Luck

Loot is rolled when you open the container or kill the mob.

Whoever opens the loot first or kills the mob first is the person whose luck is used to calculate the drops.
(It is not confirmed if Bard's Unchained Harmony rolls the loot table when it opens the containers.)

Luck is capped at 500.
It is possible to get maximum of 450 Luck in the game currently:

• 50 from Bard's Wanderer's Luck
• 150 luck roll from a large Potion of Luck
• 10 from craftable golden hands armor piece
• 40 from Golden Cloak
• 200 from max enchantment rolls on other gear

Loot Drop Tables and Drop Rate Tables

Each drop instance makes use of three pieces of information: the Loot Drop table, the Drop Rate table, and the player's Luck.

Loot Drop tables list all possible items for a specific drop instance, and for each item therein it associates a Luck Grade.
Drop Rate tables assign a "rate" to each Luck Grade; when normalized, these rates represent the probability of getting a drop of that Luck Grade.

Each Luck Grade's drop rate is split evenly between items that share that Luck Grade. This means that items sharing a Loot Drop table and Luck Grade, will always have the same probability of dropping.
However, be aware that Monsters and Containers can have multiple Loot Drop Tables, each with their own Drop Rate table. See Lich for example.

A Drop can be rolled more than once, but each roll is independent of the others.
Lich rolls their gear Loot and Drop tables twice, theoretically making it possible (though extremely unlikely) to get two Artifacts from a single HR Lich kill.

Luck Scalar

Luck Scalars are 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 and Loot Drop tables.

Luck Scalar Table

Luck	0	50	100	150	200	250	300	350	400	450	500
Junk	1.000	0.950	0.900	0.850	0.800	0.750	0.700	0.650	0.600	0.550	0.500
Poor	1.000	0.950	0.900	0.850	0.800	0.750	0.700	0.650	0.600	0.550	0.500
Common	1.000	0.975	0.950	0.925	0.900	0.875	0.850	0.825	0.800	0.775	0.750
Uncommon	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
Rare	1.000	1.476	1.901	2.277	2.602	2.878	3.103	3.279	3.404	3.480	3.505
Epic	1.000	1.547	2.036	2.468	2.842	3.159	3.418	3.620	3.765	3.751	3.881
Legendary	1.000	1.618	2.171	2.659	3.083	3.441	3.734	3.962	4.125	4.223	4.257
Unique	1.000	1.642	2.216	2.723	3.163	3.535	3.839	4.076	4.245	4.347	4.382

If the Luck Scalar Table and Graph don't cover a Scalar value you wish to see, use the desmos graph. The desmos graph displays the LaTeX equations which are continuous curves, but keep in mind that fractional values of Luck do not exist.

Luck Scalar Graph

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}<500:1+-0.001\left|L_{uckGrade}-0\right|\right\}

See Example for how to use.

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}<500:1+-0.001\left|L_{uckGrade}-0\right|\right\}

See Example for how to use.

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}<500:1+-0.001\left|L_{uckGrade}-0\right|\right\}

See Example for how to use.

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}<500:1+0\left|L_{uckGrade}-0\right|\right\}

See Example for how to use.

