Bard songs' buffs/debuffs.
Resourcefulness governs your Persuasiveness.
0 Resourcefulness starts at 0 Persuasiveness.
- 0 -> 0
- 0 to 35 = 1 each, up to 35
- 35 to 71 = 0.5 each, up to 53
- 71 to 99 = 0.25 each, up to 60
- 99 to 100 = 0 each, up to 60
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
P_{ersuasiveness}(R_{esourcefulness})=\left\{0 \le R_{esourcefulness}<35:0+1\left|R_{esourcefulness}-0\right|,35 \le R_{esourcefulness}<71:35+0.5\left|R_{esourcefulness}-35\right|,71 \le R_{esourcefulness}<99:53+0.25\left|R_{esourcefulness}-71\right|,99 \le R_{esourcefulness}<100:60+0\left|R_{esourcefulness}-99\right|\right\}
See Example for how to use.
Base buff duration formula:
Base Duration x (Persuasiveness/Base Persuasiveness) x Persuasiveness Scaling
Base Persuasiveness is currently 15 due to Bard's 15 Resourcefulness.
Each point in Persuasiveness over the base of 15 grants a 6.66% longer base duration.
The duration listed both in game and in a song's description at Bard represent the duration of the song at the base of 15 Persuasiveness. Some songs are noted as 0% Persuasiveness Scaling, meaning they always last the listed amount, before Buff/Debuff duration. Some songs technically apply no duration or their affect lasts only while Channeling, like Peacemaking and Chaotic Discord.
For example, Perfectly played Rousing Rhythms has a 90s duration (as of writing this) there if Bard has 20 Persuasiveness, outgoing base buff duration will be:
90 x 20/15 x 100% = 120 seconds
This will also then get multiplied by the receiver's Buff Duration/Debuff Duration
Can't be found on gear aside from in the form of its governing attribute.
Buff Duration Calculator
Attribute Bonus
Attributes can be multiplied by sources such as Warlock's Curse of Weakness, or Wizard's Sage perk. These multipliers are applied after all other sources of additional attributes.
Final Attribute = Attribute * (1 + Attribute Bonus)
For example, with 30 Strength, and 15% Strength Bonus, final strength would be
Final Strength = 30 * (1 + 0.15) = 34.5 Strength
Note that attributes can have decimals, though in the in game details page they will be rounded.
Not to be confused with Attribute Bonus Ratio (Scaling)
Hybrid Stats
Hybrid stats are stats which come from a combination of attributes. For example, Health is determined by both Strength and Vigor.
Hybrid stats are calculated by first using separate weights to combine the relevant attributes into a Rating (which is not displayed in the Details screen), and then converting that Rating into the value displayed in the Details screen. This intermediate Rating can be fractional and is not rounded before being converted to the appropriate stat.
Base Health
Base Health partially determines your characters maximum Health.
Strength and Vigor governs your Base Health.
Strength gives 0.25 Base Health Rating, and Vigor gives 0.75 Base Health Rating, which then get summed into a total Base Health Rating and finally converted into Base Health using the graph.
Base Health Rating = Strength * 0.25 + Vigor * 0.75
0 Base Health Rating starts at 80 Base Health.
- 0 -> 80
- 0 to 34 = 2 each, up to 148
- 34 to 50 = 1.5 each, up to 172
- 50 to 75 = 1 each, up to 197
- 75 to 100 = 0.5 each, up to 209.5
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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B_{aseHealth}(S_{um})=\left\{0 \le S_{um}<34:80+2\left|S_{um}-0\right|,34 \le S_{um}<50:148+1.5\left|S_{um}-34\right|,50 \le S_{um}<75:172+1\left|S_{um}-50\right|,75 \le S_{um}<100:197+0.5\left|S_{um}-75\right|\right\}
See Example for how to use.
Final Health formula with examples can be found on the Health page.
Action Speed
Action Speed governs the speed at which you interact with your weapons, meaning stowing, swapping, reloading or attacking with weapons, as well as the speed of usage of consumables. See Action/Interaction/Cast_Speed for more.
Agility and Dexterity governs your Action Speed.
Agility gives 0.25 Action Speed Rating, and Dexterity gives 0.75 Action Speed Rating, which then get summed into a total Action Speed Rating and finally converted into Action Speed using the graph.
Action Speed Rating = Agility * 0.25 + Dexterity * 0.75
0 Action Speed Rating starts at -38% Action Speed.
- 0 -> -38%
- 0 to 10 = 3% each, up to -8%
- 10 to 13 = 2% each, up to -2%
- 13 to 25 = 1% each, up to 10%
- 25 to 41 = 1.5% each, up to 34%
- 41 to 50 = 1% each, up to 43%
- 50 to 100 = 0.5% each, up to 68%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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A_{ctionSpeed}(S_{um})=\left\{0 \le S_{um}<10:-0.38+0.03\left|S_{um}-0\right|,10 \le S_{um}<13:-0.08+0.02\left|S_{um}-10\right|,13 \le S_{um}<25:-0.02+0.01\left|S_{um}-13\right|,25 \le S_{um}<41:0.1+0.015\left|S_{um}-25\right|,41 \le S_{um}<50:0.34+0.01\left|S_{um}-41\right|,50 \le S_{um}<100:0.43+0.005\left|S_{um}-50\right|\right\}
See Example for how to use.
An Action Speed of 50% results in the animation lasting for only 67% of the base animation length.
New animation length = Base animation length / (1 + Action Speed)
Regular Interaction Speed
Regular Interaction Speed governs the speed at which you interact with objects/mechanisms in the dungeon. See Action/Interaction/Cast_Speed for more.
Agility and Resourcefulness governs your Regular Interaction Speed.
Agility gives 0.4 Regular Interaction Speed Rating, and Resourcefulness gives 0.6 Regular Interaction Speed Rating, which then get summed into a total Regular Interaction Speed Rating and finally converted into Regular Interaction Speed using the graph.
Regular Interaction Speed Rating = Agility * 0.4 + Resourcefulness * 0.6
0 Regular Interaction Speed Rating starts at -26% Regular Interaction Speed.
- 0 -> -26%
- 0 to 7 = 2% each, up to -12%
- 7 to 15 = 1.5% each, up to 0%
- 15 to 20 = 7% each, up to 35%
- 20 to 25 = 6% each, up to 65%
- 25 to 30 = 5% each, up to 90%
- 30 to 35 = 4% each, up to 110%
- 35 to 40 = 3% each, up to 125%
- 40 to 45 = 2% each, up to 135%
- 45 to 100 = 1% each, up to 190%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
R_{egularInteractionSpeed}(S_{um})=\left\{0 \le S_{um}<7:-0.26+0.02\left|S_{um}-0\right|,7 \le S_{um}<15:-0.12+0.015\left|S_{um}-7\right|,15 \le S_{um}<20:0+0.07\left|S_{um}-15\right|,20 \le S_{um}<25:0.35+0.06\left|S_{um}-20\right|,25 \le S_{um}<30:0.65+0.05\left|S_{um}-25\right|,30 \le S_{um}<35:0.9+0.04\left|S_{um}-30\right|,35 \le S_{um}<40:1.1+0.03\left|S_{um}-35\right|,40 \le S_{um}<45:1.25+0.02\left|S_{um}-40\right|,45 \le S_{um}<100:1.35+0.01\left|S_{um}-45\right|\right\}
See Example for how to use.
New interaction length = Base interaction length / (1 + interaction speed)
For example, an Interaction Speed of 100% results in the interaction time lasting for only 50% of the base interaction length.
Surgical Kits and Bandages have 50% Scaling on regular interaction speed, therefore, their formula looks like
New interaction length = Base interaction length / (1 + interaction speed * .5)
Other Stats
Armor Rating
Armor Rating (AR) is determined from the armor your wearing, but can also be increased in some ways such as Fighter's Barricade (Armor Rating) or Fighter's Defense Mastery (Armor Rating Bonus).
Formula can be simplified as:
Final Armor Rating = Armor Rating * (1 + Armor Rating Bonus)
Note that Fighter's Defense Mastery and Rogue's Weakpoint Attack are specifically Item Armor Rating Bonus, meaning they only affect the AR from Items (excluding enchants), where the following formula should be applied.
Final Armor Rating = Armor Rating from armor * (1 + Item Armor Rating Bonus) + other Armor Rating * (1 + Armor Rating Bonus)
Note that only Item Armor Rating Bonus exists currently, and not Armor Rating Bonus. Therefore, the shortest form of this expanded formula can be written as:
Final Armor Rating = Armor Rating from armor * (1 + Item Armor Rating bonus) + other Armor Rating
Example using the last formula:
With 100 AR from equipped Items, 20 from Enchantments, and -40% Item Armor Rating Bonus, the player would result in
100 * (1 + -0.4) + 20 = 80 Armor Rating
Physical Damage Reduction
Physical Damage Reduction governs your resistance to physical damage dealing weapons and projectiles. Unlike Magic Resistance that is increased by Will, Armor Rating does not have an attribute stat that it scales off.
Armor Rating governs your Physical Damage Reduction.
-300 Armor Rating starts at -619% Physical Damage Reduction.
- -300 -> -619%
- -300 to -12 = 2% each, up to -43%
- -12 to -4 = 1.5% each, up to -31%
- -4 to 0 = 1.2% each, up to -26.2%
- 0 to 20 = 1% each, up to -6.2%
- 20 to 30 = 0.5% each, up to -1.2%
- 30 to 45 = 0.4% each, up to 4.8%
- 45 to 65 = 0.3% each, up to 10.8%
- 65 to 125 = 0.25% each, up to 25.8%
- 125 to 275 = 0.2% each, up to 55.8%
- 275 to 312 = 0.15% each, up to 61.35%
- 312 to 313 = 0.12% each, up to 61.47%
- 313 to 314 = 0.18% each, up to 61.65%
- 314 to 315 = 0.15% each, up to 61.8%
- 315 to 374 = 0.1% each, up to 67.7%
- 374 to 455 = 0.05% each, up to 71.75%
- 455 to 456 = 0.03% each, up to 71.78%
- 456 to 457 = 0.07% each, up to 71.85%
- 457 to 475 = 0.05% each, up to 72.75%
- 475 to 476 = 0.03% each, up to 72.78%
- 476 to 477 = 0.065% each, up to 72.845%
- 477 to 478 = 0.055% each, up to 72.9%
- 478 to 500 = 0.05% each, up to 74%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
P_{hysicalDamageReduction}(A_{rmorRating})=\left\{-300 \le A_{rmorRating}<-12:-6.19+0.02\left|A_{rmorRating}--300\right|,-12 \le A_{rmorRating}<-4:-0.43+0.015\left|A_{rmorRating}--12\right|,-4 \le A_{rmorRating}<0:-0.31+0.012\left|A_{rmorRating}--4\right|,0 \le A_{rmorRating}<20:-0.262+0.01\left|A_{rmorRating}-0\right|,20 \le A_{rmorRating}<30:-0.062+0.005\left|A_{rmorRating}-20\right|,30 \le A_{rmorRating}<45:-0.012+0.004\left|A_{rmorRating}-30\right|,45 \le A_{rmorRating}<65:0.048+0.003\left|A_{rmorRating}-45\right|,65 \le A_{rmorRating}<125:0.108+0.003\left|A_{rmorRating}-65\right|,125 \le A_{rmorRating}<275:0.258+0.002\left|A_{rmorRating}-125\right|,275 \le A_{rmorRating}<312:0.558+0.001\left|A_{rmorRating}-275\right|,312 \le A_{rmorRating}<313:0.614+0.001\left|A_{rmorRating}-312\right|,313 \le A_{rmorRating}<314:0.615+0.002\left|A_{rmorRating}-313\right|,314 \le A_{rmorRating}<315:0.617+0.001\left|A_{rmorRating}-314\right|,315 \le A_{rmorRating}<374:0.618+0.001\left|A_{rmorRating}-315\right|,374 \le A_{rmorRating}<455:0.677+0\left|A_{rmorRating}-374\right|,455 \le A_{rmorRating}<456:0.718+0\left|A_{rmorRating}-455\right|,456 \le A_{rmorRating}<457:0.718+0.001\left|A_{rmorRating}-456\right|,457 \le A_{rmorRating}<475:0.719+0.001\left|A_{rmorRating}-457\right|,475 \le A_{rmorRating}<476:0.728+0\left|A_{rmorRating}-475\right|,476 \le A_{rmorRating}<477:0.728+0.001\left|A_{rmorRating}-476\right|,477 \le A_{rmorRating}<478:0.728+0.001\left|A_{rmorRating}-477\right|,478 \le A_{rmorRating}<500:0.729+0.001\left|A_{rmorRating}-478\right|\right\}
See Example for how to use.
Physical Damage Reduction is capped to 65%
Impact Power
Impact Power governs the strength of your weapon strikes against a target, it determines if you can break objects and stagger blocking enemies.
Can't be found on gear (aside from the base values for each weapon) and is not affected by other stats.
Item Swap Speed
Speed at which items are swapped as the current active item. Note that this is separate from Wearing Time Speed.
Affected by Action Speed.
Wearing Time Speed
Speed at which items are worn by equipping them from the inventory. Note that this is separate from Item Swap Speed.
Affected by Item Equip Speed.
Luck
Luck affects the Loot that is rolled when you open a container or kill a monster.
Whoever opens the container first or lands the killing blow on the monster is the character whose Luck is used to calculate the drops.
Luck is capped at 500.
It is possible to reach the Luck cap:
Needs further testing!
Expand
Which character's Luck is used if a monster or the environment kills a monster? Do monsters/traps have Luck? Is loot instead rolled when the monster is first looted? Contribute by joining the Spells & Guns discord!
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Luck Scalar
Luck Scalars are but one piece of information needed to calculate drop probability at X Luck.
The calculation is not a simple multiplication, so do not expect Uniques to be 4.382 times more common at 500 Luck.
The true effect of Luck varies depending on Drop Rate tables.
See the Luck subsection Probabilities from Luck for an in-depth explanation of how Luck Scalars affect probabilities of drops.
Additionally, luck works with a hidden property called Luck Grade. Many loot tables will match item rarity one to one with item luck grade, but there are exceptions, see the Cave Troll's quest drops for a counterexample.
Luck Scalar Graphs
Updated for
Patch:6.8#Patch 8! The domain has been adjusted from 0-500 to 0-5000 to better reflect user-collected findings.
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
L_{uckGrade00}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<5000:1+0\left|L_{uckGrade}-0\right|\right\}
See Example for how to use.
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
L_{uckGrade01}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<5000:1+0\left|L_{uckGrade}-0\right|\right\}
See Example for how to use.
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
L_{uckGrade02}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<5000:1+0\left|L_{uckGrade}-0\right|\right\}
See Example for how to use.
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
L_{uckGrade03}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<5000:1+0\left|L_{uckGrade}-0\right|\right\}
See Example for how to use.
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
L_{uckGrade04}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<130:1+0\left|L_{uckGrade}-0\right|,130 \le L_{uckGrade}<140:1.039+0\left|L_{uckGrade}-130\right|,140 \le L_{uckGrade}<220:1.041+0\left|L_{uckGrade}-140\right|,220 \le L_{uckGrade}<230:1.065+0\left|L_{uckGrade}-220\right|,230 \le L_{uckGrade}<290:1.067+0\left|L_{uckGrade}-230\right|,290 \le L_{uckGrade}<300:1.085+0\left|L_{uckGrade}-290\right|,300 \le L_{uckGrade}<340:1.087+0\left|L_{uckGrade}-300\right|,340 \le L_{uckGrade}<350:1.099+0\left|L_{uckGrade}-340\right|,350 \le L_{uckGrade}<390:1.101+0\left|L_{uckGrade}-350\right|,390 \le L_{uckGrade}<400:1.113+0\left|L_{uckGrade}-390\right|,400 \le L_{uckGrade}<430:1.115+0\left|L_{uckGrade}-400\right|,430 \le L_{uckGrade}<440:1.124+0\left|L_{uckGrade}-430\right|,440 \le L_{uckGrade}<470:1.126+0\left|L_{uckGrade}-440\right|,470 \le L_{uckGrade}<480:1.135+0\left|L_{uckGrade}-470\right|,480 \le L_{uckGrade}<500:1.137+0\left|L_{uckGrade}-480\right|,500 \le L_{uckGrade}<510:1.143+0\left|L_{uckGrade}-500\right|,510 \le L_{uckGrade}<530:1.145+0\left|L_{uckGrade}-510\right|,530 \le L_{uckGrade}<540:1.151+0\left|L_{uckGrade}-530\right|,540 \le L_{uckGrade}<560:1.153+0\left|L_{uckGrade}-540\right|,560 \le L_{uckGrade}<570:1.159+0\left|L_{uckGrade}-560\right|,570 \le L_{uckGrade}<590:1.161+0\left|L_{uckGrade}-570\right|,590 \le L_{uckGrade}<600:1.167+0\left|L_{uckGrade}-590\right|,600 \le L_{uckGrade}<620:1.169+0\left|L_{uckGrade}-600\right|,620 \le L_{uckGrade}<630:1.175+0\left|L_{uckGrade}-620\right|,630 \le L_{uckGrade}<650:1.177+0\left|L_{uckGrade}-630\right|,650 \le L_{uckGrade}<660:1.183+0\left|L_{uckGrade}-650\right|,660 \le L_{uckGrade}<670:1.185+0\left|L_{uckGrade}-660\right|,670 \le L_{uckGrade}<680:1.188+0\left|L_{uckGrade}-670\right|,680 \le L_{uckGrade}<700:1.19+0\left|L_{uckGrade}-680\right|,700 \le L_{uckGrade}<710:1.196+0\left|L_{uckGrade}-700\right|,710 \le L_{uckGrade}<720:1.198+0\left|L_{uckGrade}-710\right|,720 \le L_{uckGrade}<730:1.201+0\left|L_{uckGrade}-720\right|,730 \le L_{uckGrade}<740:1.203+0\left|L_{uckGrade}-730\right|,740 \le L_{uckGrade}<750:1.206+0\left|L_{uckGrade}-740\right|,750 \le L_{uckGrade}<760:1.208+0\left|L_{uckGrade}-750\right|,760 \le L_{uckGrade}<770:1.211+0\left|L_{uckGrade}-760\right|,770 \le L_{uckGrade}<790:1.213+0\left|L_{uckGrade}-770\right|,790 \le L_{uckGrade}<800:1.219+0\left|L_{uckGrade}-790\right|,800 \le L_{uckGrade}<810:1.221+0\left|L_{uckGrade}-800\right|,810 \le L_{uckGrade}<820:1.224+0\left|L_{uckGrade}-810\right|,820 \le L_{uckGrade}<830:1.226+0\left|L_{uckGrade}-820\right|,830 \le L_{uckGrade}<840:1.229+0\left|L_{uckGrade}-830\right|,840 \le L_{uckGrade}<850:1.231+0\left|L_{uckGrade}-840\right|,850 \le L_{uckGrade}<860:1.234+0\left|L_{uckGrade}-850\right|,860 \le L_{uckGrade}<870:1.236+0\left|L_{uckGrade}-860\right|,870 \le L_{uckGrade}<880:1.239+0\left|L_{uckGrade}-870\right|,880 \le L_{uckGrade}<890:1.241+0\left|L_{uckGrade}-880\right|,890 \le L_{uckGrade}<910:1.244+0\left|L_{uckGrade}-890\right|,910 \le L_{uckGrade}<920:1.248+0\left|L_{uckGrade}-910\right|,920 \le L_{uckGrade}<930:1.251+0\left|L_{uckGrade}-920\right|,930 \le L_{uckGrade}<940:1.253+0\left|L_{uckGrade}-930\right|,940 \le L_{uckGrade}<950:1.256+0\left|L_{uckGrade}-940\right|,950 \le L_{uckGrade}<960:1.258+0\left|L_{uckGrade}-950\right|,960 \le L_{uckGrade}<980:1.261+0\left|L_{uckGrade}-960\right|,980 \le L_{uckGrade}<990:1.265+0\left|L_{uckGrade}-980\right|,990 \le L_{uckGrade}<1000:1.268+0\left|L_{uckGrade}-990\right|,1000 \le L_{uckGrade}<1010:1.27+0\left|L_{uckGrade}-1000\right|,1010 \le L_{uckGrade}<1030:1.273+0\left|L_{uckGrade}-1010\right|,1030 \le L_{uckGrade}<1040:1.277+0\left|L_{uckGrade}-1030\right|,1040 \le L_{uckGrade}<1050:1.28+0\left|L_{uckGrade}-1040\right|,1050 \le L_{uckGrade}<1060:1.282+0\left|L_{uckGrade}-1050\right|,1060 \le L_{uckGrade}<1080:1.285+0\left|L_{uckGrade}-1060\right|,1080 \le L_{uckGrade}<1090:1.289+0\left|L_{uckGrade}-1080\right|,1090 \le L_{uckGrade}<1110:1.292+0\left|L_{uckGrade}-1090\right|,1110 \le L_{uckGrade}<1120:1.296+0\left|L_{uckGrade}-1110\right|,1120 \le L_{uckGrade}<1140:1.299+0\left|L_{uckGrade}-1120\right|,1140 \le L_{uckGrade}<1150:1.303+0\left|L_{uckGrade}-1140\right|,1150 \le L_{uckGrade}<1170:1.306+0\left|L_{uckGrade}-1150\right|,1170 \le L_{uckGrade}<1180:1.31+0\left|L_{uckGrade}-1170\right|,1180 \le L_{uckGrade}<1210:1.313+0\left|L_{uckGrade}-1180\right|,1210 \le L_{uckGrade}<1220:1.319+0\left|L_{uckGrade}-1210\right|,1220 \le L_{uckGrade}<1240:1.322+0\left|L_{uckGrade}-1220\right|,1240 \le L_{uckGrade}<1250:1.326+0\left|L_{uckGrade}-1240\right|,1250 \le L_{uckGrade}<1290:1.329+0\left|L_{uckGrade}-1250\right|,1290 \le L_{uckGrade}<1300:1.337+0\left|L_{uckGrade}-1290\right|,1300 \le L_{uckGrade}<1330:1.34+0\left|L_{uckGrade}-1300\right|,1330 \le L_{uckGrade}<1340:1.346+0\left|L_{uckGrade}-1330\right|,1340 \le L_{uckGrade}<1390:1.349+0\left|L_{uckGrade}-1340\right|,1390 \le L_{uckGrade}<1400:1.359+0\left|L_{uckGrade}-1390\right|,1400 \le L_{uckGrade}<1460:1.362+0\left|L_{uckGrade}-1400\right|,1460 \le L_{uckGrade}<1470:1.374+0\left|L_{uckGrade}-1460\right|,1470 \le L_{uckGrade}<1560:1.377+0\left|L_{uckGrade}-1470\right|,1560 \le L_{uckGrade}<1570:1.395+0\left|L_{uckGrade}-1560\right|,1570 \le L_{uckGrade}<1770:1.398+0\left|L_{uckGrade}-1570\right|,1770 \le L_{uckGrade}<1780:1.438+0\left|L_{uckGrade}-1770\right|,1780 \le L_{uckGrade}<1880:1.439+0\left|L_{uckGrade}-1780\right|,1880 \le L_{uckGrade}<1890:1.459+0\left|L_{uckGrade}-1880\right|,1890 \le L_{uckGrade}<1950:1.46+0\left|L_{uckGrade}-1890\right|,1950 \le L_{uckGrade}<1960:1.472+0\left|L_{uckGrade}-1950\right|,1960 \le L_{uckGrade}<2000:1.473+0\left|L_{uckGrade}-1960\right|,2000 \le L_{uckGrade}<2010:1.481+0\left|L_{uckGrade}-2000\right|,2010 \le L_{uckGrade}<2050:1.482+0\left|L_{uckGrade}-2010\right|,2050 \le L_{uckGrade}<2060:1.49+0\left|L_{uckGrade}-2050\right|,2060 \le L_{uckGrade}<2090:1.491+0\left|L_{uckGrade}-2060\right|,2090 \le L_{uckGrade}<2100:1.497+0\left|L_{uckGrade}-2090\right|,2100 \le L_{uckGrade}<2130:1.498+0\left|L_{uckGrade}-2100\right|,2130 \le L_{uckGrade}<2140:1.504+0\left|L_{uckGrade}-2130\right|,2140 \le L_{uckGrade}<2160:1.505+0\left|L_{uckGrade}-2140\right|,2160 \le L_{uckGrade}<2170:1.509+0\left|L_{uckGrade}-2160\right|,2170 \le L_{uckGrade}<2190:1.51+0\left|L_{uckGrade}-2170\right|,2190 \le L_{uckGrade}<2200:1.514+0\left|L_{uckGrade}-2190\right|,2200 \le L_{uckGrade}<2220:1.515+0\left|L_{uckGrade}-2200\right|,2220 \le L_{uckGrade}<2230:1.519+0\left|L_{uckGrade}-2220\right|,2230 \le L_{uckGrade}<2250:1.52+0\left|L_{uckGrade}-2230\right|,2250 \le L_{uckGrade}<2260:1.524+0\left|L_{uckGrade}-2250\right|,2260 \le L_{uckGrade}<2280:1.525+0\left|L_{uckGrade}-2260\right|,2280 \le L_{uckGrade}<2290:1.529+0\left|L_{uckGrade}-2280\right|,2290 \le L_{uckGrade}<2310:1.53+0\left|L_{uckGrade}-2290\right|,2310 \le L_{uckGrade}<2320:1.534+0\left|L_{uckGrade}-2310\right|,2320 \le L_{uckGrade}<2330:1.535+0\left|L_{uckGrade}-2320\right|,2330 \le L_{uckGrade}<2340:1.537+0\left|L_{uckGrade}-2330\right|,2340 \le L_{uckGrade}<2360:1.538+0\left|L_{uckGrade}-2340\right|,2360 \le L_{uckGrade}<2370:1.542+0\left|L_{uckGrade}-2360\right|,2370 \le L_{uckGrade}<2380:1.543+0\left|L_{uckGrade}-2370\right|,2380 \le L_{uckGrade}<2390:1.545+0\left|L_{uckGrade}-2380\right|,2390 \le L_{uckGrade}<2400:1.546+0\left|L_{uckGrade}-2390\right|,2400 \le L_{uckGrade}<2410:1.548+0\left|L_{uckGrade}-2400\right|,2410 \le L_{uckGrade}<2430:1.549+0\left|L_{uckGrade}-2410\right|,2430 \le L_{uckGrade}<2440:1.553+0\left|L_{uckGrade}-2430\right|,2440 \le L_{uckGrade}<2450:1.554+0\left|L_{uckGrade}-2440\right|,2450 \le L_{uckGrade}<2460:1.556+0\left|L_{uckGrade}-2450\right|,2460 \le L_{uckGrade}<2470:1.557+0\left|L_{uckGrade}-2460\right|,2470 \le L_{uckGrade}<2480:1.559+0\left|L_{uckGrade}-2470\right|,2480 \le L_{uckGrade}<2490:1.56+0\left|L_{uckGrade}-2480\right|,2490 \le L_{uckGrade}<2500:1.562+0\left|L_{uckGrade}-2490\right|,2500 \le L_{uckGrade}<2510:1.563+0\left|L_{uckGrade}-2500\right|,2510 \le L_{uckGrade}<2520:1.565+0\left|L_{uckGrade}-2510\right|,2520 \le L_{uckGrade}<2530:1.566+0\left|L_{uckGrade}-2520\right|,2530 \le L_{uckGrade}<2540:1.568+0\left|L_{uckGrade}-2530\right|,2540 \le L_{uckGrade}<2550:1.569+0\left|L_{uckGrade}-2540\right|,2550 \le L_{uckGrade}<2560:1.571+0\left|L_{uckGrade}-2550\right|,2560 \le L_{uckGrade}<2570:1.572+0\left|L_{uckGrade}-2560\right|,2570 \le L_{uckGrade}<2580:1.574+0\left|L_{uckGrade}-2570\right|,2580 \le L_{uckGrade}<2590:1.575+0\left|L_{uckGrade}-2580\right|,2590 \le L_{uckGrade}<2610:1.577+0\left|L_{uckGrade}-2590\right|,2610 \le L_{uckGrade}<2620:1.579+0\left|L_{uckGrade}-2610\right|,2620 \le L_{uckGrade}<2630:1.581+0\left|L_{uckGrade}-2620\right|,2630 \le L_{uckGrade}<2640:1.582+0\left|L_{uckGrade}-2630\right|,2640 \le L_{uckGrade}<2650:1.584+0\left|L_{uckGrade}-2640\right|,2650 \le L_{uckGrade}<2660:1.585+0\left|L_{uckGrade}-2650\right|,2660 \le L_{uckGrade}<2680:1.587+0\left|L_{uckGrade}-2660\right|,2680 \le L_{uckGrade}<2690:1.589+0\left|L_{uckGrade}-2680\right|,2690 \le L_{uckGrade}<2710:1.591+0\left|L_{uckGrade}-2690\right|,2710 \le L_{uckGrade}<2720:1.593+0\left|L_{uckGrade}-2710\right|,2720 \le L_{uckGrade}<2730:1.595+0\left|L_{uckGrade}-2720\right|,2730 \le L_{uckGrade}<2740:1.596+0\left|L_{uckGrade}-2730\right|,2740 \le L_{uckGrade}<2760:1.598+0\left|L_{uckGrade}-2740\right|,2760 \le L_{uckGrade}<2770:1.6+0\left|L_{uckGrade}-2760\right|,2770 \le L_{uckGrade}<2790:1.602+0\left|L_{uckGrade}-2770\right|,2790 \le L_{uckGrade}<2800:1.604+0\left|L_{uckGrade}-2790\right|,2800 \le L_{uckGrade}<2820:1.606+0\left|L_{uckGrade}-2800\right|,2820 \le L_{uckGrade}<2830:1.608+0\left|L_{uckGrade}-2820\right|,2830 \le L_{uckGrade}<2860:1.61+0\left|L_{uckGrade}-2830\right|,2860 \le L_{uckGrade}<2870:1.613+0\left|L_{uckGrade}-2860\right|,2870 \le L_{uckGrade}<2890:1.615+0\left|L_{uckGrade}-2870\right|,2890 \le L_{uckGrade}<2900:1.617+0\left|L_{uckGrade}-2890\right|,2900 \le L_{uckGrade}<2930:1.619+0\left|L_{uckGrade}-2900\right|,2930 \le L_{uckGrade}<2940:1.622+0\left|L_{uckGrade}-2930\right|,2940 \le L_{uckGrade}<2980:1.624+0\left|L_{uckGrade}-2940\right|,2980 \le L_{uckGrade}<2990:1.628+0\left|L_{uckGrade}-2980\right|,2990 \le L_{uckGrade}<3030:1.63+0\left|L_{uckGrade}-2990\right|,3030 \le L_{uckGrade}<3040:1.634+0\left|L_{uckGrade}-3030\right|,3040 \le L_{uckGrade}<3090:1.636+0\left|L_{uckGrade}-3040\right|,3090 \le L_{uckGrade}<3100:1.641+0\left|L_{uckGrade}-3090\right|,3100 \le L_{uckGrade}<3170:1.643+0\left|L_{uckGrade}-3100\right|,3170 \le L_{uckGrade}<3180:1.65+0\left|L_{uckGrade}-3170\right|,3180 \le L_{uckGrade}<3500:1.652+0\left|L_{uckGrade}-3180\right|,3500 \le L_{uckGrade}<3510:1.684+0\left|L_{uckGrade}-3500\right|,3510 \le L_{uckGrade}<3580:1.684+0\left|L_{uckGrade}-3510\right|,3580 \le L_{uckGrade}<3590:1.691+0\left|L_{uckGrade}-3580\right|,3590 \le L_{uckGrade}<3640:1.691+0\left|L_{uckGrade}-3590\right|,3640 \le L_{uckGrade}<3650:1.696+0\left|L_{uckGrade}-3640\right|,3650 \le L_{uckGrade}<3690:1.696+0\left|L_{uckGrade}-3650\right|,3690 \le L_{uckGrade}<3700:1.7+0\left|L_{uckGrade}-3690\right|,3700 \le L_{uckGrade}<3730:1.7+0\left|L_{uckGrade}-3700\right|,3730 \le L_{uckGrade}<3740:1.703+0\left|L_{uckGrade}-3730\right|,3740 \le L_{uckGrade}<3770:1.703+0\left|L_{uckGrade}-3740\right|,3770 \le L_{uckGrade}<3780:1.706+0\left|L_{uckGrade}-3770\right|,3780 \le L_{uckGrade}<3810:1.706+0\left|L_{uckGrade}-3780\right|,3810 \le L_{uckGrade}<3820:1.709+0\left|L_{uckGrade}-3810\right|,3820 \le L_{uckGrade}<3840:1.709+0\left|L_{uckGrade}-3820\right|,3840 \le L_{uckGrade}<3850:1.711+0\left|L_{uckGrade}-3840\right|,3850 \le L_{uckGrade}<3880:1.711+0\left|L_{uckGrade}-3850\right|,3880 \le L_{uckGrade}<3890:1.714+0\left|L_{uckGrade}-3880\right|,3890 \le L_{uckGrade}<3910:1.714+0\left|L_{uckGrade}-3890\right|,3910 \le L_{uckGrade}<3920:1.716+0\left|L_{uckGrade}-3910\right|,3920 \le L_{uckGrade}<3930:1.716+0\left|L_{uckGrade}-3920\right|,3930 \le L_{uckGrade}<3940:1.717+0\left|L_{uckGrade}-3930\right|,3940 \le L_{uckGrade}<3960:1.717+0\left|L_{uckGrade}-3940\right|,3960 \le L_{uckGrade}<3970:1.719+0\left|L_{uckGrade}-3960\right|,3970 \le L_{uckGrade}<3990:1.719+0\left|L_{uckGrade}-3970\right|,3990 \le L_{uckGrade}<4000:1.721+0\left|L_{uckGrade}-3990\right|,4000 \le L_{uckGrade}<4010:1.721+0\left|L_{uckGrade}-4000\right|,4010 \le L_{uckGrade}<4020:1.722+0\left|L_{uckGrade}-4010\right|,4020 \le L_{uckGrade}<4040:1.722+0\left|L_{uckGrade}-4020\right|,4040 \le L_{uckGrade}<4050:1.724+0\left|L_{uckGrade}-4040\right|,4050 \le L_{uckGrade}<4060:1.724+0\left|L_{uckGrade}-4050\right|,4060 \le L_{uckGrade}<4070:1.725+0\left|L_{uckGrade}-4060\right|,4070 \le L_{uckGrade}<4080:1.725+0\left|L_{uckGrade}-4070\right|,4080 \le L_{uckGrade}<4090:1.726+0\left|L_{uckGrade}-4080\right|,4090 \le L_{uckGrade}<4100:1.726+0\left|L_{uckGrade}-4090\right|,4100 \le L_{uckGrade}<4110:1.727+0\left|L_{uckGrade}-4100\right|,4110 \le L_{uckGrade}<4130:1.727+0\left|L_{uckGrade}-4110\right|,4130 \le L_{uckGrade}<4140:1.729+0\left|L_{uckGrade}-4130\right|,4140 \le L_{uckGrade}<4150:1.729+0\left|L_{uckGrade}-4140\right|,4150 \le L_{uckGrade}<4160:1.73+0\left|L_{uckGrade}-4150\right|,4160 \le L_{uckGrade}<4170:1.73+0\left|L_{uckGrade}-4160\right|,4170 \le L_{uckGrade}<4180:1.731+0\left|L_{uckGrade}-4170\right|,4180 \le L_{uckGrade}<4190:1.731+0\left|L_{uckGrade}-4180\right|,4190 \le L_{uckGrade}<4200:1.732+0\left|L_{uckGrade}-4190\right|,4200 \le L_{uckGrade}<4210:1.732+0\left|L_{uckGrade}-4200\right|,4210 \le L_{uckGrade}<4230:1.733+0\left|L_{uckGrade}-4210\right|,4230 \le L_{uckGrade}<4240:1.733+0\left|L_{uckGrade}-4230\right|,4240 \le L_{uckGrade}<4250:1.734+0\left|L_{uckGrade}-4240\right|,4250 \le L_{uckGrade}<4260:1.734+0\left|L_{uckGrade}-4250\right|,4260 \le L_{uckGrade}<4270:1.735+0\left|L_{uckGrade}-4260\right|,4270 \le L_{uckGrade}<4280:1.735+0\left|L_{uckGrade}-4270\right|,4280 \le L_{uckGrade}<4290:1.736+0\left|L_{uckGrade}-4280\right|,4290 \le L_{uckGrade}<4300:1.736+0\left|L_{uckGrade}-4290\right|,4300 \le L_{uckGrade}<4320:1.737+0\left|L_{uckGrade}-4300\right|,4320 \le L_{uckGrade}<4330:1.737+0\left|L_{uckGrade}-4320\right|,4330 \le L_{uckGrade}<4340:1.738+0\left|L_{uckGrade}-4330\right|,4340 \le L_{uckGrade}<4350:1.738+0\left|L_{uckGrade}-4340\right|,4350 \le L_{uckGrade}<4370:1.739+0\left|L_{uckGrade}-4350\right|,4370 \le L_{uckGrade}<4380:1.739+0\left|L_{uckGrade}-4370\right|,4380 \le L_{uckGrade}<4390:1.74+0\left|L_{uckGrade}-4380\right|,4390 \le L_{uckGrade}<4400:1.74+0\left|L_{uckGrade}-4390\right|,4400 \le L_{uckGrade}<4420:1.741+0\left|L_{uckGrade}-4400\right|,4420 \le L_{uckGrade}<4430:1.741+0\left|L_{uckGrade}-4420\right|,4430 \le L_{uckGrade}<4450:1.742+0\left|L_{uckGrade}-4430\right|,4450 \le L_{uckGrade}<4460:1.742+0\left|L_{uckGrade}-4450\right|,4460 \le L_{uckGrade}<4480:1.743+0\left|L_{uckGrade}-4460\right|,4480 \le L_{uckGrade}<4490:1.743+0\left|L_{uckGrade}-4480\right|,4490 \le L_{uckGrade}<4520:1.744+0\left|L_{uckGrade}-4490\right|,4520 \le L_{uckGrade}<4530:1.744+0\left|L_{uckGrade}-4520\right|,4530 \le L_{uckGrade}<4550:1.745+0\left|L_{uckGrade}-4530\right|,4550 \le L_{uckGrade}<4560:1.745+0\left|L_{uckGrade}-4550\right|,4560 \le L_{uckGrade}<4590:1.746+0\left|L_{uckGrade}-4560\right|,4590 \le L_{uckGrade}<4600:1.746+0\left|L_{uckGrade}-4590\right|,4600 \le L_{uckGrade}<4630:1.747+0\left|L_{uckGrade}-4600\right|,4630 \le L_{uckGrade}<4640:1.747+0\left|L_{uckGrade}-4630\right|,4640 \le L_{uckGrade}<4680:1.748+0\left|L_{uckGrade}-4640\right|,4680 \le L_{uckGrade}<4690:1.748+0\left|L_{uckGrade}-4680\right|,4690 \le L_{uckGrade}<4740:1.749+0\left|L_{uckGrade}-4690\right|,4740 \le L_{uckGrade}<4750:1.749+0\left|L_{uckGrade}-4740\right|,4750 \le L_{uckGrade}<4820:1.75+0\left|L_{uckGrade}-4750\right|,4820 \le L_{uckGrade}<4830:1.75+0\left|L_{uckGrade}-4820\right|,4830 \le L_{uckGrade}<4990:1.751+0\left|L_{uckGrade}-4830\right|,4990 \le L_{uckGrade}<5000:1.751+0\left|L_{uckGrade}-4990\right|\right\}
See Example for how to use.