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}<13:1+0.003\left|L_{uckGrade}-0\right|,13 \le L_{uckGrade}<14:1.039+0.002\left|L_{uckGrade}-13\right|,14 \le L_{uckGrade}<22:1.041+0.003\left|L_{uckGrade}-14\right|,22 \le L_{uckGrade}<23:1.065+0.002\left|L_{uckGrade}-22\right|,23 \le L_{uckGrade}<29:1.067+0.003\left|L_{uckGrade}-23\right|,29 \le L_{uckGrade}<30:1.085+0.002\left|L_{uckGrade}-29\right|,30 \le L_{uckGrade}<34:1.087+0.003\left|L_{uckGrade}-30\right|,34 \le L_{uckGrade}<35:1.099+0.002\left|L_{uckGrade}-34\right|,35 \le L_{uckGrade}<39:1.101+0.003\left|L_{uckGrade}-35\right|,39 \le L_{uckGrade}<40:1.113+0.002\left|L_{uckGrade}-39\right|,40 \le L_{uckGrade}<43:1.115+0.003\left|L_{uckGrade}-40\right|,43 \le L_{uckGrade}<44:1.124+0.002\left|L_{uckGrade}-43\right|,44 \le L_{uckGrade}<47:1.126+0.003\left|L_{uckGrade}-44\right|,47 \le L_{uckGrade}<48:1.135+0.002\left|L_{uckGrade}-47\right|,48 \le L_{uckGrade}<50:1.137+0.003\left|L_{uckGrade}-48\right|,50 \le L_{uckGrade}<51:1.143+0.002\left|L_{uckGrade}-50\right|,51 \le L_{uckGrade}<53:1.145+0.003\left|L_{uckGrade}-51\right|,53 \le L_{uckGrade}<54:1.151+0.002\left|L_{uckGrade}-53\right|,54 \le L_{uckGrade}<56:1.153+0.003\left|L_{uckGrade}-54\right|,56 \le L_{uckGrade}<57:1.159+0.002\left|L_{uckGrade}-56\right|,57 \le L_{uckGrade}<59:1.161+0.003\left|L_{uckGrade}-57\right|,59 \le L_{uckGrade}<60:1.167+0.002\left|L_{uckGrade}-59\right|,60 \le L_{uckGrade}<62:1.169+0.003\left|L_{uckGrade}-60\right|,62 \le L_{uckGrade}<63:1.175+0.002\left|L_{uckGrade}-62\right|,63 \le L_{uckGrade}<65:1.177+0.003\left|L_{uckGrade}-63\right|,65 \le L_{uckGrade}<66:1.183+0.002\left|L_{uckGrade}-65\right|,66 \le L_{uckGrade}<67:1.185+0.003\left|L_{uckGrade}-66\right|,67 \le L_{uckGrade}<68:1.188+0.002\left|L_{uckGrade}-67\right|,68 \le L_{uckGrade}<70:1.19+0.003\left|L_{uckGrade}-68\right|,70 \le L_{uckGrade}<71:1.196+0.002\left|L_{uckGrade}-70\right|,71 \le L_{uckGrade}<72:1.198+0.003\left|L_{uckGrade}-71\right|,72 \le L_{uckGrade}<73:1.201+0.002\left|L_{uckGrade}-72\right|,73 \le L_{uckGrade}<74:1.203+0.003\left|L_{uckGrade}-73\right|,74 \le L_{uckGrade}<75:1.206+0.002\left|L_{uckGrade}-74\right|,75 \le L_{uckGrade}<76:1.208+0.003\left|L_{uckGrade}-75\right|,76 \le L_{uckGrade}<77:1.211+0.002\left|L_{uckGrade}-76\right|,77 \le L_{uckGrade}<79:1.213+0.003\left|L_{uckGrade}-77\right|,79 \le L_{uckGrade}<80:1.219+0.002\left|L_{uckGrade}-79\right|,80 \le L_{uckGrade}<81:1.221+0.003\left|L_{uckGrade}-80\right|,81 \le L_{uckGrade}<82:1.224+0.002\left|L_{uckGrade}-81\right|,82 \le L_{uckGrade}<83:1.226+0.003\left|L_{uckGrade}-82\right|,83 \le L_{uckGrade}<84:1.229+0.002\left|L_{uckGrade}-83\right|,84 \le L_{uckGrade}<85:1.231+0.003\left|L_{uckGrade}-84\right|,85 \le L_{uckGrade}<86:1.234+0.002\left|L_{uckGrade}-85\right|,86 \le L_{uckGrade}<87:1.236+0.003\left|L_{uckGrade}-86\right|,87 \le L_{uckGrade}<88:1.239+0.002\left|L_{uckGrade}-87\right|,88 \le L_{uckGrade}<89:1.241+0.003\left|L_{uckGrade}-88\right|,89 \le L_{uckGrade}<91:1.244+0.002\left|L_{uckGrade}-89\right|,91 \le L_{uckGrade}<92:1.248+0.003\left|L_{uckGrade}-91\right|,92 \le L_{uckGrade}<93:1.251+0.002\left|L_{uckGrade}-92\right|,93 \le L_{uckGrade}<94:1.253+0.003\left|L_{uckGrade}-93\right|,94 \le L_{uckGrade}<95:1.256+0.002\left|L_{uckGrade}-94\right|,95 \le L_{uckGrade}<96:1.258+0.003\left|L_{uckGrade}-95\right|,96 \le L_{uckGrade}<98:1.261+0.002\left|L_{uckGrade}-96\right|,98 \le L_{uckGrade}<99:1.265+0.003\left|L_{uckGrade}-98\right|,99 \le L_{uckGrade}<100:1.268+0.002\left|L_{uckGrade}-99\right|,100 \le L_{uckGrade}<101:1.27+0.003\left|L_{uckGrade}-100\right|,101 \le L_{uckGrade}<103:1.273+0.002\left|L_{uckGrade}-101\right|,103 \le L_{uckGrade}<104:1.277+0.003\left|L_{uckGrade}-103\right|,104 \le L_{uckGrade}<105:1.28+0.002\left|L_{uckGrade}-104\right|,105 \le L_{uckGrade}<106:1.282+0.003\left|L_{uckGrade}-105\right|,106 \le L_{uckGrade}<108:1.285+0.002\left|L_{uckGrade}-106\right|,108 \le L_{uckGrade}<109:1.289+0.003\left|L_{uckGrade}-108\right|,109 \le L_{uckGrade}<111:1.292+0.002\left|L_{uckGrade}-109\right|,111 \le L_{uckGrade}<112:1.296+0.003\left|L_{uckGrade}-111\right|,112 \le L_{uckGrade}<114:1.299+0.002\left|L_{uckGrade}-112\right|,114 \le L_{uckGrade}<115:1.303+0.003\left|L_{uckGrade}-114\right|,115 \le L_{uckGrade}<117:1.306+0.002\left|L_{uckGrade}-115\right|,117 \le L_{uckGrade}<118:1.31+0.003\left|L_{uckGrade}-117\right|,118 \le L_{uckGrade}<121:1.313+0.002\left|L_{uckGrade}-118\right|,121 \le L_{uckGrade}<122:1.319+0.003\left|L_{uckGrade}-121\right|,122 \le L_{uckGrade}<124:1.322+0.002\left|L_{uckGrade}-122\right|,124 \le L_{uckGrade}<125:1.326+0.003\left|L_{uckGrade}-124\right|,125 \le L_{uckGrade}<129:1.329+0.002\left|L_{uckGrade}-125\right|,129 \le L_{uckGrade}<130:1.337+0.003\left|L_{uckGrade}-129\right|,130 \le L_{uckGrade}<133:1.34+0.002\left|L_{uckGrade}-130\right|,133 \le L_{uckGrade}<134:1.346+0.003\left|L_{uckGrade}-133\right|,134 \le L_{uckGrade}<139:1.349+0.002\left|L_{uckGrade}-134\right|,139 \le L_{uckGrade}<140:1.359+0.003\left|L_{uckGrade}-139\right|,140 \le L_{uckGrade}<146:1.362+0.002\left|L_{uckGrade}-140\right|,146 \le L_{uckGrade}<147:1.374+0.003\left|L_{uckGrade}-146\right|,147 \le L_{uckGrade}<156:1.377+0.002\left|L_{uckGrade}-147\right|,156 \le L_{uckGrade}<157:1.395+0.003\left|L_{uckGrade}-156\right|,157 \le L_{uckGrade}<177:1.398+0.002\left|L_{uckGrade}-157\right|,177 \le L_{uckGrade}<178:1.438+0.001\left|L_{uckGrade}-177\right|,178 \le L_{uckGrade}<188:1.439+0.002\left|L_{uckGrade}-178\right|,188 \le L_{uckGrade}<189:1.459+0.001\left|L_{uckGrade}-188\right|,189 \le L_{uckGrade}<195:1.46+0.002\left|L_{uckGrade}-189\right|,195 \le L_{uckGrade}<196:1.472+0.001\left|L_{uckGrade}-195\right|,196 \le L_{uckGrade}<200:1.473+0.002\left|L_{uckGrade}-196\right|,200 \le L_{uckGrade}<201:1.481+0.001\left|L_{uckGrade}-200\right|,201 \le L_{uckGrade}<205:1.482+0.002\left|L_{uckGrade}-201\right|,205 \le L_{uckGrade}<206:1.49+0.001\left|L_{uckGrade}-205\right|,206 \le L_{uckGrade}<209:1.491+0.002\left|L_{uckGrade}-206\right|,209 \le L_{uckGrade}<210:1.497+0.001\left|L_{uckGrade}-209\right|,210 \le L_{uckGrade}<213:1.498+0.002\left|L_{uckGrade}-210\right|,213 \le L_{uckGrade}<214:1.504+0.001\left|L_{uckGrade}-213\right|,214 \le L_{uckGrade}<216:1.505+0.002\left|L_{uckGrade}-214\right|,216 \le L_{uckGrade}<217:1.509+0.001\left|L_{uckGrade}-216\right|,217 \le L_{uckGrade}<219:1.51+0.002\left|L_{uckGrade}-217\right|,219 \le L_{uckGrade}<220:1.514+0.001\left|L_{uckGrade}-219\right|,220 \le L_{uckGrade}<222:1.515+0.002\left|L_{uckGrade}-220\right|,222 \le L_{uckGrade}<223:1.519+0.001\left|L_{uckGrade}-222\right|,223 \le L_{uckGrade}<225:1.52+0.002\left|L_{uckGrade}-223\right|,225 \le L_{uckGrade}<226:1.524+0.001\left|L_{uckGrade}-225\right|,226 \le L_{uckGrade}<228:1.525+0.002\left|L_{uckGrade}-226\right|,228 \le L_{uckGrade}<229:1.529+0.001\left|L_{uckGrade}-228\right|,229 \le L_{uckGrade}<231:1.53+0.002\left|L_{uckGrade}-229\right|,231 \le L_{uckGrade}<232:1.534+0.001\left|L_{uckGrade}-231\right|,232 \le L_{uckGrade}<233:1.535+0.002\left|L_{uckGrade}-232\right|,233 \le L_{uckGrade}<234:1.537+0.001\left|L_{uckGrade}-233\right|,234 \le L_{uckGrade}<236:1.538+0.002\left|L_{uckGrade}-234\right|,236 \le L_{uckGrade}<237:1.542+0.001\left|L_{uckGrade}-236\right|,237 \le L_{uckGrade}<238:1.543+0.002\left|L_{uckGrade}-237\right|,238 \le L_{uckGrade}<239:1.545+0.001\left|L_{uckGrade}-238\right|,239 \le L_{uckGrade}<240:1.546+0.002\left|L_{uckGrade}-239\right|,240 \le L_{uckGrade}<241:1.548+0.001\left|L_{uckGrade}-240\right|,241 \le L_{uckGrade}<243:1.549+0.002\left|L_{uckGrade}-241\right|,243 \le L_{uckGrade}<244:1.553+0.001\left|L_{uckGrade}-243\right|,244 \le L_{uckGrade}<245:1.554+0.002\left|L_{uckGrade}-244\right|,245 \le L_{uckGrade}<246:1.556+0.001\left|L_{uckGrade}-245\right|,246 \le L_{uckGrade}<247:1.557+0.002\left|L_{uckGrade}-246\right|,247 \le L_{uckGrade}<248:1.559+0.001\left|L_{uckGrade}-247\right|,248 \le L_{uckGrade}<249:1.56+0.002\left|L_{uckGrade}-248\right|,249 \le L_{uckGrade}<250:1.562+0.001\left|L_{uckGrade}-249\right|,250 \le L_{uckGrade}<251:1.563+0.002\left|L_{uckGrade}-250\right|,251 \le L_{uckGrade}<252:1.565+0.001\left|L_{uckGrade}-251\right|,252 \le L_{uckGrade}<253:1.566+0.002\left|L_{uckGrade}-252\right|,253 \le L_{uckGrade}<254:1.568+0.001\left|L_{uckGrade}-253\right|,254 \le L_{uckGrade}<255:1.569+0.002\left|L_{uckGrade}-254\right|,255 \le L_{uckGrade}<256:1.571+0.001\left|L_{uckGrade}-255\right|,256 \le L_{uckGrade}<257:1.572+0.002\left|L_{uckGrade}-256\right|,257 \le L_{uckGrade}<258:1.574+0.001\left|L_{uckGrade}-257\right|,258 \le L_{uckGrade}<259:1.575+0.002\left|L_{uckGrade}-258\right|,259 \le L_{uckGrade}<261:1.577+0.001\left|L_{uckGrade}-259\right|,261 \le L_{uckGrade}<262:1.579+0.002\left|L_{uckGrade}-261\right|,262 \le L_{uckGrade}<263:1.581+0.001\left|L_{uckGrade}-262\right|,263 \le L_{uckGrade}<264:1.582+0.002\left|L_{uckGrade}-263\right|,264 \le L_{uckGrade}<265:1.584+0.001\left|L_{uckGrade}-264\right|,265 \le L_{uckGrade}<266:1.585+0.002\left|L_{uckGrade}-265\right|,266 \le L_{uckGrade}<268:1.587+0.001\left|L_{uckGrade}-266\right|,268 \le L_{uckGrade}<269:1.589+0.002\left|L_{uckGrade}-268\right|,269 \le L_{uckGrade}<271:1.591+0.001\left|L_{uckGrade}-269\right|,271 \le L_{uckGrade}<272:1.593+0.002\left|L_{uckGrade}-271\right|,272 \le L_{uckGrade}<273:1.595+0.001\left|L_{uckGrade}-272\right|,273 \le L_{uckGrade}<274:1.596+0.002\left|L_{uckGrade}-273\right|,274 \le L_{uckGrade}<276:1.598+0.001\left|L_{uckGrade}-274\right|,276 \le L_{uckGrade}<277:1.6+0.002\left|L_{uckGrade}-276\right|,277 \le L_{uckGrade}<279:1.602+0.001\left|L_{uckGrade}-277\right|,279 \le L_{uckGrade}<280:1.604+0.002\left|L_{uckGrade}-279\right|,280 \le L_{uckGrade}<282:1.606+0.001\left|L_{uckGrade}-280\right|,282 \le L_{uckGrade}<283:1.608+0.002\left|L_{uckGrade}-282\right|,283 \le L_{uckGrade}<286:1.61+0.001\left|L_{uckGrade}-283\right|,286 \le L_{uckGrade}<287:1.613+0.002\left|L_{uckGrade}-286\right|,287 \le L_{uckGrade}<289:1.615+0.001\left|L_{uckGrade}-287\right|,289 \le L_{uckGrade}<290:1.617+0.002\left|L_{uckGrade}-289\right|,290 \le L_{uckGrade}<293:1.619+0.001\left|L_{uckGrade}-290\right|,293 \le L_{uckGrade}<294:1.622+0.002\left|L_{uckGrade}-293\right|,294 \le L_{uckGrade}<298:1.624+0.001\left|L_{uckGrade}-294\right|,298 \le L_{uckGrade}<299:1.628+0.002\left|L_{uckGrade}-298\right|,299 \le L_{uckGrade}<303:1.63+0.001\left|L_{uckGrade}-299\right|,303 \le L_{uckGrade}<304:1.634+0.002\left|L_{uckGrade}-303\right|,304 \le L_{uckGrade}<309:1.636+0.001\left|L_{uckGrade}-304\right|,309 \le L_{uckGrade}<310:1.641+0.002\left|L_{uckGrade}-309\right|,310 \le L_{uckGrade}<317:1.643+0.001\left|L_{uckGrade}-310\right|,317 \le L_{uckGrade}<318:1.65+0.002\left|L_{uckGrade}-317\right|,318 \le L_{uckGrade}<350:1.652+0.001\left|L_{uckGrade}-318\right|,350 \le L_{uckGrade}<351:1.684+0\left|L_{uckGrade}-350\right|,351 \le L_{uckGrade}<358:1.684+0.001\left|L_{uckGrade}-351\right|,358 \le L_{uckGrade}<359:1.691+0\left|L_{uckGrade}-358\right|,359 \le L_{uckGrade}<364:1.691+0.001\left|L_{uckGrade}-359\right|,364 \le L_{uckGrade}<365:1.696+0\left|L_{uckGrade}-364\right|,365 \le L_{uckGrade}<369:1.696+0.001\left|L_{uckGrade}-365\right|,369 \le L_{uckGrade}<370:1.7+0\left|L_{uckGrade}-369\right|,370 \le L_{uckGrade}<373:1.7+0.001\left|L_{uckGrade}-370\right|,373 \le L_{uckGrade}<374:1.703+0\left|L_{uckGrade}-373\right|,374 \le L_{uckGrade}<377:1.703+0.001\left|L_{uckGrade}-374\right|,377 \le L_{uckGrade}<378:1.706+0\left|L_{uckGrade}-377\right|,378 \le L_{uckGrade}<381:1.706+0.001\left|L_{uckGrade}-378\right|,381 \le L_{uckGrade}<382:1.709+0\left|L_{uckGrade}-381\right|,382 \le L_{uckGrade}<384:1.709+0.001\left|L_{uckGrade}-382\right|,384 \le L_{uckGrade}<385:1.711+0\left|L_{uckGrade}-384\right|,385 \le L_{uckGrade}<388:1.711+0.001\left|L_{uckGrade}-385\right|,388 \le L_{uckGrade}<389:1.714+0\left|L_{uckGrade}-388\right|,389 \le L_{uckGrade}<391:1.714+0.001\left|L_{uckGrade}-389\right|,391 \le L_{uckGrade}<392:1.716+0\left|L_{uckGrade}-391\right|,392 \le L_{uckGrade}<393:1.716+0.001\left|L_{uckGrade}-392\right|,393 \le L_{uckGrade}<394:1.717+0\left|L_{uckGrade}-393\right|,394 \le L_{uckGrade}<396:1.717+0.001\left|L_{uckGrade}-394\right|,396 \le L_{uckGrade}<397:1.719+0\left|L_{uckGrade}-396\right|,397 \le L_{uckGrade}<399:1.719+0.001\left|L_{uckGrade}-397\right|,399 \le L_{uckGrade}<400:1.721+0\left|L_{uckGrade}-399\right|,400 \le L_{uckGrade}<401:1.721+0.001\left|L_{uckGrade}-400\right|,401 \le L_{uckGrade}<402:1.722+0\left|L_{uckGrade}-401\right|,402 \le L_{uckGrade}<404:1.722+0.001\left|L_{uckGrade}-402\right|,404 \le L_{uckGrade}<405:1.724+0\left|L_{uckGrade}-404\right|,405 \le L_{uckGrade}<406:1.724+0.001\left|L_{uckGrade}-405\right|,406 \le L_{uckGrade}<407:1.725+0\left|L_{uckGrade}-406\right|,407 \le L_{uckGrade}<408:1.725+0.001\left|L_{uckGrade}-407\right|,408 \le L_{uckGrade}<409:1.726+0\left|L_{uckGrade}-408\right|,409 \le L_{uckGrade}<410:1.726+0.001\left|L_{uckGrade}-409\right|,410 \le L_{uckGrade}<411:1.727+0\left|L_{uckGrade}-410\right|,411 \le L_{uckGrade}<413:1.727+0.001\left|L_{uckGrade}-411\right|,413 \le L_{uckGrade}<414:1.729+0\left|L_{uckGrade}-413\right|,414 \le L_{uckGrade}<415:1.729+0.001\left|L_{uckGrade}-414\right|,415 \le L_{uckGrade}<416:1.73+0\left|L_{uckGrade}-415\right|,416 \le L_{uckGrade}<417:1.73+0.001\left|L_{uckGrade}-416\right|,417 \le L_{uckGrade}<418:1.731+0\left|L_{uckGrade}-417\right|,418 \le L_{uckGrade}<419:1.731+0.001\left|L_{uckGrade}-418\right|,419 \le L_{uckGrade}<420:1.732+0\left|L_{uckGrade}-419\right|,420 \le L_{uckGrade}<421:1.732+0.001\left|L_{uckGrade}-420\right|,421 \le L_{uckGrade}<423:1.733+0\left|L_{uckGrade}-421\right|,423 \le L_{uckGrade}<424:1.733+0.001\left|L_{uckGrade}-423\right|,424 \le L_{uckGrade}<425:1.734+0\left|L_{uckGrade}-424\right|,425 \le L_{uckGrade}<426:1.734+0.001\left|L_{uckGrade}-425\right|,426 \le L_{uckGrade}<427:1.735+0\left|L_{uckGrade}-426\right|,427 \le L_{uckGrade}<428:1.735+0.001\left|L_{uckGrade}-427\right|,428 \le L_{uckGrade}<429:1.736+0\left|L_{uckGrade}-428\right|,429 \le L_{uckGrade}<430:1.736+0.001\left|L_{uckGrade}-429\right|,430 \le L_{uckGrade}<432:1.737+0\left|L_{uckGrade}-430\right|,432 \le L_{uckGrade}<433:1.737+0.001\left|L_{uckGrade}-432\right|,433 \le L_{uckGrade}<434:1.738+0\left|L_{uckGrade}-433\right|,434 \le L_{uckGrade}<435:1.738+0.001\left|L_{uckGrade}-434\right|,435 \le L_{uckGrade}<437:1.739+0\left|L_{uckGrade}-435\right|,437 \le L_{uckGrade}<438:1.739+0.001\left|L_{uckGrade}-437\right|,438 \le L_{uckGrade}<439:1.74+0\left|L_{uckGrade}-438\right|,439 \le L_{uckGrade}<440:1.74+0.001\left|L_{uckGrade}-439\right|,440 \le L_{uckGrade}<442:1.741+0\left|L_{uckGrade}-440\right|,442 \le L_{uckGrade}<443:1.741+0.001\left|L_{uckGrade}-442\right|,443 \le L_{uckGrade}<445:1.742+0\left|L_{uckGrade}-443\right|,445 \le L_{uckGrade}<446:1.742+0.001\left|L_{uckGrade}-445\right|,446 \le L_{uckGrade}<448:1.743+0\left|L_{uckGrade}-446\right|,448 \le L_{uckGrade}<449:1.743+0.001\left|L_{uckGrade}-448\right|,449 \le L_{uckGrade}<452:1.744+0\left|L_{uckGrade}-449\right|,452 \le L_{uckGrade}<453:1.744+0.001\left|L_{uckGrade}-452\right|,453 \le L_{uckGrade}<455:1.745+0\left|L_{uckGrade}-453\right|,455 \le L_{uckGrade}<456:1.745+0.001\left|L_{uckGrade}-455\right|,456 \le L_{uckGrade}<459:1.746+0\left|L_{uckGrade}-456\right|,459 \le L_{uckGrade}<460:1.746+0.001\left|L_{uckGrade}-459\right|,460 \le L_{uckGrade}<463:1.747+0\left|L_{uckGrade}-460\right|,463 \le L_{uckGrade}<464:1.747+0.001\left|L_{uckGrade}-463\right|,464 \le L_{uckGrade}<468:1.748+0\left|L_{uckGrade}-464\right|,468 \le L_{uckGrade}<469:1.748+0.001\left|L_{uckGrade}-468\right|,469 \le L_{uckGrade}<474:1.749+0\left|L_{uckGrade}-469\right|,474 \le L_{uckGrade}<475:1.749+0.001\left|L_{uckGrade}-474\right|,475 \le L_{uckGrade}<482:1.75+0\left|L_{uckGrade}-475\right|,482 \le L_{uckGrade}<483:1.75+0.001\left|L_{uckGrade}-482\right|,483 \le L_{uckGrade}<499:1.751+0\left|L_{uckGrade}-483\right|,499 \le L_{uckGrade}<500:1.751+0.001\left|L_{uckGrade}-499\right|\right\}