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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L_{uckGrade05}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<10:1+0.001\left|L_{uckGrade}-0\right|,10 \le L_{uckGrade}<20:1.006+0.001\left|L_{uckGrade}-10\right|,20 \le L_{uckGrade}<50:1.013+0.001\left|L_{uckGrade}-20\right|,50 \le L_{uckGrade}<60:1.031+0.001\left|L_{uckGrade}-50\right|,60 \le L_{uckGrade}<90:1.038+0.001\left|L_{uckGrade}-60\right|,90 \le L_{uckGrade}<100:1.056+0.001\left|L_{uckGrade}-90\right|,100 \le L_{uckGrade}<140:1.063+0.001\left|L_{uckGrade}-100\right|,140 \le L_{uckGrade}<150:1.087+0.001\left|L_{uckGrade}-140\right|,150 \le L_{uckGrade}<370:1.094+0.001\left|L_{uckGrade}-150\right|,370 \le L_{uckGrade}<380:1.226+0.001\left|L_{uckGrade}-370\right|,380 \le L_{uckGrade}<430:1.231+0.001\left|L_{uckGrade}-380\right|,430 \le L_{uckGrade}<440:1.261+0.001\left|L_{uckGrade}-430\right|,440 \le L_{uckGrade}<470:1.266+0.001\left|L_{uckGrade}-440\right|,470 \le L_{uckGrade}<480:1.284+0\left|L_{uckGrade}-470\right|,480 \le L_{uckGrade}<500:1.289+0.001\left|L_{uckGrade}-480\right|,500 \le L_{uckGrade}<510:1.301+0.001\left|L_{uckGrade}-500\right|,510 \le L_{uckGrade}<530:1.306+0.001\left|L_{uckGrade}-510\right|,530 \le L_{uckGrade}<540:1.318+0\left|L_{uckGrade}-530\right|,540 \le L_{uckGrade}<560:1.323+0.001\left|L_{uckGrade}-540\right|,560 \le L_{uckGrade}<570:1.335+0.001\left|L_{uckGrade}-560\right|,570 \le L_{uckGrade}<590:1.34+0.001\left|L_{uckGrade}-570\right|,590 \le L_{uckGrade}<600:1.352+0\left|L_{uckGrade}-590\right|,600 \le L_{uckGrade}<610:1.357+0.001\left|L_{uckGrade}-600\right|,610 \le L_{uckGrade}<620:1.363+0.001\left|L_{uckGrade}-610\right|,620 \le L_{uckGrade}<630:1.368+0.001\left|L_{uckGrade}-620\right|,630 \le L_{uckGrade}<640:1.374+0\left|L_{uckGrade}-630\right|,640 \le L_{uckGrade}<650:1.379+0.001\left|L_{uckGrade}-640\right|,650 \le L_{uckGrade}<660:1.385+0\left|L_{uckGrade}-650\right|,660 \le L_{uckGrade}<670:1.39+0.001\left|L_{uckGrade}-660\right|,670 \le L_{uckGrade}<680:1.396+0.001\left|L_{uckGrade}-670\right|,680 \le L_{uckGrade}<690:1.401+0.001\left|L_{uckGrade}-680\right|,690 \le L_{uckGrade}<700:1.407+0\left|L_{uckGrade}-690\right|,700 \le L_{uckGrade}<710:1.412+0.001\left|L_{uckGrade}-700\right|,710 \le L_{uckGrade}<730:1.418+0.001\left|L_{uckGrade}-710\right|,730 \le L_{uckGrade}<740:1.428+0.001\left|L_{uckGrade}-730\right|,740 \le L_{uckGrade}<750:1.434+0.001\left|L_{uckGrade}-740\right|,750 \le L_{uckGrade}<760:1.439+0.001\left|L_{uckGrade}-750\right|,760 \le L_{uckGrade}<780:1.445+0.001\left|L_{uckGrade}-760\right|,780 \le L_{uckGrade}<790:1.455+0.001\left|L_{uckGrade}-780\right|,790 \le L_{uckGrade}<810:1.461+0.001\left|L_{uckGrade}-790\right|,810 \le L_{uckGrade}<820:1.471+0.001\left|L_{uckGrade}-810\right|,820 \le L_{uckGrade}<850:1.477+0\left|L_{uckGrade}-820\right|,850 \le L_{uckGrade}<860:1.492+0.001\left|L_{uckGrade}-850\right|,860 \le L_{uckGrade}<890:1.498+0\left|L_{uckGrade}-860\right|,890 \le L_{uckGrade}<900:1.513+0.001\left|L_{uckGrade}-890\right|,900 \le L_{uckGrade}<950:1.519+0.001\left|L_{uckGrade}-900\right|,950 \le L_{uckGrade}<960:1.544+0.001\left|L_{uckGrade}-950\right|,960 \le L_{uckGrade}<1140:1.55+0\left|L_{uckGrade}-960\right|,1140 \le L_{uckGrade}<1150:1.64+0\left|L_{uckGrade}-1140\right|,1150 \le L_{uckGrade}<1200:1.644+0.001\left|L_{uckGrade}-1150\right|,1200 \le L_{uckGrade}<1210:1.669+0\left|L_{uckGrade}-1200\right|,1210 \le L_{uckGrade}<1250:1.673+0.001\left|L_{uckGrade}-1210\right|,1250 \le L_{uckGrade}<1260:1.693+0\left|L_{uckGrade}-1250\right|,1260 \le L_{uckGrade}<1280:1.697+0.001\left|L_{uckGrade}-1260\right|,1280 \le L_{uckGrade}<1290:1.707+0\left|L_{uckGrade}-1280\right|,1290 \le L_{uckGrade}<1320:1.711+0\left|L_{uckGrade}-1290\right|,1320 \le L_{uckGrade}<1330:1.726+0\left|L_{uckGrade}-1320\right|,1330 \le L_{uckGrade}<1340:1.73+0.001\left|L_{uckGrade}-1330\right|,1340 \le L_{uckGrade}<1350:1.735+0\left|L_{uckGrade}-1340\right|,1350 \le L_{uckGrade}<1370:1.739+0.001\left|L_{uckGrade}-1350\right|,1370 \le L_{uckGrade}<1380:1.749+0\left|L_{uckGrade}-1370\right|,1380 \le L_{uckGrade}<1390:1.753+0.001\left|L_{uckGrade}-1380\right|,1390 \le L_{uckGrade}<1400:1.758+0\left|L_{uckGrade}-1390\right|,1400 \le L_{uckGrade}<1420:1.762+0.001\left|L_{uckGrade}-1400\right|,1420 \le L_{uckGrade}<1430:1.772+0\left|L_{uckGrade}-1420\right|,1430 \le L_{uckGrade}<1440:1.776+0\left|L_{uckGrade}-1430\right|,1440 \le L_{uckGrade}<1450:1.781+0\left|L_{uckGrade}-1440\right|,1450 \le L_{uckGrade}<1460:1.785+0.001\left|L_{uckGrade}-1450\right|,1460 \le L_{uckGrade}<1480:1.79+0\left|L_{uckGrade}-1460\right|,1480 \le L_{uckGrade}<1490:1.798+0\left|L_{uckGrade}-1480\right|,1490 \le L_{uckGrade}<1500:1.803+0\left|L_{uckGrade}-1490\right|,1500 \le L_{uckGrade}<1510:1.807+0.001\left|L_{uckGrade}-1500\right|,1510 \le L_{uckGrade}<1520:1.812+0\left|L_{uckGrade}-1510\right|,1520 \le L_{uckGrade}<1530:1.816+0\left|L_{uckGrade}-1520\right|,1530 \le L_{uckGrade}<1550:1.821+0\left|L_{uckGrade}-1530\right|,1550 \le L_{uckGrade}<1560:1.829+0.001\left|L_{uckGrade}-1550\right|,1560 \le L_{uckGrade}<1580:1.834+0\left|L_{uckGrade}-1560\right|,1580 \le L_{uckGrade}<1590:1.842+0\left|L_{uckGrade}-1580\right|,1590 \le L_{uckGrade}<1610:1.847+0\left|L_{uckGrade}-1590\right|,1610 \le L_{uckGrade}<1620:1.855+0.001\left|L_{uckGrade}-1610\right|,1620 \le L_{uckGrade}<1650:1.86+0\left|L_{uckGrade}-1620\right|,1650 \le L_{uckGrade}<1660:1.872+0\left|L_{uckGrade}-1650\right|,1660 \le L_{uckGrade}<1690:1.877+0\left|L_{uckGrade}-1660\right|,1690 \le L_{uckGrade}<1700:1.889+0\left|L_{uckGrade}-1690\right|,1700 \le L_{uckGrade}<1770:1.894+0\left|L_{uckGrade}-1700\right|,1770 \le L_{uckGrade}<1780:1.922+0.001\left|L_{uckGrade}-1770\right|,1780 \le L_{uckGrade}<1910:1.927+0\left|L_{uckGrade}-1780\right|,1910 \le L_{uckGrade}<1920:1.979+0\left|L_{uckGrade}-1910\right|,1920 \le L_{uckGrade}<1980:1.982+0\left|L_{uckGrade}-1920\right|,1980 \le L_{uckGrade}<1990:2.006+0\left|L_{uckGrade}-1980\right|,1990 \le L_{uckGrade}<2030:2.009+0\left|L_{uckGrade}-1990\right|,2030 \le L_{uckGrade}<2040:2.025+0\left|L_{uckGrade}-2030\right|,2040 \le L_{uckGrade}<2070:2.028+0\left|L_{uckGrade}-2040\right|,2070 \le L_{uckGrade}<2080:2.04+0\left|L_{uckGrade}-2070\right|,2080 \le L_{uckGrade}<2100:2.043+0\left|L_{uckGrade}-2080\right|,2100 \le L_{uckGrade}<2110:2.051+0\left|L_{uckGrade}-2100\right|,2110 \le L_{uckGrade}<2130:2.054+0\left|L_{uckGrade}-2110\right|,2130 \le L_{uckGrade}<2140:2.062+0\left|L_{uckGrade}-2130\right|,2140 \le L_{uckGrade}<2150:2.065+0\left|L_{uckGrade}-2140\right|,2150 \le L_{uckGrade}<2160:2.069+0\left|L_{uckGrade}-2150\right|,2160 \le L_{uckGrade}<2180:2.072+0\left|L_{uckGrade}-2160\right|,2180 \le L_{uckGrade}<2190:2.08+0\left|L_{uckGrade}-2180\right|,2190 \le L_{uckGrade}<2200:2.083+0\left|L_{uckGrade}-2190\right|,2200 \le L_{uckGrade}<2210:2.087+0\left|L_{uckGrade}-2200\right|,2210 \le L_{uckGrade}<2220:2.09+0\left|L_{uckGrade}-2210\right|,2220 \le L_{uckGrade}<2230:2.094+0\left|L_{uckGrade}-2220\right|,2230 \le L_{uckGrade}<2240:2.097+0\left|L_{uckGrade}-2230\right|,2240 \le L_{uckGrade}<2250:2.101+0\left|L_{uckGrade}-2240\right|,2250 \le L_{uckGrade}<2260:2.104+0\left|L_{uckGrade}-2250\right|,2260 \le L_{uckGrade}<2270:2.108+0\left|L_{uckGrade}-2260\right|,2270 \le L_{uckGrade}<2280:2.111+0\left|L_{uckGrade}-2270\right|,2280 \le L_{uckGrade}<2290:2.115+0\left|L_{uckGrade}-2280\right|,2290 \le L_{uckGrade}<2300:2.118+0\left|L_{uckGrade}-2290\right|,2300 \le L_{uckGrade}<2320:2.122+0\left|L_{uckGrade}-2300\right|,2320 \le L_{uckGrade}<2330:2.128+0\left|L_{uckGrade}-2320\right|,2330 \le L_{uckGrade}<2340:2.132+0\left|L_{uckGrade}-2330\right|,2340 \le L_{uckGrade}<2350:2.135+0\left|L_{uckGrade}-2340\right|,2350 \le L_{uckGrade}<2370:2.139+0\left|L_{uckGrade}-2350\right|,2370 \le L_{uckGrade}<2380:2.145+0\left|L_{uckGrade}-2370\right|,2380 \le L_{uckGrade}<2410:2.149+0\left|L_{uckGrade}-2380\right|,2410 \le L_{uckGrade}<2420:2.158+0\left|L_{uckGrade}-2410\right|,2420 \le L_{uckGrade}<2440:2.162+0\left|L_{uckGrade}-2420\right|,2440 \le L_{uckGrade}<2450:2.168+0\left|L_{uckGrade}-2440\right|,2450 \le L_{uckGrade}<2490:2.172+0\left|L_{uckGrade}-2450\right|,2490 \le L_{uckGrade}<2500:2.184+0\left|L_{uckGrade}-2490\right|,2500 \le L_{uckGrade}<2580:2.188+0\left|L_{uckGrade}-2500\right|,2580 \le L_{uckGrade}<2590:2.212+0\left|L_{uckGrade}-2580\right|,2590 \le L_{uckGrade}<2680:2.216+0\left|L_{uckGrade}-2590\right|,2680 \le L_{uckGrade}<2690:2.243+0\left|L_{uckGrade}-2680\right|,2690 \le L_{uckGrade}<2760:2.245+0\left|L_{uckGrade}-2690\right|,2760 \le L_{uckGrade}<2770:2.266+0\left|L_{uckGrade}-2760\right|,2770 \le L_{uckGrade}<2810:2.268+0\left|L_{uckGrade}-2770\right|,2810 \le L_{uckGrade}<2820:2.28+0\left|L_{uckGrade}-2810\right|,2820 \le L_{uckGrade}<2850:2.282+0\left|L_{uckGrade}-2820\right|,2850 \le L_{uckGrade}<2860:2.291+0\left|L_{uckGrade}-2850\right|,2860 \le L_{uckGrade}<2880:2.293+0\left|L_{uckGrade}-2860\right|,2880 \le L_{uckGrade}<2890:2.299+0\left|L_{uckGrade}-2880\right|,2890 \le L_{uckGrade}<2910:2.301+0\left|L_{uckGrade}-2890\right|,2910 \le L_{uckGrade}<2920:2.307+0\left|L_{uckGrade}-2910\right|,2920 \le L_{uckGrade}<2940:2.309+0\left|L_{uckGrade}-2920\right|,2940 \le L_{uckGrade}<2950:2.315+0\left|L_{uckGrade}-2940\right|,2950 \le L_{uckGrade}<2960:2.317+0\left|L_{uckGrade}-2950\right|,2960 \le L_{uckGrade}<2970:2.32+0\left|L_{uckGrade}-2960\right|,2970 \le L_{uckGrade}<2990:2.322+0\left|L_{uckGrade}-2970\right|,2990 \le L_{uckGrade}<3000:2.328+0\left|L_{uckGrade}-2990\right|,3000 \le L_{uckGrade}<3010:2.33+0\left|L_{uckGrade}-3000\right|,3010 \le L_{uckGrade}<3020:2.333+0\left|L_{uckGrade}-3010\right|,3020 \le L_{uckGrade}<3030:2.335+0\left|L_{uckGrade}-3020\right|,3030 \le L_{uckGrade}<3040:2.338+0\left|L_{uckGrade}-3030\right|,3040 \le L_{uckGrade}<3050:2.34+0\left|L_{uckGrade}-3040\right|,3050 \le L_{uckGrade}<3060:2.343+0\left|L_{uckGrade}-3050\right|,3060 \le L_{uckGrade}<3070:2.345+0\left|L_{uckGrade}-3060\right|,3070 \le L_{uckGrade}<3090:2.348+0\left|L_{uckGrade}-3070\right|,3090 \le L_{uckGrade}<3100:2.352+0\left|L_{uckGrade}-3090\right|,3100 \le L_{uckGrade}<3110:2.355+0\left|L_{uckGrade}-3100\right|,3110 \le L_{uckGrade}<3120:2.357+0\left|L_{uckGrade}-3110\right|,3120 \le L_{uckGrade}<3140:2.36+0\left|L_{uckGrade}-3120\right|,3140 \le L_{uckGrade}<3150:2.364+0\left|L_{uckGrade}-3140\right|,3150 \le L_{uckGrade}<3170:2.367+0\left|L_{uckGrade}-3150\right|,3170 \le L_{uckGrade}<3180:2.371+0\left|L_{uckGrade}-3170\right|,3180 \le L_{uckGrade}<3200:2.374+0\left|L_{uckGrade}-3180\right|,3200 \le L_{uckGrade}<3210:2.378+0\left|L_{uckGrade}-3200\right|,3210 \le L_{uckGrade}<3240:2.381+0\left|L_{uckGrade}-3210\right|,3240 \le L_{uckGrade}<3250:2.387+0\left|L_{uckGrade}-3240\right|,3250 \le