See Example for how to use.

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_{uckGrade05}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<1:1+0.006\left|L_{uckGrade}-0\right|,1 \le L_{uckGrade}<2:1.006+0.007\left|L_{uckGrade}-1\right|,2 \le L_{uckGrade}<5:1.013+0.006\left|L_{uckGrade}-2\right|,5 \le L_{uckGrade}<6:1.031+0.007\left|L_{uckGrade}-5\right|,6 \le L_{uckGrade}<9:1.038+0.006\left|L_{uckGrade}-6\right|,9 \le L_{uckGrade}<10:1.056+0.007\left|L_{uckGrade}-9\right|,10 \le L_{uckGrade}<14:1.063+0.006\left|L_{uckGrade}-10\right|,14 \le L_{uckGrade}<15:1.087+0.007\left|L_{uckGrade}-14\right|,15 \le L_{uckGrade}<37:1.094+0.006\left|L_{uckGrade}-15\right|,37 \le L_{uckGrade}<38:1.226+0.005\left|L_{uckGrade}-37\right|,38 \le L_{uckGrade}<43:1.231+0.006\left|L_{uckGrade}-38\right|,43 \le L_{uckGrade}<44:1.261+0.005\left|L_{uckGrade}-43\right|,44 \le L_{uckGrade}<47:1.266+0.006\left|L_{uckGrade}-44\right|,47 \le L_{uckGrade}<48:1.284+0.005\left|L_{uckGrade}-47\right|,48 \le L_{uckGrade}<50:1.289+0.006\left|L_{uckGrade}-48\right|,50 \le L_{uckGrade}<51:1.301+0.005\left|L_{uckGrade}-50\right|,51 \le L_{uckGrade}<53:1.306+0.006\left|L_{uckGrade}-51\right|,53 \le L_{uckGrade}<54:1.318+0.005\left|L_{uckGrade}-53\right|,54 \le L_{uckGrade}<56:1.323+0.006\left|L_{uckGrade}-54\right|,56 \le L_{uckGrade}<57:1.335+0.005\left|L_{uckGrade}-56\right|,57 \le L_{uckGrade}<59:1.34+0.006\left|L_{uckGrade}-57\right|,59 \le L_{uckGrade}<60:1.352+0.005\left|L_{uckGrade}-59\right|,60 \le L_{uckGrade}<61:1.357+0.006\left|L_{uckGrade}-60\right|,61 \le L_{uckGrade}<62:1.363+0.005\left|L_{uckGrade}-61\right|,62 \le L_{uckGrade}<63:1.368+0.006\left|L_{uckGrade}-62\right|,63 \le L_{uckGrade}<64:1.374+0.005\left|L_{uckGrade}-63\right|,64 \le L_{uckGrade}<65:1.379+0.006\left|L_{uckGrade}-64\right|,65 \le L_{uckGrade}<66:1.385+0.005\left|L_{uckGrade}-65\right|,66 \le L_{uckGrade}<67:1.39+0.006\left|L_{uckGrade}-66\right|,67 \le L_{uckGrade}<68:1.396+0.005\left|L_{uckGrade}-67\right|,68 \le L_{uckGrade}<69:1.401+0.006\left|L_{uckGrade}-68\right|,69 \le L_{uckGrade}<70:1.407+0.005\left|L_{uckGrade}-69\right|,70 \le L_{uckGrade}<71:1.412+0.006\left|L_{uckGrade}-70\right|,71 \le L_{uckGrade}<73:1.418+0.005\left|L_{uckGrade}-71\right|,73 \le L_{uckGrade}<74:1.428+0.006\left|L_{uckGrade}-73\right|,74 \le L_{uckGrade}<75:1.434+0.005\left|L_{uckGrade}-74\right|,75 \le L_{uckGrade}<76:1.439+0.006\left|L_{uckGrade}-75\right|,76 \le L_{uckGrade}<78:1.445+0.005\left|L_{uckGrade}-76\right|,78 \le L_{uckGrade}<79:1.455+0.006\left|L_{uckGrade}-78\right|,79 \le L_{uckGrade}<81:1.461+0.005\left|L_{uckGrade}-79\right|,81 \le L_{uckGrade}<82:1.471+0.006\left|L_{uckGrade}-81\right|,82 \le L_{uckGrade}<85:1.477+0.005\left|L_{uckGrade}-82\right|,85 \le L_{uckGrade}<86:1.492+0.006\left|L_{uckGrade}-85\right|,86 \le L_{uckGrade}<89:1.498+0.005\left|L_{uckGrade}-86\right|,89 \le L_{uckGrade}<90:1.513+0.006\left|L_{uckGrade}-89\right|,90 \le L_{uckGrade}<95:1.519+0.005\left|L_{uckGrade}-90\right|,95 \le L_{uckGrade}<96:1.544+0.006\left|L_{uckGrade}-95\right|,96 \le L_{uckGrade}<114:1.55+0.005\left|L_{uckGrade}-96\right|,114 \le L_{uckGrade}<115:1.64+0.004\left|L_{uckGrade}-114\right|,115 \le L_{uckGrade}<120:1.644+0.005\left|L_{uckGrade}-115\right|,120 \le L_{uckGrade}<121:1.669+0.004\left|L_{uckGrade}-120\right|,121 \le L_{uckGrade}<125:1.673+0.005\left|L_{uckGrade}-121\right|,125 \le L_{uckGrade}<126:1.693+0.004\left|L_{uckGrade}-125\right|,126 \le L_{uckGrade}<128:1.697+0.005\left|L_{uckGrade}-126\right|,128 \le L_{uckGrade}<129:1.707+0.004\left|L_{uckGrade}-128\right|,129 \le L_{uckGrade}<132:1.711+0.005\left|L_{uckGrade}-129\right|,132 \le L_{uckGrade}<133:1.726+0.004\left|L_{uckGrade}-132\right|,133 \le L_{uckGrade}<134:1.73+0.005\left|L_{uckGrade}-133\right|,134 \le L_{uckGrade}<135:1.735+0.004\left|L_{uckGrade}-134\right|,135 \le L_{uckGrade}<137:1.739+0.005\left|L_{uckGrade}-135\right|,137 \le L_{uckGrade}<138:1.749+0.004\left|L_{uckGrade}-137\right|,138 \le L_{uckGrade}<139:1.753+0.005\left|L_{uckGrade}-138\right|,139 \le L_{uckGrade}<140:1.758+0.004\left|L_{uckGrade}-139\right|,140 \le L_{uckGrade}<142:1.762+0.005\left|L_{uckGrade}-140\right|,142 \le L_{uckGrade}<143:1.772+0.004\left|L_{uckGrade}-142\right|,143 \le L_{uckGrade}<144:1.776+0.005\left|L_{uckGrade}-143\right|,144 \le L_{uckGrade}<145:1.781+0.004\left|L_{uckGrade}-144\right|,145 \le L_{uckGrade}<146:1.785+0.005\left|L_{uckGrade}-145\right|,146 \le L_{uckGrade}<148:1.79+0.004\left|L_{uckGrade}-146\right|,148 \le L_{uckGrade}<149:1.798+0.005\left|L_{uckGrade}-148\right|,149 \le L_{uckGrade}<150:1.803+0.004\left|L_{uckGrade}-149\right|,150 \le L_{uckGrade}<151:1.807+0.005\left|L_{uckGrade}-150\right|,151 \le L_{uckGrade}<152:1.812+0.004\left|L_{uckGrade}-151\right|,152 \le L_{uckGrade}<153:1.816+0.005\left|L_{uckGrade}-152\right|,153 \le L_{uckGrade}<155:1.821+0.004\left|L_{uckGrade}-153\right|,155 \le L_{uckGrade}<156:1.829+0.005\left|L_{uckGrade}-155\right|,156 \le L_{uckGrade}<158:1.834+0.004\left|L_{uckGrade}-156\right|,158 \le L_{uckGrade}<159:1.842+0.005\left|L_{uckGrade}-158\right|,159 \le L_{uckGrade}<161:1.847+0.004\left|L_{uckGrade}-159\right|,161 \le L_{uckGrade}<162:1.855+0.005\left|L_{uckGrade}-161\right|,162 \le L_{uckGrade}<165:1.86+0.004\left|L_{uckGrade}-162\right|,165 \le L_{uckGrade}<166:1.872+0.005\left|L_{uckGrade}-165\right|,166 \le L_{uckGrade}<169:1.877+0.004\left|L_{uckGrade}-166\right|,169 \le L_{uckGrade}<170:1.889+0.005\left|L_{uckGrade}-169\right|,170 \le L_{uckGrade}<177:1.894+0.004\left|L_{uckGrade}-170\right|,177 \le L_{uckGrade}<178:1.922+0.005\left|L_{uckGrade}-177\right|,178 \le L_{uckGrade}<191:1.927+0.004\left|L_{uckGrade}-178\right|,191 \le L_{uckGrade}<192:1.979+0.003\left|L_{uckGrade}-191\right|,192 \le L_{uckGrade}<198:1.982+0.004\left|L_{uckGrade}-192\right|,198 \le L_{uckGrade}<199:2.006+0.003\left|L_{uckGrade}-198\right|,199 \le L_{uckGrade}<203:2.009+0.004\left|L_{uckGrade}-199\right|,203 \le L_{uckGrade}<204:2.025+0.003\left|L_{uckGrade}-203\right|,204 \le L_{uckGrade}<207:2.028+0.004\left|L_{uckGrade}-204\right|,207 \le L_{uckGrade}<208:2.04+0.003\left|L_{uckGrade}-207\right|,208 \le L_{uckGrade}<210:2.043+0.004\left|L_{uckGrade}-208\right|,210 \le L_{uckGrade}<211:2.051+0.003\left|L_{uckGrade}-210\right|,211 \le L_{uckGrade}<213:2.054+0.004\left|L_{uckGrade}-211\right|,213 \le L_{uckGrade}<214:2.062+0.003\left|L_{uckGrade}-213\right|,214 \le L_{uckGrade}<215:2.065+0.004\left|L_{uckGrade}-214\right|,215 \le L_{uckGrade}<216:2.069+0.003\left|L_{uckGrade}-215\right|,216 \le L_{uckGrade}<218:2.072+0.004\left|L_{uckGrade}-216\right|,218 \le L_{uckGrade}<219:2.08+0.003\left|L_{uckGrade}-218\right|,219 \le L_{uckGrade}<220:2.083+0.004\left|L_{uckGrade}-219\right|,220 \le L_{uckGrade}<221:2.087+0.003\left|L_{uckGrade}-220\right|,221 \le L_{uckGrade}<222:2.09+0.004\left|L_{uckGrade}-221\right|,222 \le L_{uckGrade}<223:2.094+0.003\left|L_{uckGrade}-222\right|,223 \le L_{uckGrade}<224:2.097+0.004\left|L_{uckGrade}-223\right|,224 \le L_{uckGrade}<225:2.101+0.003\left|L_{uckGrade}-224\right|,225 \le L_{uckGrade}<226:2.104+0.004\left|L_{uckGrade}-225\right|,226 \le L_{uckGrade}<227:2.108+0.003\left|L_{uckGrade}-226\right|,227 \le L_{uckGrade}<228:2.111+0.004\left|L_{uckGrade}-227\right|,228 \le L_{uckGrade}<229:2.115+0.003\left|L_{uckGrade}-228\right|,229 \le L_{uckGrade}<230:2.118+0.004\left|L_{uckGrade}-229\right|,230 \le L_{uckGrade}<232:2.122+0.003\left|L_{uckGrade}-230\right|,232 \le L_{uckGrade}<233:2.128+0.004\left|L_{uckGrade}-232\right|,233 \le L_{uckGrade}<234:2.132+0.003\left|L_{uckGrade}-233\right|,234 \le L_{uckGrade}<235:2.135+0.004\left|L_{uckGrade}-234\right|,235 \le L_{uckGrade}<237:2.139+0.003\left|L_{uckGrade}-235\right|,237 \le L_{uckGrade}<238:2.145+0.004\left|L_{uckGrade}-237\right|,238 \le L_{uckGrade}<241:2.149+0.003\left|L_{uckGrade}-238\right|,241 \le L_{uckGrade}<242:2.158+0.004\left|L_{uckGrade}-241\right|,242 \le L_{uckGrade}<244:2.162+0.003\left|L_{uckGrade}-242\right|,244 \le