L_{uckGrade}<3290:2.39+0\left|L_{uckGrade}-3250\right|,3290 \le L_{uckGrade}<3300:2.398+0\left|L_{uckGrade}-3290\right|,3300 \le L_{uckGrade}<3400:2.401+0\left|L_{uckGrade}-3300\right|,3400 \le L_{uckGrade}<3410:2.421+0\left|L_{uckGrade}-3400\right|,3410 \le L_{uckGrade}<3440:2.424+0\left|L_{uckGrade}-3410\right|,3440 \le L_{uckGrade}<3450:2.43+0\left|L_{uckGrade}-3440\right|,3450 \le L_{uckGrade}<3550:2.431+0\left|L_{uckGrade}-3450\right|,3550 \le L_{uckGrade}<3560:2.451+0\left|L_{uckGrade}-3550\right|,3560 \le L_{uckGrade}<3600:2.452+0\left|L_{uckGrade}-3560\right|,3600 \le L_{uckGrade}<3610:2.46+0\left|L_{uckGrade}-3600\right|,3610 \le L_{uckGrade}<3640:2.461+0\left|L_{uckGrade}-3610\right|,3640 \le L_{uckGrade}<3650:2.467+0\left|L_{uckGrade}-3640\right|,3650 \le L_{uckGrade}<3670:2.468+0\left|L_{uckGrade}-3650\right|,3670 \le L_{uckGrade}<3680:2.472+0\left|L_{uckGrade}-3670\right|,3680 \le L_{uckGrade}<3700:2.473+0\left|L_{uckGrade}-3680\right|,3700 \le L_{uckGrade}<3710:2.477+0\left|L_{uckGrade}-3700\right|,3710 \le L_{uckGrade}<3730:2.478+0\left|L_{uckGrade}-3710\right|,3730 \le L_{uckGrade}<3740:2.482+0\left|L_{uckGrade}-3730\right|,3740 \le L_{uckGrade}<3750:2.483+0\left|L_{uckGrade}-3740\right|,3750 \le L_{uckGrade}<3760:2.485+0\left|L_{uckGrade}-3750\right|,3760 \le L_{uckGrade}<3770:2.486+0\left|L_{uckGrade}-3760\right|,3770 \le L_{uckGrade}<3780:2.488+0\left|L_{uckGrade}-3770\right|,3780 \le L_{uckGrade}<3800:2.489+0\left|L_{uckGrade}-3780\right|,3800 \le L_{uckGrade}<3810:2.493+0\left|L_{uckGrade}-3800\right|,3810 \le L_{uckGrade}<3820:2.494+0\left|L_{uckGrade}-3810\right|,3820 \le L_{uckGrade}<3830:2.496+0\left|L_{uckGrade}-3820\right|,3830 \le L_{uckGrade}<3840:2.497+0\left|L_{uckGrade}-3830\right|,3840 \le L_{uckGrade}<3860:2.499+0\left|L_{uckGrade}-3840\right|,3860 \le L_{uckGrade}<3870:2.501+0\left|L_{uckGrade}-3860\right|,3870 \le L_{uckGrade}<3880:2.503+0\left|L_{uckGrade}-3870\right|,3880 \le L_{uckGrade}<3890:2.504+0\left|L_{uckGrade}-3880\right|,3890 \le L_{uckGrade}<3900:2.506+0\left|L_{uckGrade}-3890\right|,3900 \le L_{uckGrade}<3910:2.507+0\left|L_{uckGrade}-3900\right|,3910 \le L_{uckGrade}<3930:2.509+0\left|L_{uckGrade}-3910\right|,3930 \le L_{uckGrade}<3940:2.511+0\left|L_{uckGrade}-3930\right|,3940 \le L_{uckGrade}<3960:2.513+0\left|L_{uckGrade}-3940\right|,3960 \le L_{uckGrade}<3970:2.515+0\left|L_{uckGrade}-3960\right|,3970 \le L_{uckGrade}<3990:2.517+0\left|L_{uckGrade}-3970\right|,3990 \le L_{uckGrade}<4000:2.519+0\left|L_{uckGrade}-3990\right|,4000 \le L_{uckGrade}<4030:2.521+0\left|L_{uckGrade}-4000\right|,4030 \le L_{uckGrade}<4040:2.524+0\left|L_{uckGrade}-4030\right|,4040 \le L_{uckGrade}<4090:2.526+0\left|L_{uckGrade}-4040\right|,4090 \le L_{uckGrade}<4100:2.531+0\left|L_{uckGrade}-4090\right|,4100 \le L_{uckGrade}<4330:2.533+0\left|L_{uckGrade}-4100\right|,4330 \le L_{uckGrade}<4340:2.556+0\left|L_{uckGrade}-4330\right|,4340 \le L_{uckGrade}<4380:2.556+0\left|L_{uckGrade}-4340\right|,4380 \le L_{uckGrade}<4390:2.56+0\left|L_{uckGrade}-4380\right|,4390 \le L_{uckGrade}<4430:2.56+0\left|L_{uckGrade}-4390\right|,4430 \le L_{uckGrade}<4440:2.564+0\left|L_{uckGrade}-4430\right|,4440 \le L_{uckGrade}<4460:2.564+0\left|L_{uckGrade}-4440\right|,4460 \le L_{uckGrade}<4470:2.566+0\left|L_{uckGrade}-4460\right|,4470 \le L_{uckGrade}<4490:2.566+0\left|L_{uckGrade}-4470\right|,4490 \le L_{uckGrade}<4500:2.568+0\left|L_{uckGrade}-4490\right|,4500 \le L_{uckGrade}<4520:2.568+0\left|L_{uckGrade}-4500\right|,4520 \le L_{uckGrade}<4530:2.57+0\left|L_{uckGrade}-4520\right|,4530 \le L_{uckGrade}<4540:2.57+0\left|L_{uckGrade}-4530\right|,4540 \le L_{uckGrade}<4550:2.571+0\left|L_{uckGrade}-4540\right|,4550 \le L_{uckGrade}<4560:2.571+0\left|L_{uckGrade}-4550\right|,4560 \le L_{uckGrade}<4570:2.572+0\left|L_{uckGrade}-4560\right|,4570 \le L_{uckGrade}<4590:2.572+0\left|L_{uckGrade}-4570\right|,4590 \le L_{uckGrade}<4600:2.574+0\left|L_{uckGrade}-4590\right|,4600 \le L_{uckGrade}<4610:2.574+0\left|L_{uckGrade}-4600\right|,4610 \le L_{uckGrade}<4620:2.575+0\left|L_{uckGrade}-4610\right|,4620 \le L_{uckGrade}<4630:2.575+0\left|L_{uckGrade}-4620\right|,4630 \le L_{uckGrade}<4650:2.576+0\left|L_{uckGrade}-4630\right|,4650 \le L_{uckGrade}<4660:2.576+0\left|L_{uckGrade}-4650\right|,4660 \le L_{uckGrade}<4670:2.577+0\left|L_{uckGrade}-4660\right|,4670 \le L_{uckGrade}<4680:2.577+0\left|L_{uckGrade}-4670\right|,4680 \le L_{uckGrade}<4690:2.578+0\left|L_{uckGrade}-4680\right|,4690 \le L_{uckGrade}<4700:2.578+0\left|L_{uckGrade}-4690\right|,4700 \le L_{uckGrade}<4720:2.579+0\left|L_{uckGrade}-4700\right|,4720 \le L_{uckGrade}<4730:2.579+0\left|L_{uckGrade}-4720\right|,4730 \le L_{uckGrade}<4750:2.58+0\left|L_{uckGrade}-4730\right|,4750 \le L_{uckGrade}<4760:2.58+0\left|L_{uckGrade}-4750\right|,4760 \le L_{uckGrade}<4790:2.581+0\left|L_{uckGrade}-4760\right|,4790 \le L_{uckGrade}<4800:2.581+0\left|L_{uckGrade}-4790\right|,4800 \le L_{uckGrade}<4830:2.582+0\left|L_{uckGrade}-4800\right|,4830 \le L_{uckGrade}<4840:2.582+0\left|L_{uckGrade}-4830\right|,4840 \le L_{uckGrade}<4880:2.583+0\left|L_{uckGrade}-4840\right|,4880 \le L_{uckGrade}<4890:2.583+0\left|L_{uckGrade}-4880\right|,4890 \le L_{uckGrade}<5000:2.584+0\left|L_{uckGrade}-4890\right|\right\}
See Example for how to use.
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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L_{uckGrade06}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<150:1+0.001\left|L_{uckGrade}-0\right|,150 \le L_{uckGrade}<160:1.135+0.001\left|L_{uckGrade}-150\right|,160 \le L_{uckGrade}<200:1.143+0.001\left|L_{uckGrade}-160\right|,200 \le L_{uckGrade}<210:1.179+0.001\left|L_{uckGrade}-200\right|,210 \le L_{uckGrade}<230:1.187+0.001\left|L_{uckGrade}-210\right|,230 \le L_{uckGrade}<240:1.205+0.001\left|L_{uckGrade}-230\right|,240 \le L_{uckGrade}<260:1.213+0.001\left|L_{uckGrade}-240\right|,260 \le L_{uckGrade}<270:1.231+0.001\left|L_{uckGrade}-260\right|,270 \le L_{uckGrade}<290:1.239+0.001\left|L_{uckGrade}-270\right|,290 \le L_{uckGrade}<300:1.257+0.001\left|L_{uckGrade}-290\right|,300 \le L_{uckGrade}<310:1.265+0.001\left|L_{uckGrade}-300\right|,310 \le L_{uckGrade}<320:1.274+0.001\left|L_{uckGrade}-310\right|,320 \le L_{uckGrade}<330:1.282+0.001\left|L_{uckGrade}-320\right|,330 \le L_{uckGrade}<340:1.291+0.001\left|L_{uckGrade}-330\right|,340 \le L_{uckGrade}<350:1.299+0.001\left|L_{uckGrade}-340\right|,350 \le L_{uckGrade}<360:1.308+0.001\left|L_{uckGrade}-350\right|,360 \le L_{uckGrade}<370:1.316+0.001\left|L_{uckGrade}-360\right|,370 \le L_{uckGrade}<390:1.325+0.001\left|L_{uckGrade}-370\right|,390 \le L_{uckGrade}<400:1.341+0.001\left|L_{uckGrade}-390\right|,400 \le L_{uckGrade}<410:1.35+0.001\left|L_{uckGrade}-400\right|,410 \le L_{uckGrade}<420:1.358+0.001\left|L_{uckGrade}-410\right|,420 \le L_{uckGrade}<450:1.367+0.001\left|L_{uckGrade}-420\right|,450 \le L_{uckGrade}<460:1.391+0.001\left|L_{uckGrade}-450\right|,460 \le L_{uckGrade}<490:1.4+0.001\left|L_{uckGrade}-460\right|,490 \le L_{uckGrade}<500:1.424+0.001\left|L_{uckGrade}-490\right|,500 \le L_{uckGrade}<550:1.433+0.001\left|L_{uckGrade}-500\right|,550 \le L_{uckGrade}<560:1.473+0.001\left|L_{uckGrade}-550\right|,560 \le L_{uckGrade}<660:1.482+0.001\left|L_{uckGrade}-560\right|,660 \le L_{uckGrade}<670:1.562+0.001\left|L_{uckGrade}-660\right|,670 \le L_{uckGrade}<720:1.569+0.001\left|L_{uckGrade}-670\right|,720 \le L_{uckGrade}<730:1.609+0.001\left|L_{uckGrade}-720\right|,730 \le L_{uckGrade}<760:1.616+0.001\left|L_{uckGrade}-730\right|,760 \le L_{uckGrade}<770:1.64+0.001\left|L_{uckGrade}-760\right|,770 \le L_{uckGrade}<790:1.647+0.001\left|L_{uckGrade}-770\right|,790 \le L_{uckGrade}<800:1.663+0.001\left|L_{uckGrade}-790\right|,800 \le L_{uckGrade}<820:1.67+0.001\left|L_{uckGrade}-800\right|,820 \le L_{uckGrade}<830:1.686+0.001\left|L_{uckGrade}-820\right|,830 \le L_{uckGrade}<850:1.693+0.001\left|L_{uckGrade}-830\right|,850 \le L_{uckGrade}<860:1.709+0.001\left|L_{uckGrade}-850\right|,860 \le L_{uckGrade}<870:1.716+0.001\left|L_{uckGrade}-860\right|,870 \le L_{uckGrade}<880:1.724+0.001\left|L_{uckGrade}-870\right|,880 \le L_{uckGrade}<890:1.731+0.001\left|L_{uckGrade}-880\right|,890 \le L_{uckGrade}<900:1.739+0.001\left|L_{uckGrade}-890\right|,900 \le L_{uckGrade}<910:1.746+0.001\left|L_{uckGrade}-900\right|,910 \le L_{uckGrade}<930:1.754+0.001\left|L_{uckGrade}-910\right|,930 \le L_{uckGrade}<940:1.768+0.001\left|L_{uckGrade}-930\right|,940 \le L_{uckGrade}<950:1.776+0.001\left|L_{uckGrade}-940\right|,950 \le L_{uckGrade}<960:1.783+0.001\left|L_{uckGrade}-950\right|,960 \le L_{uckGrade}<980:1.791+0.001\left|L_{uckGrade}-960\right|,980 \le L_{uckGrade}<990:1.805+0.001\left|L_{uckGrade}-980\right|,990 \le L_{uckGrade}<1020:1.813+0.001\left|L_{uckGrade}-990\right|,1020 \le L_{uckGrade}<1030:1.834+0.001\left|L_{uckGrade}-1020\right|,1030 \le L_{uckGrade}<1070:1.842+0.001\left|L_{uckGrade}-1030\right|,1070 \le L_{uckGrade}<1080:1.87+0.001\left|L_{uckGrade}-1070\right|,1080 \le L_{uckGrade}<1240:1.878+0.001\left|L_{uckGrade}-1080\right|,1240 \le L_{uckGrade}<1250:1.99+0.001\left|L_{uckGrade}-1240\right|,1250 \le L_{uckGrade}<1290:1.996+0.001\left|L_{uckGrade}-1250\right|,1290 \le L_{uckGrade}<1300:2.024+0.001\left|L_{uckGrade}-1290\right|,1300 \le L_{uckGrade}<1330:2.03+0.001\left|L_{uckGrade}-1300\right|,1330 \le L_{uckGrade}<1340:2.051+0.001\left|L_{uckGrade}-1330\right|,1340 \le L_{uckGrade}<1360:2.057+0.001\left|L_{uckGrade}-1340\right|,1360 \le L_{uckGrade}<1370:2.071+0.001\left|L_{uckGrade}-1360\right|,1370 \le L_{uckGrade}<1380:2.077+0.001\left|L_{uckGrade}-1370\right|,1380 \le L_{uckGrade}<1390:2.084+0.001\left|L_{uckGrade}-1380\right|,1390 \le L_{uckGrade}<1400:2.09+0.001\left|L_{uckGrade}-1390\right|,1400 \le L_{uckGrade}<1410:2.097+0.001\left|L_{uckGrade}-1400\right|,1410 \le L_{uckGrade}<1430:2.103+0.001\left|L_{uckGrade}-1410\right|,1430 \le L_{uckGrade}<1450:2.117+0.001\left|L_{uckGrade}-1430\right|,1450 \le L_{uckGrade}<1460:2.129+0.001\left|L_{uckGrade}-1450\right|,1460 \le L_{uckGrade}<1470:2.136+0.001\left|L_{uckGrade}-1460\right|,1470 \le L_{uckGrade}<1480:2.142+0.001\left|L_{uckGrade}-1470\right|,1480 \le L_{uckGrade}<1490:2.149+0.001\left|L_{uckGrade}-1480\right|,1490 \le L_{uckGrade}<1500:2.155+0.001\left|L_{uckGrade}-1490\right|,1500 \le L_{uckGrade}<1520:2.162+0.001\left|L_{uckGrade}-1500\right|,1520 \le L_{uckGrade}<1530:2.174+0.001\left|L_{uckGrade}-1520\right|,1530 \le L_{uckGrade}<1550:2.181+0.001\left|L_{uckGrade}-1530\right|,1550 \le L_{uckGrade}<1560:2.193+0.001\left|L_{uckGrade}-1550\right|,1560 \le L_{uckGrade}<1600:2.2+0.001\left|L_{uckGrade}-1560\right|,1600 \le L_{uckGrade}<1610:2.224+0.001\left|L_{uckGrade}-1600\right|,1610 \le L_{uckGrade}<1680:2.231+0.001\left|L_{uckGrade}-1610\right|,1680 \le L_{uckGrade}<1690:2.273+0.001\left|L_{uckGrade}-1680\right|,1690 \le L_{uckGrade}<1730:2.28+0.001\left|L_{uckGrade}-1690\right|,1730 \le L_{uckGrade}<1740:2.304+0.001\left|L_{uckGrade}-1730\right|,1740 \le L_{uckGrade}<1810:2.309+0.001\left|L_{uckGrade}-1740\right|,1810 \le L_{uckGrade}<1820:2.351+0\left|L_{uckGrade}-1810\right|,1820 \le L_{uckGrade}<1850:2.356+0.001\left|L_{uckGrade}-1820\right|,1850 \le L_{uckGrade}<1860:2.374+0\left|L_{uckGrade}-1850\right|,1860 \le L_{uckGrade}<1890:2.379+0.001\left|L_{uckGrade}-1860\right|,1890 \le L_{uckGrade}<1900:2.397+0.001\left|L_{uckGrade}-1890\right|,1900 \le L_{uckGrade}<1910:2.402+0.001\left|L_{uckGrade}-1900\right|,1910 \le L_{uckGrade}<1920:2.408+0\left|L_{uckGrade}-1910\right|,1920 \le L_{uckGrade}<1940:2.413+0.001\left|L_{uckGrade}-1920\right|,1940 \le L_{uckGrade}<1950:2.425+0.001\left|L_{uckGrade}-1940\right|,1950 \le L_{uckGrade}<1960:2.43+0.001\left|L_{uckGrade}-1950\right|,1960 \le L_{uckGrade}<1970:2.436+0\left|L_{uckGrade}-1960\right|,1970 \le L_{uckGrade}<1980:2.441+0.001\left|L_{uckGrade}-1970\right|,1980 \le L_{uckGrade}<1990:2.447+0\left|L_{uckGrade}-1980\right|,1990 \le L_{uckGrade}<2000:2.452+0.001\left|L_{uckGrade}-1990\right|,2000 \le L_{uckGrade}<2010:2.458+0\left|L_{uckGrade}-2000\right|,2010 \le L_{uckGrade}<2020:2.463+0.001\left|L_{uckGrade}-2010\right|,2020 \le L_{uckGrade}<2030:2.469+0.001\left|L_{uckGrade}-2020\right|,2030 \le L_{uckGrade}<2040:2.474+0.001\left|L_{uckGrade}-2030\right|,2040 \le L_{uckGrade}<2060:2.48+0.001\left|L_{uckGrade}-2040\right|,2060 \le L_{uckGrade}<2070:2.49+0.001\left|L_{uckGrade}-2060\right|,2070 \le L_{uckGrade}<2090:2.496+0\left|L_{uckGrade}-2070\right|,2090 \le L_{uckGrade}<2100:2.506+0.001\left|L_{uckGrade}-2090\right|,2100 \le L_{uckGrade}<2130:2.512+0.001\left|L_{uckGrade}-2100\right|,2130 \le L_{uckGrade}<2140:2.527+0.001\left|L_{uckGrade}-2130\right|,2140 \le L_{uckGrade}<2190:2.533+0\left|L_{uckGrade}-2140\right|,2190 \le L_{uckGrade}<2200:2.558+0.001\left|L_{uckGrade}-2190\right|,2200 \le L_{uckGrade}<2320:2.564+0.001\left|L_{uckGrade}-2200\right|,2320 \le L_{uckGrade}<2330:2.624+0\left|L_{uckGrade}-2320\right|,2330 \le L_{uckGrade}<2380:2.628+0\left|L_{uckGrade}-2330\right|,2380 \le L_{uckGrade}<2390:2.653+0\left|L_{uckGrade}-2380\right|,2390 \le L_{uckGrade}<2410:2.657+0\left|L_{uckGrade}-2390\right|,2410 \le L_{uckGrade}<2420:2.667+0\left|L_{uckGrade}-2410\right|,2420 \le L_{uckGrade}<2450:2.671+0.001\left|L_{uckGrade}-2420\right|,2450 \le L_{uckGrade}<2460:2.686+0\left|L_{uckGrade}-2450\right|,2460 \le L_{uckGrade}<2470:2.69+0\left|L_{uckGrade}-2460\right|,2470 \le L_{uckGrade}<2480:2.695+0\left|L_{uckGrade}-2470\right|,2480 \le L_{uckGrade}<2500:2.699+0.001\left|L_{uckGrade}-2480\right|,2500 \le L_{uckGrade}<2510:2.709+0\left|L_{uckGrade}-2500\right|,2510 \le L_{uckGrade}<2520:2.713+0\left|L_{uckGrade}-2510\right|,2520 \le L_{uckGrade}<2530:2.718+0\left|L_{uckGrade}-2520\right|,2530 \le L_{uckGrade}<2540:2.722+0\left|L_{uckGrade}-2530\right|,2540 \le L_{uckGrade}<2550:2.727+0\left|L_{uckGrade}-2540\right|,2550 \le L_{uckGrade}<2560:2.731+0.001\left|L_{uckGrade}-2550\right|,2560 \le L_{uckGrade}<2580:2.736+0\left|L_{uckGrade}-2560\right|,2580 \le L_{uckGrade}<2590:2.744+0\left|L_{uckGrade}-2580\right|,2590 \le L_{uckGrade}<2600:2.749+0\left|L_{uckGrade}-2590\right|,2600 \le L_{uckGrade}<2610:2.753+0\left|L_{uckGrade}-2600\right|,2610 \le L_{uckGrade}<2630:2.758+0\left|L_{uckGrade}-2610\right|,2630 \le L_{uckGrade}<2640:2.766+0\left|L_{uckGrade}-2630\right|,2640 \le L_{uckGrade}<2670:2.771+0\left|L_{uckGrade}-2640\right|,2670 \le L_{uckGrade}<2680:2.783+0\left|L_{uckGrade}-2670\right|,2680 \le L_{uckGrade}<2720:2.788+0\left|L_{uckGrade}-2680\right|,2720 \le L_{uckGrade}<2730:2.804+0.001\left|L_{uckGrade}-2720\right|,2730 \le L_{uckGrade}<2880:2.809+0\left|L_{uckGrade}-2730\right|,2880 \le L_{uckGrade}<2890:2.869+0\left|L_{uckGrade}-2880\right|,2890 \le L_{uckGrade}<2940:2.872+0\left|L_{uckGrade}-2890\right|,2940 \le L_{uckGrade}<2950:2.892+0\left|L_{uckGrade}-2940\right|,2950 \le L_{uckGrade}<2970:2.895+0\left|L_{uckGrade}-2950\right|,2970 \le L_{uckGrade}<2980:2.903+0\left|L_{uckGrade}-2970\right|,2980 \le L_{uckGrade}<3000:2.906+0\left|L_{uckGrade}-2980\right|,3000 \le L_{uckGrade}<3010:2.914+0\left|L_{uckGrade}-3000\right|,3010 \le L_{uckGrade}<3030:2.917+0\left|L_{uckGrade}-3010\right|,3030 \le L_{uckGrade}<3040:2.925+0\left|L_{uckGrade}-3030\right|,3040 \le L_{uckGrade}<3050:2.928+0\left|L_{uckGrade}-3040\right|,3050 \le L_{uckGrade}<3060:2.932+0\left|L_{uckGrade}-3050\right|,3060 \le L_{uckGrade}<3070:2.935+0\left|L_{uckGrade}-3060\right|,3070 \le L_{uckGrade}<3080:2.939+0\left|L_{uckGrade}-3070\right|,3080 \le L_{uckGrade}<3090:2.942+0\left|L_{uckGrade}-3080\right|,3090 \le L_{uckGrade}<3100:2.946+0\left|L_{uckGrade}-3090\right|,3100 \le L_{uckGrade}<3110:2.949+0\left|L_{uckGrade}-3100\right|,3110 \le L_{uckGrade}<3120:2.953+0\left|L_{uckGrade}-3110\right|,3120 \le L_{uckGrade}<3130:2.956+0\left|L_{uckGrade}-3120\right|,3130 \le L_{uckGrade}<3150:2.96+0\left|L_{uckGrade}-3130\right|,3150 \le L_{uckGrade}<3160:2.966+0\left|L_{uckGrade}-3150\right|,3160 \le L_{uckGrade}<3180:2.97+0\left|L_{uckGrade}-3160\right|,3180 \le L_{uckGrade}<3190:2.976+0\left|L_{uckGrade}-3180\right|,3190 \le L_{uckGrade}<3210:2.98+0\left|L_{uckGrade}-3190\right|,3210 \le L_{uckGrade}<3220:2.986+0\left|L_{uckGrade}-3210\right|,3220 \le L_{uckGrade}<3260:2.99+0\left|L_{uckGrade}-3220\right|,3260 \le L_{uckGrade}<3270:3.002+0\left|L_{uckGrade}-3260\right|,3270 \le L_{uckGrade}<3450:3.006+0\left|L_{uckGrade}-3270\right|,3450 \le L_{uckGrade}<3460:3.06+0\left|L_{uckGrade}-3450\right|,3460 \le L_{uckGrade}<3490:3.062+0\left|L_{uckGrade}-3460\right|,3490 \le L_{uckGrade}<3500:3.071+0\left|L_{uckGrade}-3490\right|,3500 \le L_{uckGrade}<3530:3.073+0\left|L_{uckGrade}-3500\right|,3530 \le L_{uckGrade}<3540:3.082+0\left|L_{uckGrade}-3530\right|,3540 \le L_{uckGrade}<3560:3.084+0\left|L_{uckGrade}-3540\right|,3560 \le L_{uckGrade}<3570:3.09+0\left|L_{uckGrade}-3560\right|,3570 \le L_{uckGrade}<3580:3.092+0\left|L_{uckGrade}-3570\right|,3580 \le L_{uckGrade}<3590:3.095+0\left|L_{uckGrade}-3580\right|,3590 \le L_{uckGrade}<3600:3.097+0\left|L_{uckGrade}-3590\right|,3600 \le L_{uckGrade}<3610:3.1+0\left|L_{uckGrade}-3600\right|,3610 \le L_{uckGrade}<3630:3.102+0\left|L_{uckGrade}-3610\right|,3630 \le L_{uckGrade}<3650:3.108+0\left|L_{uckGrade}-3630\right|,3650 \le L_{uckGrade}<3660:3.112+0\left|L_{uckGrade}-3650\right|,3660 \le L_{uckGrade}<3670:3.115+0\left|L_{uckGrade}-3660\right|,3670 \le L_{uckGrade}<3680:3.117+0\left|L_{uckGrade}-3670\right|,3680 \le L_{uckGrade}<3690:3.12+0\left|L_{uckGrade}-3680\right|,3690 \le L_{uckGrade}<3700:3.122+0\left|L_{uckGrade}-3690\right|,3700 \le L_{uckGrade}<3720:3.125+0\left|L_{uckGrade}-3700\right|,3720 \le L_{uckGrade}<3730:3.129+0\left|L_{uckGrade}-3720\right|,3730 \le L_{uckGrade}<3750:3.132+0\left|L_{uckGrade}-3730\right|,3750 \le L_{uckGrade}<3760:3.136+0\left|L_{uckGrade}-3750\right|,3760 \le L_{uckGrade}<3800:3.139+0\left|L_{uckGrade}-3760\right|,3800 \le L_{uckGrade}<3810:3.147+0\left|L_{uckGrade}-3800\right|,3810 \le L_{uckGrade}<4000:3.15+0\left|L_{uckGrade}-3810\right|,4000 \le L_{uckGrade}<4010:3.188+0\left|L_{uckGrade}-4000\right|,4010 \le L_{uckGrade}<4050:3.189+0\left|L_{uckGrade}-4010\right|,4050 \le L_{uckGrade}<4060:3.197+0\left|L_{uckGrade}-4050\right|,4060 \le L_{uckGrade}<4080:3.198+0\left|L_{uckGrade}-4060\right|,4080 \le L_{uckGrade}<4090:3.202+0\left|L_{uckGrade}-4080\right|,4090 \le L_{uckGrade}<4110:3.203+0\left|L_{uckGrade}-4090\right|,4110 \le L_{uckGrade}<4120:3.207+0\left|L_{uckGrade}-4110\right|,4120 \le L_{uckGrade}<4130:3.208+0\left|L_{uckGrade}-4120\right|,4130 \le L_{uckGrade}<4140:3.21+0\left|L_{uckGrade}-4130\right|,4140 \le L_{uckGrade}<4160:3.211+0\left|L_{uckGrade}-4140\right|,4160 \le L_{uckGrade}<4170:3.215+0\left|L_{uckGrade}-4160\right|,4170 \le L_{uckGrade}<4180:3.216+0\left|L_{uckGrade}-4170\right|,4180 \le L_{uckGrade}<4190:3.218+0\left|L_{uckGrade}-4180\right|,4190 \le L_{uckGrade}<4200:3.219+0\left|L_{uckGrade}-4190\right|,4200 \le L_{uckGrade}<4220:3.221+0\left|L_{uckGrade}-4200\right|,4220 \le L_{uckGrade}<4230:3.223+0\left|L_{uckGrade}-4220\right|,4230 \le L_{uckGrade}<4240:3.225+0\left|L_{uckGrade}-4230\right|,4240 \le L_{uckGrade}<4250:3.226+0\left|L_{uckGrade}-4240\right|,4250 \le L_{uckGrade}<4270:3.228+0\left|L_{uckGrade}-4250\right|,4270 \le L_{uckGrade}<4280:3.23+0\left|L_{uckGrade}-4270\right|,4280 \le L_{uckGrade}<4300:3.232+0\left|L_{uckGrade}-4280\right|,4300 \le L_{uckGrade}<4310:3.234+0\left|L_{uckGrade}-4300\right|,4310 \le L_{uckGrade}<4340:3.236+0\left|L_{uckGrade}-4310\right|,4340 \le L_{uckGrade}<4350:3.239+0\left|L_{uckGrade}-4340\right|,4350 \le L_{uckGrade}<4430:3.241+0\left|L_{uckGrade}-4350\right|,4430 \le L_{uckGrade}<4440:3.249+0\left|L_{uckGrade}-4430\right|,4440 \le L_{uckGrade}<4470:3.251+0\left|L_{uckGrade}-4440\right|,4470 \le L_{uckGrade}<4480:3.254+0\left|L_{uckGrade}-4470\right|,4480 \le L_{uckGrade}<4560:3.254+0\left|L_{uckGrade}-4480\right|,4560 \le L_{uckGrade}<4570:3.262+0\left|L_{uckGrade}-4560\right|,4570 \le L_{uckGrade}<4600:3.262+0\left|L_{uckGrade}-4570\right|,4600 \le L_{uckGrade}<4610:3.265+0\left|L_{uckGrade}-4600\right|,4610 \le L_{uckGrade}<4630:3.265+0\left|L_{uckGrade}-4610\right|,4630 \le L_{uckGrade}<4640:3.267+0\left|L_{uckGrade}-4630\right|,4640 \le L_{uckGrade}<4660:3.267+0\left|L_{uckGrade}-4640\right|,4660 \le L_{uckGrade}<4670:3.269+0\left|L_{uckGrade}-4660\right|,4670 \le L_{uckGrade}<4690:3.269+0\left|L_{uckGrade}-4670\right|,4690 \le L_{uckGrade}<4700:3.271+0\left|L_{uckGrade}-4690\right|,4700 \le L_{uckGrade}<4710:3.271+0\left|L_{uckGrade}-4700\right|,4710 \le L_{uckGrade}<4720:3.272+0\left|L_{uckGrade}-4710\right|,4720 \le L_{uckGrade}<4730:3.272+0\left|L_{uckGrade}-4720\right|,4730 \le L_{uckGrade}<4740:3.273+0\left|L_{uckGrade}-4730\right|,4740 \le L_{uckGrade}<4750:3.273+0\left|L_{uckGrade}-4740\right|,4750 \le L_{uckGrade}<4760:3.274+0\left|L_{uckGrade}-4750\right|,4760 \le L_{uckGrade}<4770:3.274+0\left|L_{uckGrade}-4760\right|,4770 \le L_{uckGrade}<4790:3.275+0\left|L_{uckGrade}-4770\right|,4790 \le L_{uckGrade}<4800:3.275+0\left|L_{uckGrade}-4790\right|,4800 \le L_{uckGrade}<4820:3.276+0\left|L_{uckGrade}-4800\right|,4820 \le L_{uckGrade}<4830:3.276+0\left|L_{uckGrade}-4820\right|,4830 \le L_{uckGrade}<4850:3.277+0\left|L_{uckGrade}-4830\right|,4850 \le L_{uckGrade}<4860:3.277+0\left|L_{uckGrade}-4850\right|,4860 \le L_{uckGrade}<4890:3.278+0\left|L_{uckGrade}-4860\right|,4890 \le L_{uckGrade}<4900:3.278+0\left|L_{uckGrade}-4890\right|,4900 \le L_{uckGrade}<4980:3.279+0\left|L_{uckGrade}-4900\right|,4980 \le L_{uckGrade}<4990:3.279+0\left|L_{uckGrade}-4980\right|,4990 \le L_{uckGrade}<5000:3.28+0\left|L_{uckGrade}-4990\right|\right\}
See Example for how to use.
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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L_{uckGrade07}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<20:1+0.001\left|L_{uckGrade}-0\right|,20 \le L_{uckGrade}<30:1.022+0.001\left|L_{uckGrade}-20\right|,30 \le L_{uckGrade}<50:1.032+0.001\left|L_{uckGrade}-30\right|,50 \le L_{uckGrade}<60:1.054+0.001\left|L_{uckGrade}-50\right|,60 \le L_{uckGrade}<80:1.064+0.001\left|L_{uckGrade}-60\right|,80 \le L_{uckGrade}<90:1.086+0.001\left|L_{uckGrade}-80\right|,90 \le L_{uckGrade}<110:1.096+0.001\left|L_{uckGrade}-90\right|,110 \le L_{uckGrade}<120:1.118+0.001\left|L_{uckGrade}-110\right|,120 \le L_{uckGrade}<130:1.128+0.001\left|L_{uckGrade}-120\right|,130 \le L_{uckGrade}<140:1.139+0.001\left|L_{uckGrade}-130\right|,140 \le L_{uckGrade}<150:1.149+0.001\left|L_{uckGrade}-140\right|,150 \le L_{uckGrade}<160:1.16+0.001\left|L_{uckGrade}-150\right|,160 \le L_{uckGrade}<170:1.17+0.001\left|L_{uckGrade}-160\right|,170 \le L_{uckGrade}<180:1.181+0.001\left|L_{uckGrade}-170\right|,180 \le L_{uckGrade}<190:1.191+0.001\left|L_{uckGrade}-180\right|,190 \le L_{uckGrade}<210:1.202+0.001\left|L_{uckGrade}-190\right|,210 \le L_{uckGrade}<220:1.222+0.001\left|L_{uckGrade}-210\right|,220 \le L_{uckGrade}<240:1.233+0.001\left|L_{uckGrade}-220\right|,240 \le L_{uckGrade}<250:1.253+0.001\left|L_{uckGrade}-240\right|,250 \le L_{uckGrade}<290:1.264+0.001\left|L_{uckGrade}-250\right|,290 \le L_{uckGrade}<300:1.304+0.001\left|L_{uckGrade}-290\right|,300 \le L_{uckGrade}<450:1.315+0.001\left|L_{uckGrade}-300\right|,450 \le L_{uckGrade}<460:1.465+0.001\left|L_{uckGrade}-450\right|,460 \le L_{uckGrade}<500:1.474+0.001\left|L_{uckGrade}-460\right|,500 \le L_{uckGrade}<510:1.514+0.001\left|L_{uckGrade}-500\right|,510 \le L_{uckGrade}<530:1.523+0.001\left|L_{uckGrade}-510\right|,530 \le L_{uckGrade}<540:1.543+0.001\left|L_{uckGrade}-530\right|,540 \le L_{uckGrade}<560:1.552+0.001\left|L_{uckGrade}-540\right|,560 \le L_{uckGrade}<570:1.572+0.001\left|L_{uckGrade}-560\right|,570 \le L_{uckGrade}<580:1.581+0.001\left|L_{uckGrade}-570\right|,580 \le L_{uckGrade}<590:1.591+0.001\left|L_{uckGrade}-580\right|,590 \le L_{uckGrade}<600:1.6+0.001\left|L_{uckGrade}-590\right|,600 \le L_{uckGrade}<610:1.61+0.001\left|L_{uckGrade}-600\right|,610 \le L_{uckGrade}<620:1.619+0.001\left|L_{uckGrade}-610\right|,620 \le L_{uckGrade}<630:1.629+0.001\left|L_{uckGrade}-620\right|,630 \le L_{uckGrade}<640:1.638+0.001\left|L_{uckGrade}-630\right|,640 \le L_{uckGrade}<660:1.648+0.001\left|L_{uckGrade}-640\right|,660 \le L_{uckGrade}<670:1.666+0.001\left|L_{uckGrade}-660\right|,670 \le L_{uckGrade}<680:1.676+0.001\left|L_{uckGrade}-670\right|,680 \le L_{uckGrade}<690:1.685+0.001\left|L_{uckGrade}-680\right|,690 \le L_{uckGrade}<720:1.695+0.001\left|L_{uckGrade}-690\right|,720 \le L_{uckGrade}<730:1.722+0.001\left|L_{uckGrade}-720\right|,730 \le L_{uckGrade}<770:1.732+0.001\left|L_{uckGrade}-730\right|,770 \le L_{uckGrade}<780:1.768+0.001\left|L_{uckGrade}-770\right|,780 \le L_{uckGrade}<890:1.778+0.001\left|L_{uckGrade}-780\right|,890 \le L_{uckGrade}<900:1.877+0.001\left|L_{uckGrade}-890\right|,900 \le L_{uckGrade}<950:1.885+0.001\left|L_{uckGrade}-900\right|,950 \le L_{uckGrade}<960:1.93+0.001\left|L_{uckGrade}-950\right|,960 \le L_{uckGrade}<980:1.938+0.001\left|L_{uckGrade}-960\right|,980 \le L_{uckGrade}<990:1.956+0.001\left|L_{uckGrade}-980\right|,990 \le L_{uckGrade}<1010:1.964+0.001\left|L_{uckGrade}-990\right|,1010 \le L_{uckGrade}<1020:1.982+0.001\left|L_{uckGrade}-1010\right|,1020 \le L_{uckGrade}<1040:1.99+0.001\left|L_{uckGrade}-1020\right|,1040 \le L_{uckGrade}<1050:2.008+0.001\left|L_{uckGrade}-1040\right|,1050 \le L_{uckGrade}<1060:2.016+0.001\left|L_{uckGrade}-1050\right|,1060 \le L_{uckGrade}<1070:2.025+0.001\left|L_{uckGrade}-1060\right|,1070 \le L_{uckGrade}<1080:2.033+0.001\left|L_{uckGrade}-1070\right|,1080 \le L_{uckGrade}<1090:2.042+0.001\left|L_{uckGrade}-1080\right|,1090 \le L_{uckGrade}<1100:2.05+0.001\left|L_{uckGrade}-1090\right|,1100 \le L_{uckGrade}<1120:2.059+0.001\left|L_{uckGrade}-1100\right|,1120 \le L_{uckGrade}<1130:2.075+0.001\left|L_{uckGrade}-1120\right|,1130 \le L_{uckGrade}<1150:2.084+0.001\left|L_{uckGrade}-1130\right|,1150 \le L_{uckGrade}<1160:2.1+0.001\left|L_{uckGrade}-1150\right|,1160 \le L_{uckGrade}<1180:2.109+0.001\left|L_{uckGrade}-1160\right|,1180 \le L_{uckGrade}<1190:2.125+0.001\left|L_{uckGrade}-1180\right|,1190 \le L_{uckGrade}<1240:2.134+0.001\left|L_{uckGrade}-1190\right|,1240 \le L_{uckGrade}<1250:2.174+0.001\left|L_{uckGrade}-1240\right|,1250 \le L_{uckGrade}<1360:2.183+0.001\left|L_{uckGrade}-1250\right|,1360 \le L_{uckGrade}<1370:2.271+0.001\left|L_{uckGrade}-1360\right|,1370 \le L_{uckGrade}<1410:2.278+0.001\left|L_{uckGrade}-1370\right|,1410 \le L_{uckGrade}<1420:2.31+0.001\left|L_{uckGrade}-1410\right|,1420 \le L_{uckGrade}<1440:2.317+0.001\left|L_{uckGrade}-1420\right|,1440 \le L_{uckGrade}<1450:2.333+0.001\left|L_{uckGrade}-1440\right|,1450 \le L_{uckGrade}<1470:2.34+0.001\left|L_{uckGrade}-1450\right|,1470 \le L_{uckGrade}<1480:2.356+0.001\left|L_{uckGrade}-1470\right|,1480 \le L_{uckGrade}<1500:2.363+0.001\left|L_{uckGrade}-1480\right|,1500 \le L_{uckGrade}<1510:2.379+0.001\left|L_{uckGrade}-1500\right|,1510 \le L_{uckGrade}<1520:2.386+0.001\left|L_{uckGrade}-1510\right|,1520 \le L_{uckGrade}<1530:2.394+0.001\left|L_{uckGrade}-1520\right|,1530 \le L_{uckGrade}<1540:2.401+0.001\left|L_{uckGrade}-1530\right|,1540 \le L_{uckGrade}<1550:2.409+0.001\left|L_{uckGrade}-1540\right|,1550 \le L_{uckGrade}<1560:2.416+0.001\left|L_{uckGrade}-1550\right|,1560 \le L_{uckGrade}<1580:2.424+0.001\left|L_{uckGrade}-1560\right|,1580 \le L_{uckGrade}<1590:2.438+0.001\left|L_{uckGrade}-1580\right|,1590 \le L_{uckGrade}<1600:2.446+0.001\left|L_{uckGrade}-1590\right|,1600 \le L_{uckGrade}<1610:2.453+0.001\left|L_{uckGrade}-1600\right|,1610 \le L_{uckGrade}<1640:2.461+0.001\left|L_{uckGrade}-1610\right|,1640 \le L_{uckGrade}<1650:2.482+0.001\left|L_{uckGrade}-1640\right|,1650 \le L_{uckGrade}<1680:2.49+0.001\left|L_{uckGrade}-1650\right|,1680 \le L_{uckGrade}<1690:2.511+0.001\left|L_{uckGrade}-1680\right|,1690 \le L_{uckGrade}<1840:2.519+0.001\left|L_{uckGrade}-1690\right|,1840 \le L_{uckGrade}<1850:2.624+0.001\left|L_{uckGrade}-1840\right|,1850 \le L_{uckGrade}<1880:2.63+0.001\left|L_{uckGrade}-1850\right|,1880 \le L_{uckGrade}<1890:2.651+0.001\left|L_{uckGrade}-1880\right|,1890 \le L_{uckGrade}<1920:2.657+0.001\left|L_{uckGrade}-1890\right|,1920 \le L_{uckGrade}<1930:2.678+0.001\left|L_{uckGrade}-1920\right|,1930 \le L_{uckGrade}<1940:2.684+0.001\left|L_{uckGrade}-1930\right|,1940 \le L_{uckGrade}<1950:2.691+0.001\left|L_{uckGrade}-1940\right|,1950 \le L_{uckGrade}<1970:2.697+0.001\left|L_{uckGrade}-1950\right|,1970 \le L_{uckGrade}<1980:2.711+0.001\left|L_{uckGrade}-1970\right|,1980 \le L_{uckGrade}<1990:2.717+0.001\left|L_{uckGrade}-1980\right|,1990 \le L_{uckGrade}<2000:2.724+0.001\left|L_{uckGrade}-1990\right|,2000 \le L_{uckGrade}<2010:2.73+0.001\left|L_{uckGrade}-2000\right|,2010 \le L_{uckGrade}<2020:2.737+0.001\left|L_{uckGrade}-2010\right|,2020 \le L_{uckGrade}<2030:2.743+0.001\left|L_{uckGrade}-2020\right|,2030 \le L_{uckGrade}<2050:2.75+0.001\left|L_{uckGrade}-2030\right|,2050 \le L_{uckGrade}<2060:2.762+0.001\left|L_{uckGrade}-2050\right|,2060 \le L_{uckGrade}<2080:2.769+0.001\left|L_{uckGrade}-2060\right|,2080 \le L_{uckGrade}<2090:2.781+0.001\left|L_{uckGrade}-2080\right|,2090 \le L_{uckGrade}<2120:2.788+0.001\left|L_{uckGrade}-2090\right|,2120 \le L_{uckGrade}<2130:2.806+0.001\left|L_{uckGrade}-2120\right|,2130 \le L_{uckGrade}<2180:2.813+0.001\left|L_{uckGrade}-2130\right|,2180 \le L_{uckGrade}<2190:2.843+0.001\left|L_{uckGrade}-2180\right|,2190 \le L_{uckGrade}<2270:2.85+0.001\left|L_{uckGrade}-2190\right|,2270 \le L_{uckGrade}<2280:2.898+0\left|L_{uckGrade}-2270\right|,2280 \le L_{uckGrade}<2330:2.903+0.001\left|L_{uckGrade}-2280\right|,2330 \le L_{uckGrade}<2340:2.933+0.001\left|L_{uckGrade}-2330\right|,2340 \le L_{uckGrade}<2370:2.938+0.001\left|L_{uckGrade}-2340\right|,2370 \le L_{uckGrade}<2380:2.956+0\left|L_{uckGrade}-2370\right|,2380 \le L_{uckGrade}<2400:2.961+0.001\left|L_{uckGrade}-2380\right|,2400 \le L_{uckGrade}<2410:2.973+0.001\left|L_{uckGrade}-2400\right|,2410 \le L_{uckGrade}<2420:2.978+0.001\left|L_{uckGrade}-2410\right|,2420 \le L_{uckGrade}<2430:2.984+0\left|L_{uckGrade}-2420\right|,2430 \le L_{uckGrade}<2440:2.989+0.001\left|L_{uckGrade}-2430\right|,2440 \le L_{uckGrade}<2450:2.995+0\left|L_{uckGrade}-2440\right|,2450 \le L_{uckGrade}<2460:3+0.001\left|L_{uckGrade}-2450\right|,2460 \le L_{uckGrade}<2470:3.006+0.001\left|L_{uckGrade}-2460\right|,2470 \le L_{uckGrade}<2480:3.011+0.001\left|L_{uckGrade}-2470\right|,2480 \le L_{uckGrade}<2490:3.017+0\left|L_{uckGrade}-2480\right|,2490 \le L_{uckGrade}<2500:3.022+0.001\left|L_{uckGrade}-2490\right|,2500 \le L_{uckGrade}<2520:3.028+0\left|L_{uckGrade}-2500\right|,2520 \le L_{uckGrade}<2530:3.038+0.001\left|L_{uckGrade}-2520\right|,2530 \le L_{uckGrade}<2550:3.044+0\left|L_{uckGrade}-2530\right|,2550 \le L_{uckGrade}<2560:3.054+0.001\left|L_{uckGrade}-2550\right|,2560 \le L_{uckGrade}<2580:3.06+0\left|L_{uckGrade}-2560\right|,2580 \le L_{uckGrade}<2590:3.07+0.001\left|L_{uckGrade}-2580\right|,2590 \le L_{uckGrade}<2650:3.076+0\left|L_{uckGrade}-2590\right|,2650 \le L_{uckGrade}<2660:3.106+0.001\left|L_{uckGrade}-2650\right|,2660 \le L_{uckGrade}<2720:3.112+0\left|L_{uckGrade}-2660\right|,2720 \le L_{uckGrade}<2730:3.142+0\left|L_{uckGrade}-2720\right|,2730 \le L_{uckGrade}<2790:3.146+0.001\left|L_{uckGrade}-2730\right|,2790 \le L_{uckGrade}<2800:3.176+0\left|L_{uckGrade}-2790\right|,2800 \le L_{uckGrade}<2820:3.18+0\left|L_{uckGrade}-2800\right|,2820 \le L_{uckGrade}<2830:3.19+0\left|L_{uckGrade}-2820\right|,2830 \le L_{uckGrade}<2850:3.194+0.001\left|L_{uckGrade}-2830\right|,2850 \le L_{uckGrade}<2860:3.204+0\left|L_{uckGrade}-2850\right|,2860 \le L_{uckGrade}<2880:3.208+0\left|L_{uckGrade}-2860\right|,2880 \le L_{uckGrade}<2890:3.218+0\left|L_{uckGrade}-2880\right|,2890 \le L_{uckGrade}<2900:3.222+0\left|L_{uckGrade}-2890\right|,2900 \le L_{uckGrade}<2910:3.227+0\left|L_{uckGrade}-2900\right|,2910 \le L_{uckGrade}<2920:3.231+0.001\left|L_{uckGrade}-2910\right|,2920 \le L_{uckGrade}<2930:3.236+0\left|L_{uckGrade}-2920\right|,2930 \le L_{uckGrade}<2940:3.24+0\left|L_{uckGrade}-2930\right|,2940 \le L_{uckGrade}<2950:3.245+0\left|L_{uckGrade}-2940\right|,2950 \le L_{uckGrade}<2960:3.249+0\left|L_{uckGrade}-2950\right|,2960 \le L_{uckGrade}<2970:3.254+0\left|L_{uckGrade}-2960\right|,2970 \le L_{uckGrade}<2980:3.258+0\left|L_{uckGrade}-2970\right|,2980 \le L_{uckGrade}<3000:3.263+0\left|L_{uckGrade}-2980\right|,3000 \le L_{uckGrade}<3010:3.271+0\left|L_{uckGrade}-3000\right|,3010 \le L_{uckGrade}<3040:3.276+0\left|L_{uckGrade}-3010\right|,3040 \le L_{uckGrade}<3050:3.288+0.001\left|L_{uckGrade}-3040\right|,3050 \le L_{uckGrade}<3100:3.293+0\left|L_{uckGrade}-3050\right|,3100 \le L_{uckGrade}<3110:3.313+0\left|L_{uckGrade}-3100\right|,3110 \le L_{uckGrade}<3200:3.318+0\left|L_{uckGrade}-3110\right|,3200 \le L_{uckGrade}<3210:3.354+0\left|L_{uckGrade}-3200\right|,3210 \le L_{uckGrade}<3260:3.357+0\left|L_{uckGrade}-3210\right|,3260 \le L_{uckGrade}<3270:3.377+0\left|L_{uckGrade}-3260\right|,3270 \le L_{uckGrade}<3290:3.38+0\left|L_{uckGrade}-3270\right|,3290 \le L_{uckGrade}<3300:3.388+0\left|L_{uckGrade}-3290\right|,3300 \le L_{uckGrade}<3320:3.391+0\left|L_{uckGrade}-3300\right|,3320 \le L_{uckGrade}<3330:3.399+0\left|L_{uckGrade}-3320\right|,3330 \le L_{uckGrade}<3350:3.402+0\left|L_{uckGrade}-3330\right|,3350 \le L_{uckGrade}<3360:3.41+0\left|L_{uckGrade}-3350\right|,3360 \le L_{uckGrade}<3370:3.413+0\left|L_{uckGrade}-3360\right|,3370 \le L_{uckGrade}<3380:3.417+0\left|L_{uckGrade}-3370\right|,3380 \le L_{uckGrade}<3390:3.42+0\left|L_{uckGrade}-3380\right|,3390 \le L_{uckGrade}<3400:3.424+0\left|L_{uckGrade}-3390\right|,3400 \le L_{uckGrade}<3410:3.427+0\left|L_{uckGrade}-3400\right|,3410 \le L_{uckGrade}<3430:3.431+0\left|L_{uckGrade}-3410\right|,3430 \le L_{uckGrade}<3440:3.437+0\left|L_{uckGrade}-3430\right|,3440 \le L_{uckGrade}<3450:3.441+0\left|L_{uckGrade}-3440\right|,3450 \le L_{uckGrade}<3460:3.444+0\left|L_{uckGrade}-3450\right|,3460 \le L_{uckGrade}<3480:3.448+0\left|L_{uckGrade}-3460\right|,3480 \le L_{uckGrade}<3490:3.454+0\left|L_{uckGrade}-3480\right|,3490 \le L_{uckGrade}<3530:3.458+0\left|L_{uckGrade}-3490\right|,3530 \le L_{uckGrade}<3540:3.47+0\left|L_{uckGrade}-3530\right|,3540 \le L_{uckGrade}<3690:3.474+0\left|L_{uckGrade}-3540\right|,3690 \le L_{uckGrade}<3700:3.519+0\left|L_{uckGrade}-3690\right|,3700 \le L_{uckGrade}<3740:3.521+0\left|L_{uckGrade}-3700\right|,3740 \le L_{uckGrade}<3750:3.533+0\left|L_{uckGrade}-3740\right|,3750 \le L_{uckGrade}<3770:3.535+0\left|L_{uckGrade}-3750\right|,3770 \le L_{uckGrade}<3780:3.541+0\left|L_{uckGrade}-3770\right|,3780 \le L_{uckGrade}<3800:3.543+0\left|L_{uckGrade}-3780\right|,3800 \le L_{uckGrade}<3810:3.549+0\left|L_{uckGrade}-3800\right|,3810 \le L_{uckGrade}<3820:3.551+0\left|L_{uckGrade}-3810\right|,3820 \le L_{uckGrade}<3830:3.554+0\left|L_{uckGrade}-3820\right|,3830 \le L_{uckGrade}<3840:3.556+0\left|L_{uckGrade}-3830\right|,3840 \le L_{uckGrade}<3850:3.559+0\left|L_{uckGrade}-3840\right|,3850 \le L_{uckGrade}<3860:3.561+0\left|L_{uckGrade}-3850\right|,3860 \le L_{uckGrade}<3870:3.564+0\left|L_{uckGrade}-3860\right|,3870 \le L_{uckGrade}<3880:3.566+0\left|L_{uckGrade}-3870\right|,3880 \le L_{uckGrade}<3890:3.569+0\left|L_{uckGrade}-3880\right|,3890 \le L_{uckGrade}<3900:3.571+0\left|L_{uckGrade}-3890\right|,3900 \le L_{uckGrade}<3920:3.574+0\left|L_{uckGrade}-3900\right|,3920 \le L_{uckGrade}<3930:3.578+0\left|L_{uckGrade}-3920\right|,3930 \le L_{uckGrade}<3960:3.581+0\left|L_{uckGrade}-3930\right|,3960 \le L_{uckGrade}<3970:3.587+0\left|L_{uckGrade}-3960\right|,3970 \le L_{uckGrade}<4010:3.59+0\left|L_{uckGrade}-3970\right|,4010 \le L_{uckGrade}<4020:3.598+0\left|L_{uckGrade}-4010\right|,4020 \le L_{uckGrade}<4140:3.601+0\left|L_{uckGrade}-4020\right|,4140 \le L_{uckGrade}<4150:3.625+0\left|L_{uckGrade}-4140\right|,4150 \le L_{uckGrade}<4190:3.626+0\left|L_{uckGrade}-4150\right|,4190 \le L_{uckGrade}<4200:3.634+0\left|L_{uckGrade}-4190\right|,4200 \le L_{uckGrade}<4230:3.635+0\left|L_{uckGrade}-4200\right|,4230 \le L_{uckGrade}<4240:3.641+0\left|L_{uckGrade}-4230\right|,4240 \le L_{uckGrade}<4250:3.642+0\left|L_{uckGrade}-4240\right|,4250 \le L_{uckGrade}<4260:3.644+0\left|L_{uckGrade}-4250\right|,4260 \le L_{uckGrade}<4280:3.645+0\left|L_{uckGrade}-4260\right|,4280 \le L_{uckGrade}<4290:3.649+0\left|L_{uckGrade}-4280\right|,4290 \le L_{uckGrade}<4300:3.65+0\left|L_{uckGrade}-4290\right|,4300 \le L_{uckGrade}<4310:3.652+0\left|L_{uckGrade}-4300\right|,4310 \le L_{uckGrade}<4320:3.653+0\left|L_{uckGrade}-4310\right|,4320 \le L_{uckGrade}<4330:3.655+0\left|L_{uckGrade}-4320\right|,4330 \le L_{uckGrade}<4340:3.656+0\left|L_{uckGrade}-4330\right|,4340 \le L_{uckGrade}<4360:3.658+0\left|L_{uckGrade}-4340\right|,4360 \le L_{uckGrade}<4370:3.66+0\left|L_{uckGrade}-4360\right|,4370 \le L_{uckGrade}<4380:3.662+0\left|L_{uckGrade}-4370\right|,4380 \le L_{uckGrade}<4390:3.663+0\left|L_{uckGrade}-4380\right|,4390 \le L_{uckGrade}<4420:3.665+0\left|L_{uckGrade}-4390\right|,4420 \le L_{uckGrade}<4430:3.668+0\left|L_{uckGrade}-4420\right|,4430 \le L_{uckGrade}<4470:3.67+0\left|L_{uckGrade}-4430\right|,4470 \le L_{uckGrade}<4480:3.674+0\left|L_{uckGrade}-4470\right|,4480 \le L_{uckGrade}<4610:3.676+0\left|L_{uckGrade}-4480\right|,4610 \le L_{uckGrade}<4620:3.689+0\left|L_{uckGrade}-4610\right|,4620 \le L_{uckGrade}<4660:3.689+0\left|L_{uckGrade}-4620\right|,4660 \le L_{uckGrade}<4670:3.693+0\left|L_{uckGrade}-4660\right|,4670 \le L_{uckGrade}<4690:3.693+0\left|L_{uckGrade}-4670\right|,4690 \le L_{uckGrade}<4700:3.695+0\left|L_{uckGrade}-4690\right|,4700 \le L_{uckGrade}<4720:3.695+0\left|L_{uckGrade}-4700\right|,4720 \le L_{uckGrade}<4730:3.697+0\left|L_{uckGrade}-4720\right|,4730 \le L_{uckGrade}<4740:3.697+0\left|L_{uckGrade}-4730\right|,4740 \le L_{uckGrade}<4750:3.698+0\left|L_{uckGrade}-4740\right|,4750 \le L_{uckGrade}<4760:3.698+0\left|L_{uckGrade}-4750\right|,4760 \le L_{uckGrade}<4770:3.699+0\left|L_{uckGrade}-4760\right|,4770 \le L_{uckGrade}<4780:3.699+0\left|L_{uckGrade}-4770\right|,4780 \le L_{uckGrade}<4790:3.7+0\left|L_{uckGrade}-4780\right|,4790 \le L_{uckGrade}<4800:3.7+0\left|L_{uckGrade}-4790\right|,4800 \le L_{uckGrade}<4810:3.701+0\left|L_{uckGrade}-4800\right|,4810 \le L_{uckGrade}<4820:3.701+0\left|L_{uckGrade}-4810\right|,4820 \le L_{uckGrade}<4840:3.702+0\left|L_{uckGrade}-4820\right|,4840 \le L_{uckGrade}<4850:3.702+0\left|L_{uckGrade}-4840\right|,4850 \le L_{uckGrade}<4870:3.703+0\left|L_{uckGrade}-4850\right|,4870 \le L_{uckGrade}<4880:3.703+0\left|L_{uckGrade}-4870\right|,4880 \le L_{uckGrade}<4910:3.704+0\left|L_{uckGrade}-4880\right|,4910 \le L_{uckGrade}<4920:3.704+0\left|L_{uckGrade}-4910\right|,4920 \le L_{uckGrade}<5000:3.705+0\left|L_{uckGrade}-4920\right|\right\}
See Example for how to use.