L_{uckGrade}<245:2.168+0.004\left|L_{uckGrade}-244\right|,245 \le L_{uckGrade}<249:2.172+0.003\left|L_{uckGrade}-245\right|,249 \le L_{uckGrade}<250:2.184+0.004\left|L_{uckGrade}-249\right|,250 \le L_{uckGrade}<258:2.188+0.003\left|L_{uckGrade}-250\right|,258 \le L_{uckGrade}<259:2.212+0.004\left|L_{uckGrade}-258\right|,259 \le L_{uckGrade}<268:2.216+0.003\left|L_{uckGrade}-259\right|,268 \le L_{uckGrade}<269:2.243+0.002\left|L_{uckGrade}-268\right|,269 \le L_{uckGrade}<276:2.245+0.003\left|L_{uckGrade}-269\right|,276 \le L_{uckGrade}<277:2.266+0.002\left|L_{uckGrade}-276\right|,277 \le L_{uckGrade}<281:2.268+0.003\left|L_{uckGrade}-277\right|,281 \le L_{uckGrade}<282:2.28+0.002\left|L_{uckGrade}-281\right|,282 \le L_{uckGrade}<285:2.282+0.003\left|L_{uckGrade}-282\right|,285 \le L_{uckGrade}<286:2.291+0.002\left|L_{uckGrade}-285\right|,286 \le L_{uckGrade}<288:2.293+0.003\left|L_{uckGrade}-286\right|,288 \le L_{uckGrade}<289:2.299+0.002\left|L_{uckGrade}-288\right|,289 \le L_{uckGrade}<291:2.301+0.003\left|L_{uckGrade}-289\right|,291 \le L_{uckGrade}<292:2.307+0.002\left|L_{uckGrade}-291\right|,292 \le L_{uckGrade}<294:2.309+0.003\left|L_{uckGrade}-292\right|,294 \le L_{uckGrade}<295:2.315+0.002\left|L_{uckGrade}-294\right|,295 \le L_{uckGrade}<296:2.317+0.003\left|L_{uckGrade}-295\right|,296 \le L_{uckGrade}<297:2.32+0.002\left|L_{uckGrade}-296\right|,297 \le L_{uckGrade}<299:2.322+0.003\left|L_{uckGrade}-297\right|,299 \le L_{uckGrade}<300:2.328+0.002\left|L_{uckGrade}-299\right|,300 \le L_{uckGrade}<301:2.33+0.003\left|L_{uckGrade}-300\right|,301 \le L_{uckGrade}<302:2.333+0.002\left|L_{uckGrade}-301\right|,302 \le L_{uckGrade}<303:2.335+0.003\left|L_{uckGrade}-302\right|,303 \le L_{uckGrade}<304:2.338+0.002\left|L_{uckGrade}-303\right|,304 \le L_{uckGrade}<305:2.34+0.003\left|L_{uckGrade}-304\right|,305 \le L_{uckGrade}<306:2.343+0.002\left|L_{uckGrade}-305\right|,306 \le L_{uckGrade}<307:2.345+0.003\left|L_{uckGrade}-306\right|,307 \le L_{uckGrade}<309:2.348+0.002\left|L_{uckGrade}-307\right|,309 \le L_{uckGrade}<310:2.352+0.003\left|L_{uckGrade}-309\right|,310 \le L_{uckGrade}<311:2.355+0.002\left|L_{uckGrade}-310\right|,311 \le L_{uckGrade}<312:2.357+0.003\left|L_{uckGrade}-311\right|,312 \le L_{uckGrade}<314:2.36+0.002\left|L_{uckGrade}-312\right|,314 \le L_{uckGrade}<315:2.364+0.003\left|L_{uckGrade}-314\right|,315 \le L_{uckGrade}<317:2.367+0.002\left|L_{uckGrade}-315\right|,317 \le L_{uckGrade}<318:2.371+0.003\left|L_{uckGrade}-317\right|,318 \le L_{uckGrade}<320:2.374+0.002\left|L_{uckGrade}-318\right|,320 \le L_{uckGrade}<321:2.378+0.003\left|L_{uckGrade}-320\right|,321 \le L_{uckGrade}<324:2.381+0.002\left|L_{uckGrade}-321\right|,324 \le L_{uckGrade}<325:2.387+0.003\left|L_{uckGrade}-324\right|,325 \le L_{uckGrade}<329:2.39+0.002\left|L_{uckGrade}-325\right|,329 \le L_{uckGrade}<330:2.398+0.003\left|L_{uckGrade}-329\right|,330 \le L_{uckGrade}<340:2.401+0.002\left|L_{uckGrade}-330\right|,340 \le L_{uckGrade}<341:2.421+0.003\left|L_{uckGrade}-340\right|,341 \le L_{uckGrade}<344:2.424+0.002\left|L_{uckGrade}-341\right|,344 \le L_{uckGrade}<345:2.43+0.001\left|L_{uckGrade}-344\right|,345 \le L_{uckGrade}<355:2.431+0.002\left|L_{uckGrade}-345\right|,355 \le L_{uckGrade}<356:2.451+0.001\left|L_{uckGrade}-355\right|,356 \le L_{uckGrade}<360:2.452+0.002\left|L_{uckGrade}-356\right|,360 \le L_{uckGrade}<361:2.46+0.001\left|L_{uckGrade}-360\right|,361 \le L_{uckGrade}<364:2.461+0.002\left|L_{uckGrade}-361\right|,364 \le L_{uckGrade}<365:2.467+0.001\left|L_{uckGrade}-364\right|,365 \le L_{uckGrade}<367:2.468+0.002\left|L_{uckGrade}-365\right|,367 \le L_{uckGrade}<368:2.472+0.001\left|L_{uckGrade}-367\right|,368 \le L_{uckGrade}<370:2.473+0.002\left|L_{uckGrade}-368\right|,370 \le L_{uckGrade}<371:2.477+0.001\left|L_{uckGrade}-370\right|,371 \le L_{uckGrade}<373:2.478+0.002\left|L_{uckGrade}-371\right|,373 \le L_{uckGrade}<374:2.482+0.001\left|L_{uckGrade}-373\right|,374 \le L_{uckGrade}<375:2.483+0.002\left|L_{uckGrade}-374\right|,375 \le L_{uckGrade}<376:2.485+0.001\left|L_{uckGrade}-375\right|,376 \le L_{uckGrade}<377:2.486+0.002\left|L_{uckGrade}-376\right|,377 \le L_{uckGrade}<378:2.488+0.001\left|L_{uckGrade}-377\right|,378 \le L_{uckGrade}<380:2.489+0.002\left|L_{uckGrade}-378\right|,380 \le L_{uckGrade}<381:2.493+0.001\left|L_{uckGrade}-380\right|,381 \le L_{uckGrade}<382:2.494+0.002\left|L_{uckGrade}-381\right|,382 \le L_{uckGrade}<383:2.496+0.001\left|L_{uckGrade}-382\right|,383 \le L_{uckGrade}<384:2.497+0.002\left|L_{uckGrade}-383\right|,384 \le L_{uckGrade}<386:2.499+0.001\left|L_{uckGrade}-384\right|,386 \le L_{uckGrade}<387:2.501+0.002\left|L_{uckGrade}-386\right|,387 \le L_{uckGrade}<388:2.503+0.001\left|L_{uckGrade}-387\right|,388 \le L_{uckGrade}<389:2.504+0.002\left|L_{uckGrade}-388\right|,389 \le L_{uckGrade}<390:2.506+0.001\left|L_{uckGrade}-389\right|,390 \le L_{uckGrade}<391:2.507+0.002\left|L_{uckGrade}-390\right|,391 \le L_{uckGrade}<393:2.509+0.001\left|L_{uckGrade}-391\right|,393 \le L_{uckGrade}<394:2.511+0.002\left|L_{uckGrade}-393\right|,394 \le L_{uckGrade}<396:2.513+0.001\left|L_{uckGrade}-394\right|,396 \le L_{uckGrade}<397:2.515+0.002\left|L_{uckGrade}-396\right|,397 \le L_{uckGrade}<399:2.517+0.001\left|L_{uckGrade}-397\right|,399 \le L_{uckGrade}<400:2.519+0.002\left|L_{uckGrade}-399\right|,400 \le L_{uckGrade}<403:2.521+0.001\left|L_{uckGrade}-400\right|,403 \le L_{uckGrade}<404:2.524+0.002\left|L_{uckGrade}-403\right|,404 \le L_{uckGrade}<409:2.526+0.001\left|L_{uckGrade}-404\right|,409 \le L_{uckGrade}<410:2.531+0.002\left|L_{uckGrade}-409\right|,410 \le L_{uckGrade}<433:2.533+0.001\left|L_{uckGrade}-410\right|,433 \le L_{uckGrade}<434:2.556+0\left|L_{uckGrade}-433\right|,434 \le L_{uckGrade}<438:2.556+0.001\left|L_{uckGrade}-434\right|,438 \le L_{uckGrade}<439:2.56+0\left|L_{uckGrade}-438\right|,439 \le L_{uckGrade}<443:2.56+0.001\left|L_{uckGrade}-439\right|,443 \le L_{uckGrade}<444:2.564+0\left|L_{uckGrade}-443\right|,444 \le L_{uckGrade}<446:2.564+0.001\left|L_{uckGrade}-444\right|,446 \le L_{uckGrade}<447:2.566+0\left|L_{uckGrade}-446\right|,447 \le L_{uckGrade}<449:2.566+0.001\left|L_{uckGrade}-447\right|,449 \le L_{uckGrade}<450:2.568+0\left|L_{uckGrade}-449\right|,450 \le L_{uckGrade}<452:2.568+0.001\left|L_{uckGrade}-450\right|,452 \le L_{uckGrade}<453:2.57+0\left|L_{uckGrade}-452\right|,453 \le L_{uckGrade}<454:2.57+0.001\left|L_{uckGrade}-453\right|,454 \le L_{uckGrade}<455:2.571+0\left|L_{uckGrade}-454\right|,455 \le L_{uckGrade}<456:2.571+0.001\left|L_{uckGrade}-455\right|,456 \le L_{uckGrade}<457:2.572+0\left|L_{uckGrade}-456\right|,457 \le L_{uckGrade}<459:2.572+0.001\left|L_{uckGrade}-457\right|,459 \le L_{uckGrade}<460:2.574+0\left|L_{uckGrade}-459\right|,460 \le L_{uckGrade}<461:2.574+0.001\left|L_{uckGrade}-460\right|,461 \le L_{uckGrade}<462:2.575+0\left|L_{uckGrade}-461\right|,462 \le L_{uckGrade}<463:2.575+0.001\left|L_{uckGrade}-462\right|,463 \le L_{uckGrade}<465:2.576+0\left|L_{uckGrade}-463\right|,465 \le L_{uckGrade}<466:2.576+0.001\left|L_{uckGrade}-465\right|,466 \le L_{uckGrade}<467:2.577+0\left|L_{uckGrade}-466\right|,467 \le L_{uckGrade}<468:2.577+0.001\left|L_{uckGrade}-467\right|,468 \le L_{uckGrade}<469:2.578+0\left|L_{uckGrade}-468\right|,469 \le L_{uckGrade}<470:2.578+0.001\left|L_{uckGrade}-469\right|,470 \le L_{uckGrade}<472:2.579+0\left|L_{uckGrade}-470\right|,472 \le L_{uckGrade}<473:2.579+0.001\left|L_{uckGrade}-472\right|,473 \le L_{uckGrade}<475:2.58+0\left|L_{uckGrade}-473\right|,475 \le L_{uckGrade}<476:2.58+0.001\left|L_{uckGrade}-475\right|,476 \le L_{uckGrade}<479:2.581+0\left|L_{uckGrade}-476\right|,479 \le L_{uckGrade}<480:2.581+0.001\left|L_{uckGrade}-479\right|,480 \le L_{uckGrade}<483:2.582+0\left|L_{uckGrade}-480\right|,483 \le L_{uckGrade}<484:2.582+0.001\left|L_{uckGrade}-483\right|,484 \le L_{uckGrade}<488:2.583+0\left|L_{uckGrade}-484\right|,488 \le L_{uckGrade}<489:2.583+0.001\left|L_{uckGrade}-488\right|,489 \le L_{uckGrade}<500:2.584+0\left|L_{uckGrade}-489\right|\right\}

See Example for how to use.

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_{uckGrade06}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<15:1+0.009\left|L_{uckGrade}-0\right|,15 \le L_{uckGrade}<16:1.135+0.008\left|L_{uckGrade}-15\right|,16 \le L_{uckGrade}<20:1.143+0.009\left|L_{uckGrade}-16\right|,20 \le L_{uckGrade}<21:1.179+0.008\left|L_{uckGrade}-20\right|,21 \le L_{uckGrade}<23:1.187+0.009\left|L_{uckGrade}-21\right|,23 \le L_{uckGrade}<24:1.205+0.008\left|L_{uckGrade}-23\right|,24 \le L_{uckGrade}<26:1.213+0.009\left|L_{uckGrade}-24\right|,26 \le L_{uckGrade}<27:1.231+0.008\left|L_{uckGrade}-26\right|,27 \le L_{uckGrade}<29:1.239+0.009\left|L_{uckGrade}-27\right|,29 \le L_{uckGrade}<30:1.257+0.008\left|L_{uckGrade}-29\right|,30 \le L_{uckGrade}<31:1.265+0.009\left|L_{uckGrade}-30\right|,31 \le L_{uckGrade}<32:1.274+0.008\left|L_{uckGrade}-31\right|,32 \le L_{uckGrade}<33:1.282+0.009\left|L_{uckGrade}-32\right|,33 \le L_{uckGrade}<34:1.291+0.008\left|L_{uckGrade}-33\right|,34 \le L_{uckGrade}<35:1.299+0.009\left|L_{uckGrade}-34\right|,35 \le L_{uckGrade}<36:1.308+0.008\left|L_{uckGrade}-35\right|,36 \le L_{uckGrade}<37:1.316+0.009\left|L_{uckGrade}-36\right|,37 \le L_{uckGrade}<39:1.325+0.008\left|L_{uckGrade}-37\right|,39 \le L_{uckGrade}<40:1.341+0.009\left|L_{uckGrade}-39\right|,40 \le L_{uckGrade}<41:1.35+0.008\left|L_{uckGrade}-40\right|,41 \le L_{uckGrade}<42:1.358+0.009\left|L_{uckGrade}-41\right|,42 \le L_{uckGrade}<45:1.367+0.008\left|L_{uckGrade}-42\right|,45 \le L_{uckGrade}<46:1.391+0.009\left|L_{uckGrade}-45\right|,46 \le L_{uckGrade}<49:1.4+0.008\left|L_{uckGrade}-46\right|,49 \le L_{uckGrade}<50:1.424+0.009\left|L_{uckGrade}-49\right|,50 \le L_{uckGrade}<55:1.433+0.008\left|L_{uckGrade}-50\right|,55 \le L_{uckGrade}<56:1.473+0.009\left|L_{uckGrade}-55\right|,56 \le L_{uckGrade}<66:1.482+0.008\left|L_{uckGrade}-56\right|,66 \le L_{uckGrade}<67:1.562+0.007\left|L_{uckGrade}-66\right|,67 \le L_{uckGrade}<72:1.569+0.008\left|L_{uckGrade}-67\right|,72 \le L_{uckGrade}<73:1.609+0.007\left|L_{uckGrade}-72\right|,73 \le L_{uckGrade}<76:1.616+0.008\left|L_{uckGrade}-73\right|,76 \le L_{uckGrade}<77:1.64+0.007\left|L_{uckGrade}-76\right|,77 \le L_{uckGrade}<79:1.647+0.008\left|L_{uckGrade}-77\right|,79 \le L_{uckGrade}<80:1.663+0.007\left|L_{uckGrade}-79\right|,80 \le L_{uckGrade}<82:1.67+0.008\left|L_{uckGrade}-80\right|,82 \le L_{uckGrade}<83:1.686+0.007\left|L_{uckGrade}-82\right|,83 \le L_{uckGrade}<85:1.693+0.008\left|L_{uckGrade}-83\right|,85 \le L_{uckGrade}<86:1.709+0.007\left|L_{uckGrade}-85\right|,86 \le L_{uckGrade}<87:1.716+0.008\left|L_{uckGrade}-86\right|,87 \le L_{uckGrade}<88:1.724+0.007\left|L_{uckGrade}-87\right|,88 \le L_{uckGrade}<89:1.731+0.008\left|L_{uckGrade}-88\right|,89 \le L_{uckGrade}<90:1.739+0.007\left|L_{uckGrade}-89\right|,90 \le L_{uckGrade}<91:1.746+0.008\left|L_{uckGrade}-90\right|,91 \le L_{uckGrade}<93:1.754+0.007\left|L_{uckGrade}-91\right|,93 \le L_{uckGrade}<94:1.768+0.008\left|L_{uckGrade}-93\right|,94 \le L_{uckGrade}<95:1.776+0.007\left|L_{uckGrade}-94\right|,95 \le L_{uckGrade}<96:1.783+0.008\left|L_{uckGrade}-95\right|,96 \le L_{uckGrade}<98:1.791+0.007\left|L_{uckGrade}-96\right|,98 \le L_{uckGrade}<99:1.805+0.008\left|L_{uckGrade}-98\right|,99 \le L_{uckGrade}<102:1.813+0.007\left|L_{uckGrade}-99\right|,102 \le L_{uckGrade}<103:1.834+0.008\left|L_{uckGrade}-102\right|,103 \le L_{uckGrade}<107:1.842+0.007\left|L_{uckGrade}-103\right|,107 \le L_{uckGrade}<108:1.87+0.008\left|L_{uckGrade}-107\right|,108 \le L_{uckGrade}<124:1.878+0.007\left|L_{uckGrade}-108\right|,124 \le L_{uckGrade}<125:1.99+0.006\left|L_{uckGrade}-124\right|,125 \le L_{uckGrade}<129:1.996+0.007\left|L_{uckGrade}-125\right|,129 \le L_{uckGrade}<130:2.024+0.006\left|L_{uckGrade}-129\right|,130 \le L_{uckGrade}<133:2.03+0.007\left|L_{uckGrade}-130\right|,133 \le L_{uckGrade}<134:2.051+0.006\left|L_{uckGrade}-133\right|,134 \le L_{uckGrade}<136:2.057+0.007\left|L_{uckGrade}-134\right|,136 \le L_{uckGrade}<137:2.071+0.006\left|L_{uckGrade}-136\right|,137 \le L_{uckGrade}<138:2.077+0.007\left|L_{uckGrade}-137\right|,138 \le L_{uckGrade}<139:2.084+0.006\left|L_{uckGrade}-138\right|,139 \le L_{uckGrade}<140:2.09+0.007\left|L_{uckGrade}-139\right|,140 \le L_{uckGrade}<141:2.097+0.006\left|L_{uckGrade}-140\right|,141 \le L_{uckGrade}<143:2.103+0.007\left|L_{uckGrade}-141\right|,143 \le L_{uckGrade}<145:2.117+0.006\left|L_{uckGrade}-143\right|,145 \le L_{uckGrade}<146:2.129+0.007\left|L_{uckGrade}-145\right|,146 \le L_{uckGrade}<147:2.136+0.006\left|L_{uckGrade}-146\right|,147 \le L_{uckGrade}<148:2.142+0.007\left|L_{uckGrade}-147\right|,148 \le L_{uckGrade}<149:2.149+0.006\left|L_{uckGrade}-148\right|,149 \le L_{uckGrade}<150:2.155+0.007\left|L_{uckGrade}-149\right|,150 \le L_{uckGrade}<152:2.162+0.006\left|L_{uckGrade}-150\right|,152 \le L_{uckGrade}<153:2.174+0.007\left|L_{uckGrade}-152\right|,153 \le L_{uckGrade}<155:2.181+0.006\left|L_{uckGrade}-153\right|,155 \le L_{uckGrade}<156:2.193+0.007\left|L_{uckGrade}-155\right|,156 \le L_{uckGrade}<160:2.2+0.006\left|L_{uckGrade}-156\right|,160 \le L_{uckGrade}<161:2.224+0.007\left|L_{uckGrade}-160\right|,161 \le L_{uckGrade}<168:2.231+0.006\left|L_{uckGrade}-161\right|,168 \le L_{uckGrade}<169:2.273+0.007\left|L_{uckGrade}-168\right|,169 \le L_{uckGrade}<173:2.28+0.006\left|L_{uckGrade}-169\right|,173 \le L_{uckGrade}<174:2.304+0.005\left|L_{uckGrade}-173\right|,174 \le L_{uckGrade}<181:2.309+0.006\left|L_{uckGrade}-174\right|,181 \le L_{uckGrade}<182:2.351+0.005\left|L_{uckGrade}-181\right|,182 \le L_{uckGrade}<185:2.356+0.006\left|L_{uckGrade}-182\right|,185 \le L_{uckGrade}<186:2.374+0.005\left|L_{uckGrade}-185\right|,186 \le L_{uckGrade}<189:2.379+0.006\left|L_{uckGrade}-186\right|,189 \le L_{uckGrade}<190:2.397+0.005\left|L_{uckGrade}-189\right|,190 \le L_{uckGrade}<191:2.402+0.006\left|L_{uckGrade}-190\right|,191 \le L_{uckGrade}<192:2.408+0.005\left|L_{uckGrade}-191\right|,192 \le L_{uckGrade}<194:2.413+0.006\left|L_{uckGrade}-192\right|,194 \le L_{uckGrade}<195:2.425+0.005\left|L_{uckGrade}-194\right|,195 \le L_{uckGrade}<196:2.43+0.006\left|L_{uckGrade}-195\right|,196 \le L_{uckGrade}<197:2.436+0.005\left|L_{uckGrade}-196\right|,197 \le L_{uckGrade}<198:2.441+0.006\left|L_{uckGrade}-197\right|,198 \le L_{uckGrade}<199:2.447+0.005\left|L_{uckGrade}-198\right|,199 \le L_{uckGrade}<200:2.452+0.006\left|L_{uckGrade}-199\right|,200 \le L_{uckGrade}<201:2.458+0.005\left|L_{uckGrade}-200\right|,201 \le L_{uckGrade}<202:2.463+0.006\left|L_{uckGrade}-201\right|,202 \le L_{uckGrade}<203:2.469+0.005\left|L_{uckGrade}-202\right|,203 \le L_{uckGrade}<204:2.474+0.006\left|L_{uckGrade}-203\right|,204 \le L_{uckGrade}<206:2.48+0.005\left|L_{uckGrade}-204\right|,206 \le L_{uckGrade}<207:2.49+0.006\left|L_{uckGrade}-206\right|,207 \le L_{uckGrade}<209:2.496+0.005\left|L_{uckGrade}-207\right|,209 \le L_{uckGrade}<210:2.506+0.006\left|L_{uckGrade}-209\right|,210 \le L_{uckGrade}<213:2.512+0.005\left|L_{uckGrade}-210\right|,213 \le L_{uckGrade}<214:2.527+0.006\left|L_{uckGrade}-213\right|,214 \le L_{uckGrade}<219:2.533+0.005\left|L_{uckGrade}-214\right|,219 \le L_{uckGrade}<220:2.558+0.006\left|L_{uckGrade}-219\right|,220 \le L_{uckGrade}<232:2.564+0.005\left|L_{uckGrade}-220\right|,232 \le L_{uckGrade}<233:2.624+0.004\left|L_{uckGrade}-232\right|,233 \le L_{uckGrade}<238:2.628+0.005\left|L_{uckGrade}-233\right|,238 \le L_{uckGrade}<239:2.653+0.004\left|L_{uckGrade}-238\right|,239 \le L_{uckGrade}<241:2.657+0.005\left|L_{uckGrade}-239\right|,241 \le L_{uckGrade}<242:2.667+0.004\left|L_{uckGrade}-241\right|,242 \le L_{uckGrade}<245:2.671+0.005\left|L_{uckGrade}-242\right|,245 \le L_{uckGrade}<246:2.686+0.004\left|L_{uckGrade}-245\right|,246 \le L_{uckGrade}<247:2.69+0.005\left|L_{uckGrade}-246\right|,247 \le L_{uckGrade}<248:2.695+0.004\left|L_{uckGrade}-247\right|,248 \le L_{uckGrade}<250:2.699+0.005\left|L_{uckGrade}-248\right|,250 \le L_{uckGrade}<251:2.709+0.004\left|L_{uckGrade}-250\right|,251 \le L_{uckGrade}<252:2.713+0.005\left|L_{uckGrade}-251\right|,252 \le L_{uckGrade}<253:2.718+0.004\left|L_{uckGrade}-252\right|,253 \le L_{uckGrade}<254:2.722+0.005\left|L_{uckGrade}-253\right|,254 \le L_{uckGrade}<255:2.727+0.004\left|L_{uckGrade}-254\right|,255 \le L_{uckGrade}<256:2.731+0.005\left|L_{uckGrade}-255\right|,256 \le L_{uckGrade}<258:2.736+0.004\left|L_{uckGrade}-256\right|,258 \le L_{uckGrade}<259:2.744+0.005\left|L_{uckGrade}-258\right|,259 \le L_{uckGrade}<260:2.749+0.004\left|L_{uckGrade}-259\right|,260 \le L_{uckGrade}<261:2.753+0.005\left|L_{uckGrade}-260\right|,261 \le L_{uckGrade}<263:2.758+0.004\left|L_{uckGrade}-261\right|,263 \le L_{uckGrade}<264:2.766+0.005\left|L_{uckGrade}-263\right|,264 \le L_{uckGrade}<267:2.771+0.004\left|L_{uckGrade}-264\right|,267 \le L_{uckGrade}<268:2.783+0.005\left|L_{uckGrade}-267\right|,268 \le L_{uckGrade}<272:2.788+0.004\left|L_{uckGrade}-268\right|,272 \le L_{uckGrade}<273:2.804+0.005\left|L_{uckGrade}-272\right|,273 \le L_{uckGrade}<288:2.809+0.004\left|L_{uckGrade}-273\right|,288 \le L_{uckGrade}<289:2.869+0.003\left|L_{uckGrade}-288\right|,289 \le L_{uckGrade}<294:2.872+0.004\left|L_{uckGrade}-289\right|,294 \le L_{uckGrade}<295:2.892+0.003\left|L_{uckGrade}-294\right|,295 \le L_{uckGrade}<297:2.895+0.004\left|L_{uckGrade}-295\right|,297 \le L_{uckGrade}<298:2.903+0.003\left|L_{uckGrade}-297\right|,298 \le L_{uckGrade}<300:2.906+0.004\left|L_{uckGrade}-298\right|,300 \le L_{uckGrade}<301:2.914+0.003\left|L_{uckGrade}-300\right|,301 \le L_{uckGrade}<303:2.917+0.004\left|L_{uckGrade}-301\right|,303 \le L_{uckGrade}<304:2.925+0.003\left|L_{uckGrade}-303\right|,304 \le L_{uckGrade}<305:2.928+0.004\left|L_{uckGrade}-304\right|,305 \le L_{uckGrade}<306:2.932+0.003\left|L_{uckGrade}-305\right|,306 \le L_{uckGrade}<307:2.935+0.004\left|L_{uckGrade}-306\right|,307 \le L_{uckGrade}<308:2.939+0.003\left|L_{uckGrade}-307\right|,308 \le L_{uckGrade}<309:2.942+0.004\left|L_{uckGrade}-308\right|,309 \le L_{uckGrade}<310:2.946+0.003\left|L_{uckGrade}-309\right|,310 \le L_{uckGrade}<311:2.949+0.004\left|L_{uckGrade}-310\right|,311 \le L_{uckGrade}<312:2.953+0.003\left|L_{uckGrade}-311\right|,312 \le L_{uckGrade}<313:2.956+0.004\left|L_{uckGrade}-312\right|,313 \le L_{uckGrade}<315:2.96+0.003\left|L_{uckGrade}-313\right|,315 \le L_{uckGrade}<316:2.966+0.004\left|L_{uckGrade}-315\right|,316 \le L_{uckGrade}<318:2.97+0.003\left|L_{uckGrade}-316\right|,318 \le L_{uckGrade}<319:2.976+0.004\left|L_{uckGrade}-318\right|,319 \le L_{uckGrade}<321:2.98+0.003\left|L_{uckGrade}-319\right|,321 \le L_{uckGrade}<322:2.986+0.004\left|L_{uckGrade}-321\right|,322 \le L_{uckGrade}<326:2.99+0.003\left|L_{uckGrade}-322\right|,326 \le L_{uckGrade}<327:3.002+0.004\left|L_{uckGrade}-326\right|,327 \le L_{uckGrade}<345:3.006+0.003\left|L_{uckGrade}-327\right|,345 \le L_{uckGrade}<346:3.06+0.002\left|L_{uckGrade}-345\right|,346 \le L_{uckGrade}<349:3.062+0.003\left|L_{uckGrade}-346\right|,349 \le L_{uckGrade}<350:3.071+0.002\left|L_{uckGrade}-349\right|,350 \le L_{uckGrade}<353:3.073+0.003\left|L_{uckGrade}-350\right|,353 \le L_{uckGrade}<354:3.082+0.002\left|L_{uckGrade}-353\right|,354 \le L_{uckGrade}<356:3.084+0.003\left|L_{uckGrade}-354\right|,356 \le L_{uckGrade}<357:3.09+0.002\left|L_{uckGrade}-356\right|,357 \le L_{uckGrade}<358:3.092+0.003\left|L_{uckGrade}-357\right|,358 \le L_{uckGrade}<359:3.095+0.002\left|L_{uckGrade}-358\right|,359 \le L_{uckGrade}<360:3.097+0.003\left|L_{uckGrade}-359\right|,360 \le L_{uckGrade}<361:3.1+0.002\left|L_{uckGrade}-360\right|,361 \le L_{uckGrade}<363:3.102+0.003\left|L_{uckGrade}-361\right|,363 \le L_{uckGrade}<365:3.108+0.002\left|L_{uckGrade}-363\right|,365 \le L_{uckGrade}<366:3.112+0.003\left|L_{uckGrade}-365\right|,366 \le L_{uckGrade}<367:3.115+0.002\left|L_{uckGrade}-366\right|,367 \le L_{uckGrade}<368:3.117+0.003\left|L_{uckGrade}-367\right|,368 \le L_{uckGrade}<369:3.12+0.002\left|L_{uckGrade}-368\right|,369 \le L_{uckGrade}<370:3.122+0.003\left|L_{uckGrade}-369\right|,370 \le L_{uckGrade}<372:3.125+0.002\left|L_{uckGrade}-370\right|,372 \le L_{uckGrade}<373:3.129+0.003\left|L_{uckGrade}-372\right|,373 \le L_{uckGrade}<375:3.132+0.002\left|L_{uckGrade}-373\right|,375 \le L_{uckGrade}<376:3.136+0.003\left|L_{uckGrade}-375\right|,376 \le L_{uckGrade}<380:3.139+0.002\left|L_{uckGrade}-376\right|,380 \le L_{uckGrade}<381:3.147+0.003\left|L_{uckGrade}-380\right|,381 \le L_{uckGrade}<400:3.15+0.002\left|L_{uckGrade}-381\right|,400 \le L_{uckGrade}<401:3.188+0.001\left|L_{uckGrade}-400\right|,401 \le L_{uckGrade}<405:3.189+0.002\left|L_{uckGrade}-401\right|,405 \le L_{uckGrade}<406:3.197+0.001\left|L_{uckGrade}-405\right|,406 \le L_{uckGrade}<408:3.198+0.002\left|L_{uckGrade}-406\right|,408 \le L_{uckGrade}<409:3.202+0.001\left|L_{uckGrade}-408\right|,409 \le L_{uckGrade}<411:3.203+0.002\left|L_{uckGrade}-409\right|,411 \le L_{uckGrade}<412:3.207+0.001\left|L_{uckGrade}-411\right|,412 \le L_{uckGrade}<413:3.208+0.002\left|L_{uckGrade}-412\right|,413 \le L_{uckGrade}<414:3.21+0.001\left|L_{uckGrade}-413\right|,414 \le L_{uckGrade}<416:3.211+0.002\left|L_{uckGrade}-414\right|,416 \le L_{uckGrade}<417:3.215+0.001\left|L_{uckGrade}-416\right|,417 \le L_{uckGrade}<418:3.216+0.002\left|L_{uckGrade}-417\right|,418 \le L_{uckGrade}<419:3.218+0.001\left|L_{uckGrade}-418\right|,419 \le L_{uckGrade}<420:3.219+0.002\left|L_{uckGrade}-419\right|,420 \le L_{uckGrade}<422:3.221+0.001\left|L_{uckGrade}-420\right|,422 \le L_{uckGrade}<423:3.223+0.002\left|L_{uckGrade}-422\right|,423 \le L_{uckGrade}<424:3.225+0.001\left|L_{uckGrade}-423\right|,424 \le L_{uckGrade}<425:3.226+0.002\left|L_{uckGrade}-424\right|,425 \le L_{uckGrade}<427:3.228+0.001\left|L_{uckGrade}-425\right|,427 \le L_{uckGrade}<428:3.23+0.002\left|L_{uckGrade}-427\right|,428 \le L_{uckGrade}<430:3.232+0.001\left|L_{uckGrade}-428\right|,430 \le L_{uckGrade}<431:3.234+0.002\left|L_{uckGrade}-430\right|,431 \le L_{uckGrade}<434:3.236+0.001\left|L_{uckGrade}-431\right|,434 \le L_{uckGrade}<435:3.239+0.002\left|L_{uckGrade}-434\right|,435 \le L_{uckGrade}<443:3.241+0.001\left|L_{uckGrade}-435\right|,443 \le L_{uckGrade}<444:3.249+0.002\left|L_{uckGrade}-443\right|,444 \le L_{uckGrade}<447:3.251+0.001\left|L_{uckGrade}-444\right|,447 \le L_{uckGrade}<448:3.254+0\left|L_{uckGrade}-447\right|,448 \le L_{uckGrade}<456:3.254+0.001\left|L_{uckGrade}-448\right|,456 \le L_{uckGrade}<457:3.262+0\left|L_{uckGrade}-456\right|,457 \le L_{uckGrade}<460:3.262+0.001\left|L_{uckGrade}-457\right|,460 \le L_{uckGrade}<461:3.265+0\left|L_{uckGrade}-460\right|,461 \le L_{uckGrade}<463:3.265+0.001\left|L_{uckGrade}-461\right|,463 \le L_{uckGrade}<464:3.267+0\left|L_{uckGrade}-463\right|,464 \le L_{uckGrade}<466:3.267+0.001\left|L_{uckGrade}-464\right|,466 \le L_{uckGrade}<467:3.269+0\left|L_{uckGrade}-466\right|,467 \le L_{uckGrade}<469:3.269+0.001\left|L_{uckGrade}-467\right|,469 \le L_{uckGrade}<470:3.271+0\left|L_{uckGrade}-469\right|,470 \le L_{uckGrade}<471:3.271+0.001\left|L_{uckGrade}-470\right|,471 \le L_{uckGrade}<472:3.272+0\left|L_{uckGrade}-471\right|,472 \le L_{uckGrade}<473:3.272+0.001\left|L_{uckGrade}-472\right|,473 \le L_{uckGrade}<474:3.273+0\left|L_{uckGrade}-473\right|,474 \le L_{uckGrade}<475:3.273+0.001\left|L_{uckGrade}-474\right|,475 \le L_{uckGrade}<476:3.274+0\left|L_{uckGrade}-475\right|,476 \le L_{uckGrade}<477:3.274+0.001\left|L_{uckGrade}-476\right|,477 \le L_{uckGrade}<479:3.275+0\left|L_{uckGrade}-477\right|,479 \le L_{uckGrade}<480:3.275+0.001\left|L_{uckGrade}-479\right|,480 \le L_{uckGrade}<482:3.276+0\left|L_{uckGrade}-480\right|,482 \le L_{uckGrade}<483:3.276+0.001\left|L_{uckGrade}-482\right|,483 \le L_{uckGrade}<485:3.277+0\left|L_{uckGrade}-483\right|,485 \le L_{uckGrade}<486:3.277+0.001\left|L_{uckGrade}-485\right|,486 \le L_{uckGrade}<489:3.278+0\left|L_{uckGrade}-486\right|,489 \le L_{uckGrade}<490:3.278+0.001\left|L_{uckGrade}-489\right|,490 \le L_{uckGrade}<498:3.279+0\left|L_{uckGrade}-490\right|,498 \le L_{uckGrade}<499:3.279+0.001\left|L_{uckGrade}-498\right|,499 \le L_{uckGrade}<500:3.28+0\left|L_{uckGrade}-499\right|\right\}