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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L_{uckGrade08}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<20:1+0.001\left|L_{uckGrade}-0\right|,20 \le L_{uckGrade}<30:1.026+0.001\left|L_{uckGrade}-20\right|,30 \le L_{uckGrade}<60:1.038+0.001\left|L_{uckGrade}-30\right|,60 \le L_{uckGrade}<70:1.077+0.001\left|L_{uckGrade}-60\right|,70 \le L_{uckGrade}<90:1.089+0.001\left|L_{uckGrade}-70\right|,90 \le L_{uckGrade}<100:1.115+0.001\left|L_{uckGrade}-90\right|,100 \le L_{uckGrade}<110:1.127+0.001\left|L_{uckGrade}-100\right|,110 \le L_{uckGrade}<120:1.14+0.001\left|L_{uckGrade}-110\right|,120 \le L_{uckGrade}<130:1.152+0.001\left|L_{uckGrade}-120\right|,130 \le L_{uckGrade}<140:1.165+0.001\left|L_{uckGrade}-130\right|,140 \le L_{uckGrade}<150:1.177+0.001\left|L_{uckGrade}-140\right|,150 \le L_{uckGrade}<160:1.19+0.001\left|L_{uckGrade}-150\right|,160 \le L_{uckGrade}<170:1.202+0.001\left|L_{uckGrade}-160\right|,170 \le L_{uckGrade}<190:1.215+0.001\left|L_{uckGrade}-170\right|,190 \le L_{uckGrade}<200:1.239+0.001\left|L_{uckGrade}-190\right|,200 \le L_{uckGrade}<230:1.252+0.001\left|L_{uckGrade}-200\right|,230 \le L_{uckGrade}<240:1.288+0.001\left|L_{uckGrade}-230\right|,240 \le L_{uckGrade}<280:1.301+0.001\left|L_{uckGrade}-240\right|,280 \le L_{uckGrade}<290:1.349+0.001\left|L_{uckGrade}-280\right|,290 \le L_{uckGrade}<360:1.362+0.001\left|L_{uckGrade}-290\right|,360 \le L_{uckGrade}<370:1.446+0.001\left|L_{uckGrade}-360\right|,370 \le L_{uckGrade}<420:1.457+0.001\left|L_{uckGrade}-370\right|,420 \le L_{uckGrade}<430:1.517+0.001\left|L_{uckGrade}-420\right|,430 \le L_{uckGrade}<450:1.528+0.001\left|L_{uckGrade}-430\right|,450 \le L_{uckGrade}<460:1.552+0.001\left|L_{uckGrade}-450\right|,460 \le L_{uckGrade}<480:1.563+0.001\left|L_{uckGrade}-460\right|,480 \le L_{uckGrade}<490:1.587+0.001\left|L_{uckGrade}-480\right|,490 \le L_{uckGrade}<500:1.598+0.001\left|L_{uckGrade}-490\right|,500 \le L_{uckGrade}<510:1.61+0.001\left|L_{uckGrade}-500\right|,510 \le L_{uckGrade}<520:1.621+0.001\left|L_{uckGrade}-510\right|,520 \le L_{uckGrade}<530:1.633+0.001\left|L_{uckGrade}-520\right|,530 \le L_{uckGrade}<540:1.644+0.001\left|L_{uckGrade}-530\right|,540 \le L_{uckGrade}<550:1.656+0.001\left|L_{uckGrade}-540\right|,550 \le L_{uckGrade}<560:1.667+0.001\left|L_{uckGrade}-550\right|,560 \le L_{uckGrade}<580:1.679+0.001\left|L_{uckGrade}-560\right|,580 \le L_{uckGrade}<590:1.701+0.001\left|L_{uckGrade}-580\right|,590 \le L_{uckGrade}<610:1.713+0.001\left|L_{uckGrade}-590\right|,610 \le L_{uckGrade}<620:1.735+0.001\left|L_{uckGrade}-610\right|,620 \le L_{uckGrade}<660:1.747+0.001\left|L_{uckGrade}-620\right|,660 \le L_{uckGrade}<670:1.791+0.001\left|L_{uckGrade}-660\right|,670 \le L_{uckGrade}<760:1.803+0.001\left|L_{uckGrade}-670\right|,760 \le L_{uckGrade}<770:1.902+0.001\left|L_{uckGrade}-760\right|,770 \le L_{uckGrade}<810:1.912+0.001\left|L_{uckGrade}-770\right|,810 \le L_{uckGrade}<820:1.956+0.001\left|L_{uckGrade}-810\right|,820 \le L_{uckGrade}<850:1.966+0.001\left|L_{uckGrade}-820\right|,850 \le L_{uckGrade}<860:1.999+0.001\left|L_{uckGrade}-850\right|,860 \le L_{uckGrade}<870:2.009+0.001\left|L_{uckGrade}-860\right|,870 \le L_{uckGrade}<880:2.02+0.001\left|L_{uckGrade}-870\right|,880 \le L_{uckGrade}<900:2.03+0.001\left|L_{uckGrade}-880\right|,900 \le L_{uckGrade}<910:2.052+0.001\left|L_{uckGrade}-900\right|,910 \le L_{uckGrade}<920:2.062+0.001\left|L_{uckGrade}-910\right|,920 \le L_{uckGrade}<940:2.073+0.001\left|L_{uckGrade}-920\right|,940 \le L_{uckGrade}<950:2.093+0.001\left|L_{uckGrade}-940\right|,950 \le L_{uckGrade}<960:2.104+0.001\left|L_{uckGrade}-950\right|,960 \le L_{uckGrade}<970:2.114+0.001\left|L_{uckGrade}-960\right|,970 \le L_{uckGrade}<990:2.125+0.001\left|L_{uckGrade}-970\right|,990 \le L_{uckGrade}<1000:2.145+0.001\left|L_{uckGrade}-990\right|,1000 \le L_{uckGrade}<1040:2.156+0.001\left|L_{uckGrade}-1000\right|,1040 \le L_{uckGrade}<1050:2.196+0.001\left|L_{uckGrade}-1040\right|,1050 \le L_{uckGrade}<1160:2.207+0.001\left|L_{uckGrade}-1050\right|,1160 \le L_{uckGrade}<1170:2.317+0.001\left|L_{uckGrade}-1160\right|,1170 \le L_{uckGrade}<1210:2.326+0.001\left|L_{uckGrade}-1170\right|,1210 \le L_{uckGrade}<1220:2.366+0.001\left|L_{uckGrade}-1210\right|,1220 \le L_{uckGrade}<1240:2.375+0.001\left|L_{uckGrade}-1220\right|,1240 \le L_{uckGrade}<1250:2.395+0.001\left|L_{uckGrade}-1240\right|,1250 \le L_{uckGrade}<1270:2.404+0.001\left|L_{uckGrade}-1250\right|,1270 \le L_{uckGrade}<1280:2.424+0.001\left|L_{uckGrade}-1270\right|,1280 \le L_{uckGrade}<1290:2.433+0.001\left|L_{uckGrade}-1280\right|,1290 \le L_{uckGrade}<1300:2.443+0.001\left|L_{uckGrade}-1290\right|,1300 \le L_{uckGrade}<1310:2.452+0.001\left|L_{uckGrade}-1300\right|,1310 \le L_{uckGrade}<1320:2.462+0.001\left|L_{uckGrade}-1310\right|,1320 \le L_{uckGrade}<1330:2.471+0.001\left|L_{uckGrade}-1320\right|,1330 \le L_{uckGrade}<1350:2.481+0.001\left|L_{uckGrade}-1330\right|,1350 \le L_{uckGrade}<1360:2.499+0.001\left|L_{uckGrade}-1350\right|,1360 \le L_{uckGrade}<1380:2.509+0.001\left|L_{uckGrade}-1360\right|,1380 \le L_{uckGrade}<1390:2.527+0.001\left|L_{uckGrade}-1380\right|,1390 \le L_{uckGrade}<1420:2.537+0.001\left|L_{uckGrade}-1390\right|,1420 \le L_{uckGrade}<1430:2.564+0.001\left|L_{uckGrade}-1420\right|,1430 \le L_{uckGrade}<1560:2.574+0.001\left|L_{uckGrade}-1430\right|,1560 \le L_{uckGrade}<1570:2.691+0.001\left|L_{uckGrade}-1560\right|,1570 \le L_{uckGrade}<1600:2.699+0.001\left|L_{uckGrade}-1570\right|,1600 \le L_{uckGrade}<1610:2.726+0.001\left|L_{uckGrade}-1600\right|,1610 \le L_{uckGrade}<1630:2.734+0.001\left|L_{uckGrade}-1610\right|,1630 \le L_{uckGrade}<1640:2.752+0.001\left|L_{uckGrade}-1630\right|,1640 \le L_{uckGrade}<1660:2.76+0.001\left|L_{uckGrade}-1640\right|,1660 \le L_{uckGrade}<1670:2.778+0.001\left|L_{uckGrade}-1660\right|,1670 \le L_{uckGrade}<1680:2.786+0.001\left|L_{uckGrade}-1670\right|,1680 \le L_{uckGrade}<1690:2.795+0.001\left|L_{uckGrade}-1680\right|,1690 \le L_{uckGrade}<1700:2.803+0.001\left|L_{uckGrade}-1690\right|,1700 \le L_{uckGrade}<1710:2.812+0.001\left|L_{uckGrade}-1700\right|,1710 \le L_{uckGrade}<1720:2.82+0.001\left|L_{uckGrade}-1710\right|,1720 \le L_{uckGrade}<1740:2.829+0.001\left|L_{uckGrade}-1720\right|,1740 \le L_{uckGrade}<1750:2.845+0.001\left|L_{uckGrade}-1740\right|,1750 \le L_{uckGrade}<1760:2.854+0.001\left|L_{uckGrade}-1750\right|,1760 \le L_{uckGrade}<1770:2.862+0.001\left|L_{uckGrade}-1760\right|,1770 \le L_{uckGrade}<1810:2.871+0.001\left|L_{uckGrade}-1770\right|,1810 \le L_{uckGrade}<1820:2.903+0.001\left|L_{uckGrade}-1810\right|,1820 \le L_{uckGrade}<1960:2.912+0.001\left|L_{uckGrade}-1820\right|,1960 \le L_{uckGrade}<1970:3.024+0.001\left|L_{uckGrade}-1960\right|,1970 \le L_{uckGrade}<2000:3.031+0.001\left|L_{uckGrade}-1970\right|,2000 \le L_{uckGrade}<2010:3.055+0.001\left|L_{uckGrade}-2000\right|,2010 \le L_{uckGrade}<2030:3.062+0.001\left|L_{uckGrade}-2010\right|,2030 \le L_{uckGrade}<2040:3.078+0.001\left|L_{uckGrade}-2030\right|,2040 \le L_{uckGrade}<2050:3.085+0.001\left|L_{uckGrade}-2040\right|,2050 \le L_{uckGrade}<2060:3.093+0.001\left|L_{uckGrade}-2050\right|,2060 \le L_{uckGrade}<2070:3.1+0.001\left|L_{uckGrade}-2060\right|,2070 \le L_{uckGrade}<2080:3.108+0.001\left|L_{uckGrade}-2070\right|,2080 \le L_{uckGrade}<2090:3.115+0.001\left|L_{uckGrade}-2080\right|,2090 \le L_{uckGrade}<2100:3.123+0.001\left|L_{uckGrade}-2090\right|,2100 \le L_{uckGrade}<2110:3.13+0.001\left|L_{uckGrade}-2100\right|,2110 \le L_{uckGrade}<2120:3.138+0.001\left|L_{uckGrade}-2110\right|,2120 \le L_{uckGrade}<2130:3.145+0.001\left|L_{uckGrade}-2120\right|,2130 \le L_{uckGrade}<2150:3.153+0.001\left|L_{uckGrade}-2130\right|,2150 \le L_{uckGrade}<2160:3.167+0.001\left|L_{uckGrade}-2150\right|,2160 \le L_{uckGrade}<2190:3.175+0.001\left|L_{uckGrade}-2160\right|,2190 \le L_{uckGrade}<2200:3.196+0.001\left|L_{uckGrade}-2190\right|,2200 \le L_{uckGrade}<2350:3.204+0.001\left|L_{uckGrade}-2200\right|,2350 \le L_{uckGrade}<2360:3.309+0.001\left|L_{uckGrade}-2350\right|,2360 \le L_{uckGrade}<2390:3.315+0.001\left|L_{uckGrade}-2360\right|,2390 \le L_{uckGrade}<2400:3.336+0.001\left|L_{uckGrade}-2390\right|,2400 \le L_{uckGrade}<2420:3.342+0.001\left|L_{uckGrade}-2400\right|,2420 \le L_{uckGrade}<2430:3.356+0.001\left|L_{uckGrade}-2420\right|,2430 \le L_{uckGrade}<2440:3.362+0.001\left|L_{uckGrade}-2430\right|,2440 \le L_{uckGrade}<2450:3.369+0.001\left|L_{uckGrade}-2440\right|,2450 \le L_{uckGrade}<2470:3.375+0.001\left|L_{uckGrade}-2450\right|,2470 \le L_{uckGrade}<2490:3.389+0.001\left|L_{uckGrade}-2470\right|,2490 \le L_{uckGrade}<2500:3.401+0.001\left|L_{uckGrade}-2490\right|,2500 \le L_{uckGrade}<2510:3.408+0.001\left|L_{uckGrade}-2500\right|,2510 \le L_{uckGrade}<2520:3.414+0.001\left|L_{uckGrade}-2510\right|,2520 \le L_{uckGrade}<2540:3.421+0.001\left|L_{uckGrade}-2520\right|,2540 \le L_{uckGrade}<2550:3.433+0.001\left|L_{uckGrade}-2540\right|,2550 \le L_{uckGrade}<2580:3.44+0.001\left|L_{uckGrade}-2550\right|,2580 \le L_{uckGrade}<2590:3.458+0.001\left|L_{uckGrade}-2580\right|,2590 \le L_{uckGrade}<2750:3.465+0.001\left|L_{uckGrade}-2590\right|,2750 \le L_{uckGrade}<2760:3.561+0\left|L_{uckGrade}-2750\right|,2760 \le L_{uckGrade}<2780:3.566+0.001\left|L_{uckGrade}-2760\right|,2780 \le L_{uckGrade}<2790:3.578+0.001\left|L_{uckGrade}-2780\right|,2790 \le L_{uckGrade}<2810:3.583+0.001\left|L_{uckGrade}-2790\right|,2810 \le L_{uckGrade}<2820:3.595+0\left|L_{uckGrade}-2810\right|,2820 \le L_{uckGrade}<2840:3.6+0.001\left|L_{uckGrade}-2820\right|,2840 \le L_{uckGrade}<2850:3.612+0\left|L_{uckGrade}-2840\right|,2850 \le L_{uckGrade}<2860:3.617+0.001\left|L_{uckGrade}-2850\right|,2860 \le L_{uckGrade}<2870:3.623+0\left|L_{uckGrade}-2860\right|,2870 \le L_{uckGrade}<2880:3.628+0.001\left|L_{uckGrade}-2870\right|,2880 \le L_{uckGrade}<2900:3.634+0.001\left|L_{uckGrade}-2880\right|,2900 \le L_{uckGrade}<2910:3.644+0.001\left|L_{uckGrade}-2900\right|,2910 \le L_{uckGrade}<2930:3.65+0.001\left|L_{uckGrade}-2910\right|,2930 \le L_{uckGrade}<2940:3.66+0.001\left|L_{uckGrade}-2930\right|,2940 \le L_{uckGrade}<2960:3.666+0.001\left|L_{uckGrade}-2940\right|,2960 \le L_{uckGrade}<2970:3.676+0.001\left|L_{uckGrade}-2960\right|,2970 \le L_{uckGrade}<3140:3.682+0\left|L_{uckGrade}-2970\right|,3140 \le L_{uckGrade}<3150:3.767+0\left|L_{uckGrade}-3140\right|,3150 \le L_{uckGrade}<3180:3.771+0.001\left|L_{uckGrade}-3150\right|,3180 \le L_{uckGrade}<3190:3.786+0\left|L_{uckGrade}-3180\right|,3190 \le L_{uckGrade}<3200:3.79+0\left|L_{uckGrade}-3190\right|,3200 \le L_{uckGrade}<3210:3.795+0\left|L_{uckGrade}-3200\right|,3210 \le L_{uckGrade}<3230:3.799+0.001\left|L_{uckGrade}-3210\right|,3230 \le L_{uckGrade}<3240:3.809+0\left|L_{uckGrade}-3230\right|,3240 \le L_{uckGrade}<3250:3.813+0\left|L_{uckGrade}-3240\right|,3250 \le L_{uckGrade}<3260:3.818+0\left|L_{uckGrade}-3250\right|,3260 \le L_{uckGrade}<3270:3.822+0\left|L_{uckGrade}-3260\right|,3270 \le L_{uckGrade}<3290:3.827+0\left|L_{uckGrade}-3270\right|,3290 \le L_{uckGrade}<3300:3.835+0\left|L_{uckGrade}-3290\right|,3300 \le L_{uckGrade}<3310:3.84+0\left|L_{uckGrade}-3300\right|,3310 \le L_{uckGrade}<3320:3.844+0.001\left|L_{uckGrade}-3310\right|,3320 \le L_{uckGrade}<3350:3.849+0\left|L_{uckGrade}-3320\right|,3350 \le L_{uckGrade}<3360:3.861+0\left|L_{uckGrade}-3350\right|,3360 \le L_{uckGrade}<3420:3.866+0\left|L_{uckGrade}-3360\right|,3420 \le L_{uckGrade}<3430:3.89+0\left|L_{uckGrade}-3420\right|,3430 \le L_{uckGrade}<3460:3.895+0\left|L_{uckGrade}-3430\right|,3460 \le L_{uckGrade}<3470:3.907+0\left|L_{uckGrade}-3460\right|,3470 \le L_{uckGrade}<3530:3.91+0\left|L_{uckGrade}-3470\right|,3530 \le L_{uckGrade}<3540:3.934+0\left|L_{uckGrade}-3530\right|,3540 \le L_{uckGrade}<3570:3.937+0\left|L_{uckGrade}-3540\right|,3570 \le L_{uckGrade}<3580:3.949+0\left|L_{uckGrade}-3570\right|,3580 \le L_{uckGrade}<3590:3.952+0\left|L_{uckGrade}-3580\right|,3590 \le L_{uckGrade}<3600:3.956+0\left|L_{uckGrade}-3590\right|,3600 \le L_{uckGrade}<3620:3.959+0\left|L_{uckGrade}-3600\right|,3620 \le L_{uckGrade}<3630:3.967+0\left|L_{uckGrade}-3620\right|,3630 \le L_{uckGrade}<3640:3.97+0\left|L_{uckGrade}-3630\right|,3640 \le L_{uckGrade}<3650:3.974+0\left|L_{uckGrade}-3640\right|,3650 \le L_{uckGrade}<3660:3.977+0\left|L_{uckGrade}-3650\right|,3660 \le L_{uckGrade}<3670:3.981+0\left|L_{uckGrade}-3660\right|,3670 \le L_{uckGrade}<3680:3.984+0\left|L_{uckGrade}-3670\right|,3680 \le L_{uckGrade}<3700:3.988+0\left|L_{uckGrade}-3680\right|,3700 \le L_{uckGrade}<3710:3.994+0\left|L_{uckGrade}-3700\right|,3710 \le L_{uckGrade}<3740:3.998+0\left|L_{uckGrade}-3710\right|,3740 \le L_{uckGrade}<3750:4.007+0\left|L_{uckGrade}-3740\right|,3750 \le L_{uckGrade}<3800:4.011+0\left|L_{uckGrade}-3750\right|,3800 \le L_{uckGrade}<3810:4.026+0\left|L_{uckGrade}-3800\right|,3810 \le L_{uckGrade}<3860:4.03+0\left|L_{uckGrade}-3810\right|,3860 \le L_{uckGrade}<3870:4.045+0\left|L_{uckGrade}-3860\right|,3870 \le L_{uckGrade}<3920:4.047+0\left|L_{uckGrade}-3870\right|,3920 \le L_{uckGrade}<3930:4.062+0\left|L_{uckGrade}-3920\right|,3930 \le L_{uckGrade}<3960:4.064+0\left|L_{uckGrade}-3930\right|,3960 \le L_{uckGrade}<3970:4.073+0\left|L_{uckGrade}-3960\right|,3970 \le L_{uckGrade}<3990:4.075+0\left|L_{uckGrade}-3970\right|,3990 \le L_{uckGrade}<4000:4.081+0\left|L_{uckGrade}-3990\right|,4000 \le L_{uckGrade}<4010:4.083+0\left|L_{uckGrade}-4000\right|,4010 \le L_{uckGrade}<4020:4.086+0\left|L_{uckGrade}-4010\right|,4020 \le L_{uckGrade}<4030:4.088+0\left|L_{uckGrade}-4020\right|,4030 \le L_{uckGrade}<4040:4.091+0\left|L_{uckGrade}-4030\right|,4040 \le L_{uckGrade}<4050:4.093+0\left|L_{uckGrade}-4040\right|,4050 \le L_{uckGrade}<4060:4.096+0\left|L_{uckGrade}-4050\right|,4060 \le L_{uckGrade}<4070:4.098+0\left|L_{uckGrade}-4060\right|,4070 \le L_{uckGrade}<4090:4.101+0\left|L_{uckGrade}-4070\right|,4090 \le L_{uckGrade}<4100:4.105+0\left|L_{uckGrade}-4090\right|,4100 \le L_{uckGrade}<4130:4.108+0\left|L_{uckGrade}-4100\right|,4130 \le L_{uckGrade}<4140:4.114+0\left|L_{uckGrade}-4130\right|,4140 \le L_{uckGrade}<4190:4.117+0\left|L_{uckGrade}-4140\right|,4190 \le L_{uckGrade}<4200:4.127+0\left|L_{uckGrade}-4190\right|,4200 \le L_{uckGrade}<4250:4.13+0\left|L_{uckGrade}-4200\right|,4250 \le L_{uckGrade}<4260:4.14+0\left|L_{uckGrade}-4250\right|,4260 \le L_{uckGrade}<4310:4.141+0\left|L_{uckGrade}-4260\right|,4310 \le L_{uckGrade}<4320:4.151+0\left|L_{uckGrade}-4310\right|,4320 \le L_{uckGrade}<4350:4.152+0\left|L_{uckGrade}-4320\right|,4350 \le L_{uckGrade}<4360:4.158+0\left|L_{uckGrade}-4350\right|,4360 \le L_{uckGrade}<4380:4.159+0\left|L_{uckGrade}-4360\right|,4380 \le L_{uckGrade}<4390:4.163+0\left|L_{uckGrade}-4380\right|,4390 \le L_{uckGrade}<4400:4.164+0\left|L_{uckGrade}-4390\right|,4400 \le L_{uckGrade}<4410:4.166+0\left|L_{uckGrade}-4400\right|,4410 \le L_{uckGrade}<4420:4.167+0\left|L_{uckGrade}-4410\right|,4420 \le L_{uckGrade}<4430:4.169+0\left|L_{uckGrade}-4420\right|,4430 \le L_{uckGrade}<4440:4.17+0\left|L_{uckGrade}-4430\right|,4440 \le L_{uckGrade}<4450:4.172+0\left|L_{uckGrade}-4440\right|,4450 \le L_{uckGrade}<4460:4.173+0\left|L_{uckGrade}-4450\right|,4460 \le L_{uckGrade}<4480:4.175+0\left|L_{uckGrade}-4460\right|,4480 \le L_{uckGrade}<4490:4.177+0\left|L_{uckGrade}-4480\right|,4490 \le L_{uckGrade}<4520:4.179+0\left|L_{uckGrade}-4490\right|,4520 \le L_{uckGrade}<4530:4.182+0\left|L_{uckGrade}-4520\right|,4530 \le L_{uckGrade}<4570:4.184+0\left|L_{uckGrade}-4530\right|,4570 \le L_{uckGrade}<4580:4.188+0\left|L_{uckGrade}-4570\right|,4580 \le L_{uckGrade}<4650:4.19+0\left|L_{uckGrade}-4580\right|,4650 \le L_{uckGrade}<4660:4.197+0\left|L_{uckGrade}-4650\right|,4660 \le L_{uckGrade}<4710:4.197+0\left|L_{uckGrade}-4660\right|,4710 \le L_{uckGrade}<4720:4.202+0\left|L_{uckGrade}-4710\right|,4720 \le L_{uckGrade}<4740:4.202+0\left|L_{uckGrade}-4720\right|,4740 \le L_{uckGrade}<4750:4.204+0\left|L_{uckGrade}-4740\right|,4750 \le L_{uckGrade}<4770:4.204+0\left|L_{uckGrade}-4750\right|,4770 \le L_{uckGrade}<4780:4.206+0\left|L_{uckGrade}-4770\right|,4780 \le L_{uckGrade}<4790:4.206+0\left|L_{uckGrade}-4780\right|,4790 \le L_{uckGrade}<4800:4.207+0\left|L_{uckGrade}-4790\right|,4800 \le L_{uckGrade}<4810:4.207+0\left|L_{uckGrade}-4800\right|,4810 \le L_{uckGrade}<4820:4.208+0\left|L_{uckGrade}-4810\right|,4820 \le L_{uckGrade}<4830:4.208+0\left|L_{uckGrade}-4820\right|,4830 \le L_{uckGrade}<4840:4.209+0\left|L_{uckGrade}-4830\right|,4840 \le L_{uckGrade}<4850:4.209+0\left|L_{uckGrade}-4840\right|,4850 \le L_{uckGrade}<4870:4.21+0\left|L_{uckGrade}-4850\right|,4870 \le L_{uckGrade}<4880:4.21+0\left|L_{uckGrade}-4870\right|,4880 \le L_{uckGrade}<4900:4.211+0\left|L_{uckGrade}-4880\right|,4900 \le L_{uckGrade}<4910:4.211+0\left|L_{uckGrade}-4900\right|,4910 \le L_{uckGrade}<4960:4.212+0\left|L_{uckGrade}-4910\right|,4960 \le L_{uckGrade}<4970:4.212+0\left|L_{uckGrade}-4960\right|,4970 \le L_{uckGrade}<5000:4.213+0\left|L_{uckGrade}-4970\right|\right\}
See Example for how to use.
If the Luck Scalar Graph doesn't cover a Scalar value you wish to see please reference the desmos graph.
The desmos graph displays the LaTeX equations.
Note that Luck does work at all amounts, not just in intervals of 50.
Max Spell Count
Determines the number of spells that can be stored at once. For example, at base, Wizard can store up to 5 Fireballs. This can be increased with Max Spell Count Bonus multiplicatively
Can't be found on gear and is not affected by other stats.
Enchantment Stats
Stats that come from weapons, armors or jewelry imbued with item Enchantments.
Enchantments that aren't traditional Stats and only exist in a Damage/Healing formula are listed below and can also be found in Damage_Calculation and Healing.
For the possible values of Enchantments and their historical rolls, see Enchantment Values
Unimplemented Stats
These stats are not yet implemented.
Utility Effectiveness Bonus
Determines the bonus effectiveness of your utility items
I can't believe that the physical and magical curves in a game could be modified to be the same. This is too strange. Are the basic damage of melee weapons and magic weapons the same concept? What is the difference between physical damage and magical damage? This is a ridiculous change. I think there is a better solution to weaken the magic profession.I think game planners are being lazy when making this decision.
With this latest patch the notes have:
- Flattened the Physical Damage Bonus (PDB) curve at the upper end.
- Updated the Magical Damage Bonus (MDB) curve so it now matches the new PDB curve.
But in testing last night I noticed that the PDB chart still matches what is in game, while the MDB chart doesn't. Was the PDB chart updated while the other wasn't or is something else going on?
is luck working?
Something seems off with the physical power and the Magic Power chart, as a naked fighter I have 16 Physical Power, shouldn't I have 15? When I equip riveted gloves it jumps to 17 which is correct according to the graph. The same goes for Magic Power
Numbers between Magical Resistance chart and in game (Magic Resist Rating) doesn't match
A nude Fighter has 15 will which equals to 30 Magic Rating, which equals to 7,8 Magic Resis OK
But
A nude Druid has 18 will, looking at the chart this should be equal to 30 + (from 15 to 33: 4 each) 3 X 4 = 12 --> 42 Magic Resist Rating which would be equal to (33 magic resis bottom segment) 9% + (from 33 to 53: 0,3 each) 9 X 0,3 = 11,7% Magic Resis
However in game a nude Druid is displayed with 52 Magic Rating and 14,7% Magic Resis (A player with 52 magic resis does actually adds up to 14,7 magic resis, so it is the will conversion which is different in the chart)
200——300护甲值的物理伤害减免实际上比统计表上的少了0.1%
Which one is better to stack if fighting against Wizard/Warlock?
title
Did they revert the armor scaling nerf? Why does it say 175 to 230 = 0.3% each, up to 48%, it used to be 0.25% per after they nerfed it?
Why can't the loss duration bonus and gain duration bonus be applied to others?
"Cooldown Reduction reduces the cooldowns of skills/perks. Reduced cooldown length = Base Cooldown * (1 - Cooldown Reduction)
Note that perk cooldowns are in the form of a buff/debuff and are additionally affected by Buff/Debuff Duration. Reduced cooldown length = Post buff/debuff duration cooldown * (1 - Cooldown Reduction)"
Since some skills/perk also is affected by Buff/Debuff, how do you implement that to the total skill's cooldown time?
The Item Equip Speed speed section says that weapons equip instantly and therefore don't benefit from the stat, but equipping a Hand Crossbow as a Rogue does seem to have a progress bar (progress circle?). I haven't tested anything with other classes.
Physical damage reduction curve currently isn't correct; they updated it about 3 days ago for Early Access Hotfix #55: "Slightly lowered the amount of Physical Damage Resistance earned per Armor Rating within the upper sweet spot of the curve (~200 Armor Rating.)".
I tested it to double check, and the armor does indeed have some new sort of scaling in the 175-230 region that isn't described above. When I increased armor from 175 to 181, I gained 1.5% reduction instead of the expected 1.8% damage reduction (33% total), and when I increased it by another 15 armor to 196, instead of gaining 4.5% reduction, I only gained 3.7% (36.7% total)
After reading over this wiki to better understand the game and how it works, and finally reaching this page, I feel like this is something I need to point out and see if anyone else agrees: Knowledge is a really frustrating stat because of it's inequality between martial and caster classes.
I understand that Ironmace can't just give every non-caster class a base 5 in Knowledge like Barb has and allocate those extra points somewhere more useful, but it's also somewhat annoying to see that it's not even uniform amongst the other martial classes. Rogue has 10, Ranger has 12, and Fighter has 15. Granted, Fighter has 15 in *everything*, but still, I find it strange and a little irritating that the only true "dump stat" for martials is still at least a two-digit number for everything but Barb. I know Multiclassing used to be a thing sometime before the current update, which I guess is the only reason that Knowledge might be useful on a martial class, but without Multiclassing in the game currently it just feels bad to see these points allocated into a stat that does precisely nothing for martials.
And even WITH Multiclassing, only Fighter has a base Knowledge stat comparable to any of the casting classes (Warlock in particular with their base 15) to make it actually useful in any degree - which feels wrong to me, coming from a Dungeons & Dragons background. In Dungeons & Dragons, Rangers are half-casters while Eldritch Knight Fighters are only third-casters - same as Arcane Trickster Rogues. Yet based on Knowledge in this game, Fighters are on par with Warlocks, Rangers are like half-casters, and Rogues like third-casters. I know that Dark and Darker isn't meant to be one-to-one with Dungeons & Dragons (despite both sharing the D&D/DnD abbreviation, humorously enough), but it still just feels wrong to me. Even from a purely Dark and Darker perspective, if the intent is to give some martials a little bit better Knowledge to incentivize/permit multiclassing into casting, would 10 or 12 base Knowledge even be worth it? Even base 15 Knowledge feels a little limited with it's Memory Cap of 9; a base Cap of 6, and especially 4, just sounds like an awful waste of a Skill slot and Weapon slot to me. And that's even before considering the extra Knowledge, Memory Cap, Casting Speed, etc. rolls you'd want on gear just to catch up and make multiclass casting worth it - rolls which are actively competing against the standard desirable rolls for Rogues and Rangers.
Does anyone else share this sentiment about Knowledge on non-casters being a point of contention? I almost feel like Knowledge should have some other effect that isn't specifically casting-related. After all, every other stat in the game has something it influences that makes it necessary to some degree, like Action and Regular Action Speeds. Why should Knowledge be the only one that gives absolutely no upside to classes that don't have spells, yet still have upwards of 10 Knowledge? I don't even have a proposition as to what Knowledge could influence, because everything else stat-wise makes sense and is well-thought out. Knowledge just feels really weird as a stat that's only important for casters. It almost makes me think that it should be removed, and things like Memory Capacity, Recovery, and Spellcasting Speed should be delegated to other stats. But that would be unfair to casters in the same way that it's currently unfair to martial classes (well, not the SAME way; more like the opposite side of the same coin). I don't know, maybe I'm weird for thinking about it in this way, but seeing how the other stats work compared to Knowledge, it just makes Knowledge feel somewhat flawed, without an obvious fix or solution.
The curve and the spell casting speed calculation are wrong. We now have more spell casting speed than mentioned on the wiki. I did the tests by comparing and calculating with the knowledge on the game. The same may be true of regular interaction speed, which was changed at the same time as spell casting speed.
If a class can manage pull off more than 100% Armor Penetration, Example: 125% Armor Penetration 58 Windlass Crossbow
Will it do a bit more damage?
Thank you in advance!
Does Poisoned Weapon from Rogue is affected by Magic Resist?
What stats should we prioritize to increase damage with bows?
I know that the current move speed limit is 350, if my stats are calculated to 380 and I use a -30 weapon, will I move at 350 or 320?
Does this work, assuming I've got the weapon out in hand when I interact?
Does weapon damage on a spellbook make the spells more powerful? hit more?
Is any stat affect reload speed for crossbow and bow ?