See Example for how to use.

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_{uckGrade07}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<2:1+0.011\left|L_{uckGrade}-0\right|,2 \le L_{uckGrade}<3:1.022+0.01\left|L_{uckGrade}-2\right|,3 \le L_{uckGrade}<5:1.032+0.011\left|L_{uckGrade}-3\right|,5 \le L_{uckGrade}<6:1.054+0.01\left|L_{uckGrade}-5\right|,6 \le L_{uckGrade}<8:1.064+0.011\left|L_{uckGrade}-6\right|,8 \le L_{uckGrade}<9:1.086+0.01\left|L_{uckGrade}-8\right|,9 \le L_{uckGrade}<11:1.096+0.011\left|L_{uckGrade}-9\right|,11 \le L_{uckGrade}<12:1.118+0.01\left|L_{uckGrade}-11\right|,12 \le L_{uckGrade}<13:1.128+0.011\left|L_{uckGrade}-12\right|,13 \le L_{uckGrade}<14:1.139+0.01\left|L_{uckGrade}-13\right|,14 \le L_{uckGrade}<15:1.149+0.011\left|L_{uckGrade}-14\right|,15 \le L_{uckGrade}<16:1.16+0.01\left|L_{uckGrade}-15\right|,16 \le L_{uckGrade}<17:1.17+0.011\left|L_{uckGrade}-16\right|,17 \le L_{uckGrade}<18:1.181+0.01\left|L_{uckGrade}-17\right|,18 \le L_{uckGrade}<19:1.191+0.011\left|L_{uckGrade}-18\right|,19 \le L_{uckGrade}<21:1.202+0.01\left|L_{uckGrade}-19\right|,21 \le L_{uckGrade}<22:1.222+0.011\left|L_{uckGrade}-21\right|,22 \le L_{uckGrade}<24:1.233+0.01\left|L_{uckGrade}-22\right|,24 \le L_{uckGrade}<25:1.253+0.011\left|L_{uckGrade}-24\right|,25 \le L_{uckGrade}<29:1.264+0.01\left|L_{uckGrade}-25\right|,29 \le L_{uckGrade}<30:1.304+0.011\left|L_{uckGrade}-29\right|,30 \le L_{uckGrade}<45:1.315+0.01\left|L_{uckGrade}-30\right|,45 \le L_{uckGrade}<46:1.465+0.009\left|L_{uckGrade}-45\right|,46 \le L_{uckGrade}<50:1.474+0.01\left|L_{uckGrade}-46\right|,50 \le L_{uckGrade}<51:1.514+0.009\left|L_{uckGrade}-50\right|,51 \le L_{uckGrade}<53:1.523+0.01\left|L_{uckGrade}-51\right|,53 \le L_{uckGrade}<54:1.543+0.009\left|L_{uckGrade}-53\right|,54 \le L_{uckGrade}<56:1.552+0.01\left|L_{uckGrade}-54\right|,56 \le L_{uckGrade}<57:1.572+0.009\left|L_{uckGrade}-56\right|,57 \le L_{uckGrade}<58:1.581+0.01\left|L_{uckGrade}-57\right|,58 \le L_{uckGrade}<59:1.591+0.009\left|L_{uckGrade}-58\right|,59 \le L_{uckGrade}<60:1.6+0.01\left|L_{uckGrade}-59\right|,60 \le L_{uckGrade}<61:1.61+0.009\left|L_{uckGrade}-60\right|,61 \le L_{uckGrade}<62:1.619+0.01\left|L_{uckGrade}-61\right|,62 \le L_{uckGrade}<63:1.629+0.009\left|L_{uckGrade}-62\right|,63 \le L_{uckGrade}<64:1.638+0.01\left|L_{uckGrade}-63\right|,64 \le L_{uckGrade}<66:1.648+0.009\left|L_{uckGrade}-64\right|,66 \le L_{uckGrade}<67:1.666+0.01\left|L_{uckGrade}-66\right|,67 \le L_{uckGrade}<68:1.676+0.009\left|L_{uckGrade}-67\right|,68 \le L_{uckGrade}<69:1.685+0.01\left|L_{uckGrade}-68\right|,69 \le L_{uckGrade}<72:1.695+0.009\left|L_{uckGrade}-69\right|,72 \le L_{uckGrade}<73:1.722+0.01\left|L_{uckGrade}-72\right|,73 \le L_{uckGrade}<77:1.732+0.009\left|L_{uckGrade}-73\right|,77 \le L_{uckGrade}<78:1.768+0.01\left|L_{uckGrade}-77\right|,78 \le L_{uckGrade}<89:1.778+0.009\left|L_{uckGrade}-78\right|,89 \le L_{uckGrade}<90:1.877+0.008\left|L_{uckGrade}-89\right|,90 \le L_{uckGrade}<95:1.885+0.009\left|L_{uckGrade}-90\right|,95 \le L_{uckGrade}<96:1.93+0.008\left|L_{uckGrade}-95\right|,96 \le L_{uckGrade}<98:1.938+0.009\left|L_{uckGrade}-96\right|,98 \le L_{uckGrade}<99:1.956+0.008\left|L_{uckGrade}-98\right|,99 \le L_{uckGrade}<101:1.964+0.009\left|L_{uckGrade}-99\right|,101 \le L_{uckGrade}<102:1.982+0.008\left|L_{uckGrade}-101\right|,102 \le L_{uckGrade}<104:1.99+0.009\left|L_{uckGrade}-102\right|,104 \le L_{uckGrade}<105:2.008+0.008\left|L_{uckGrade}-104\right|,105 \le L_{uckGrade}<106:2.016+0.009\left|L_{uckGrade}-105\right|,106 \le L_{uckGrade}<107:2.025+0.008\left|L_{uckGrade}-106\right|,107 \le L_{uckGrade}<108:2.033+0.009\left|L_{uckGrade}-107\right|,108 \le L_{uckGrade}<109:2.042+0.008\left|L_{uckGrade}-108\right|,109 \le L_{uckGrade}<110:2.05+0.009\left|L_{uckGrade}-109\right|,110 \le L_{uckGrade}<112:2.059+0.008\left|L_{uckGrade}-110\right|,112 \le L_{uckGrade}<113:2.075+0.009\left|L_{uckGrade}-112\right|,113 \le L_{uckGrade}<115:2.084+0.008\left|L_{uckGrade}-113\right|,115 \le L_{uckGrade}<116:2.1+0.009\left|L_{uckGrade}-115\right|,116 \le L_{uckGrade}<118:2.109+0.008\left|L_{uckGrade}-116\right|,118 \le L_{uckGrade}<119:2.125+0.009\left|L_{uckGrade}-118\right|,119 \le L_{uckGrade}<124:2.134+0.008\left|L_{uckGrade}-119\right|,124 \le L_{uckGrade}<125:2.174+0.009\left|L_{uckGrade}-124\right|,125 \le L_{uckGrade}<136:2.183+0.008\left|L_{uckGrade}-125\right|,136 \le L_{uckGrade}<137:2.271+0.007\left|L_{uckGrade}-136\right|,137 \le L_{uckGrade}<141:2.278+0.008\left|L_{uckGrade}-137\right|,141 \le L_{uckGrade}<142:2.31+0.007\left|L_{uckGrade}-141\right|,142 \le L_{uckGrade}<144:2.317+0.008\left|L_{uckGrade}-142\right|,144 \le L_{uckGrade}<145:2.333+0.007\left|L_{uckGrade}-144\right|,145 \le L_{uckGrade}<147:2.34+0.008\left|L_{uckGrade}-145\right|,147 \le L_{uckGrade}<148:2.356+0.007\left|L_{uckGrade}-147\right|,148 \le L_{uckGrade}<150:2.363+0.008\left|L_{uckGrade}-148\right|,150 \le L_{uckGrade}<151:2.379+0.007\left|L_{uckGrade}-150\right|,151 \le L_{uckGrade}<152:2.386+0.008\left|L_{uckGrade}-151\right|,152 \le L_{uckGrade}<153:2.394+0.007\left|L_{uckGrade}-152\right|,153 \le L_{uckGrade}<154:2.401+0.008\left|L_{uckGrade}-153\right|,154 \le L_{uckGrade}<155:2.409+0.007\left|L_{uckGrade}-154\right|,155 \le L_{uckGrade}<156:2.416+0.008\left|L_{uckGrade}-155\right|,156 \le L_{uckGrade}<158:2.424+0.007\left|L_{uckGrade}-156\right|,158 \le L_{uckGrade}<159:2.438+0.008\left|L_{uckGrade}-158\right|,159 \le L_{uckGrade}<160:2.446+0.007\left|L_{uckGrade}-159\right|,160 \le L_{uckGrade}<161:2.453+0.008\left|L_{uckGrade}-160\right|,161 \le L_{uckGrade}<164:2.461+0.007\left|L_{uckGrade}-161\right|,164 \le L_{uckGrade}<165:2.482+0.008\left|L_{uckGrade}-164\right|,165 \le L_{uckGrade}<168:2.49+0.007\left|L_{uckGrade}-165\right|,168 \le L_{uckGrade}<169:2.511+0.008\left|L_{uckGrade}-168\right|,169 \le L_{uckGrade}<184:2.519+0.007\left|L_{uckGrade}-169\right|,184 \le L_{uckGrade}<185:2.624+0.006\left|L_{uckGrade}-184\right|,185 \le L_{uckGrade}<188:2.63+0.007\left|L_{uckGrade}-185\right|,188 \le L_{uckGrade}<189:2.651+0.006\left|L_{uckGrade}-188\right|,189 \le L_{uckGrade}<192:2.657+0.007\left|L_{uckGrade}-189\right|,192 \le L_{uckGrade}<193:2.678+0.006\left|L_{uckGrade}-192\right|,193 \le L_{uckGrade}<194:2.684+0.007\left|L_{uckGrade}-193\right|,194 \le L_{uckGrade}<195:2.691+0.006\left|L_{uckGrade}-194\right|,195 \le L_{uckGrade}<197:2.697+0.007\left|L_{uckGrade}-195\right|,197 \le L_{uckGrade}<198:2.711+0.006\left|L_{uckGrade}-197\right|,198 \le L_{uckGrade}<199:2.717+0.007\left|L_{uckGrade}-198\right|,199 \le L_{uckGrade}<200:2.724+0.006\left|L_{uckGrade}-199\right|,200 \le L_{uckGrade}<201:2.73+0.007\left|L_{uckGrade}-200\right|,201 \le L_{uckGrade}<202:2.737+0.006\left|L_{uckGrade}-201\right|,202 \le L_{uckGrade}<203:2.743+0.007\left|L_{uckGrade}-202\right|,203 \le L_{uckGrade}<205:2.75+0.006\left|L_{uckGrade}-203\right|,205 \le L_{uckGrade}<206:2.762+0.007\left|L_{uckGrade}-205\right|,206 \le L_{uckGrade}<208:2.769+0.006\left|L_{uckGrade}-206\right|,208 \le L_{uckGrade}<209:2.781+0.007\left|L_{uckGrade}-208\right|,209 \le L_{uckGrade}<212:2.788+0.006\left|L_{uckGrade}-209\right|,212 \le L_{uckGrade}<213:2.806+0.007\left|L_{uckGrade}-212\right|,213 \le L_{uckGrade}<218:2.813+0.006\left|L_{uckGrade}-213\right|,218 \le L_{uckGrade}<219:2.843+0.007\left|L_{uckGrade}-218\right|,219 \le L_{uckGrade}<227:2.85+0.006\left|L_{uckGrade}-219\right|,227 \le L_{uckGrade}<228:2.898+0.005\left|L_{uckGrade}-227\right|,228 \le L_{uckGrade}<233:2.903+0.006\left|L_{uckGrade}-228\right|,233 \le L_{uckGrade}<234:2.933+0.005\left|L_{uckGrade}-233\right|,234 \le L_{uckGrade}<237:2.938+0.006\left|L_{uckGrade}-234\right|,237 \le L_{uckGrade}<238:2.956+0.005\left|L_{uckGrade}-237\right|,238 \le L_{uckGrade}<240:2.961+0.006\left|L_{uckGrade}-238\right|,240 \le L_{uckGrade}<241:2.973+0.005\left|L_{uckGrade}-240\right|,241 \le L_{uckGrade}<242:2.978+0.006\left|L_{uckGrade}-241\right|,242 \le L_{uckGrade}<243:2.984+0.005\left|L_{uckGrade}-242\right|,243 \le L_{uckGrade}<244:2.989+0.006\left|L_{uckGrade}-243\right|,244 \le L_{uckGrade}<245:2.995+0.005\left|L_{uckGrade}-244\right|,245 \le L_{uckGrade}<246:3+0.006\left|L_{uckGrade}-245\right|,246 \le L_{uckGrade}<247:3.006+0.005\left|L_{uckGrade}-246\right|,247 \le L_{uckGrade}<248:3.011+0.006\left|L_{uckGrade}-247\right|,248 \le L_{uckGrade}<249:3.017+0.005\left|L_{uckGrade}-248\right|,249 \le L_{uckGrade}<250:3.022+0.006\left|L_{uckGrade}-249\right|,250 \le L_{uckGrade}<252:3.028+0.005\left|L_{uckGrade}-250\right|,252 \le L_{uckGrade}<253:3.038+0.006\left|L_{uckGrade}-252\right|,253 \le L_{uckGrade}<255:3.044+0.005\left|L_{uckGrade}-253\right|,255 \le L_{uckGrade}<256:3.054+0.006\left|L_{uckGrade}-255\right|,256 \le L_{uckGrade}<258:3.06+0.005\left|L_{uckGrade}-256\right|,258 \le L_{uckGrade}<259:3.07+0.006\left|L_{uckGrade}-258\right|,259 \le L_{uckGrade}<265:3.076+0.005\left|L_{uckGrade}-259\right|,265 \le L_{uckGrade}<266:3.106+0.006\left|L_{uckGrade}-265\right|,266 \le L_{uckGrade}<272:3.112+0.005\left|L_{uckGrade}-266\right|,272 \le L_{uckGrade}<273:3.142+0.004\left|L_{uckGrade}-272\right|,273 \le L_{uckGrade}<279:3.146+0.005\left|L_{uckGrade}-273\right|,279 \le L_{uckGrade}<280:3.176+0.004\left|L_{uckGrade}-279\right|,280 \le L_{uckGrade}<282:3.18+0.005\left|L_{uckGrade}-280\right|,282 \le L_{uckGrade}<283:3.19+0.004\left|L_{uckGrade}-282\right|,283 \le L_{uckGrade}<285:3.194+0.005\left|L_{uckGrade}-283\right|,285 \le L_{uckGrade}<286:3.204+0.004\left|L_{uckGrade}-285\right|,286 \le L_{uckGrade}<288:3.208+0.005\left|L_{uckGrade}-286\right|,288 \le L_{uckGrade}<289:3.218+0.004\left|L_{uckGrade}-288\right|,289 \le L_{uckGrade}<290:3.222+0.005\left|L_{uckGrade}-289\right|,290 \le L_{uckGrade}<291:3.227+0.004\left|L_{uckGrade}-290\right|,291 \le L_{uckGrade}<292:3.231+0.005\left|L_{uckGrade}-291\right|,292 \le L_{uckGrade}<293:3.236+0.004\left|L_{uckGrade}-292\right|,293 \le L_{uckGrade}<294:3.24+0.005\left|L_{uckGrade}-293\right|,294 \le L_{uckGrade}<295:3.245+0.004\left|L_{uckGrade}-294\right|,295 \le L_{uckGrade}<296:3.249+0.005\left|L_{uckGrade}-295\right|,296 \le L_{uckGrade}<297:3.254+0.004\left|L_{uckGrade}-296\right|,297 \le L_{uckGrade}<298:3.258+0.005\left|L_{uckGrade}-297\right|,298 \le L_{uckGrade}<300:3.263+0.004\left|L_{uckGrade}-298\right|,300 \le L_{uckGrade}<301:3.271+0.005\left|L_{uckGrade}-300\right|,301 \le L_{uckGrade}<304:3.276+0.004\left|L_{uckGrade}-301\right|,304 \le L_{uckGrade}<305:3.288+0.005\left|L_{uckGrade}-304\right|,305 \le L_{uckGrade}<310:3.293+0.004\left|L_{uckGrade}-305\right|,310 \le L_{uckGrade}<311:3.313+0.005\left|L_{uckGrade}-310\right|,311 \le L_{uckGrade}<320:3.318+0.004\left|L_{uckGrade}-311\right|,320 \le L_{uckGrade}<321:3.354+0.003\left|L_{uckGrade}-320\right|,321 \le L_{uckGrade}<326:3.357+0.004\left|L_{uckGrade}-321\right|,326 \le L_{uckGrade}<327:3.377+0.003\left|L_{uckGrade}-326\right|,327 \le L_{uckGrade}<329:3.38+0.004\left|L_{uckGrade}-327\right|,329 \le L_{uckGrade}<330:3.388+0.003\left|L_{uckGrade}-329\right|,330 \le L_{uckGrade}<332:3.391+0.004\left|L_{uckGrade}-330\right|,332 \le L_{uckGrade}<333:3.399+0.003\left|L_{uckGrade}-332\right|,333 \le L_{uckGrade}<335:3.402+0.004\left|L_{uckGrade}-333\right|,335 \le L_{uckGrade}<336:3.41+0.003\left|L_{uckGrade}-335\right|,336 \le L_{uckGrade}<337:3.413+0.004\left|L_{uckGrade}-336\right|,337 \le L_{uckGrade}<338:3.417+0.003\left|L_{uckGrade}-337\right|,338 \le L_{uckGrade}<339:3.42+0.004\left|L_{uckGrade}-338\right|,339 \le L_{uckGrade}<340:3.424+0.003\left|L_{uckGrade}-339\right|,340 \le L_{uckGrade}<341:3.427+0.004\left|L_{uckGrade}-340\right|,341 \le L_{uckGrade}<343:3.431+0.003\left|L_{uckGrade}-341\right|,343 \le L_{uckGrade}<344:3.437+0.004\left|L_{uckGrade}-343\right|,344 \le L_{uckGrade}<345:3.441+0.003\left|L_{uckGrade}-344\right|,345 \le L_{uckGrade}<346:3.444+0.004\left|L_{uckGrade}-345\right|,346 \le L_{uckGrade}<348:3.448+0.003\left|L_{uckGrade}-346\right|,348 \le L_{uckGrade}<349:3.454+0.004\left|L_{uckGrade}-348\right|,349 \le L_{uckGrade}<353:3.458+0.003\left|L_{uckGrade}-349\right|,353 \le L_{uckGrade}<354:3.47+0.004\left|L_{uckGrade}-353\right|,354 \le L_{uckGrade}<369:3.474+0.003\left|L_{uckGrade}-354\right|,369 \le L_{uckGrade}<370:3.519+0.002\left|L_{uckGrade}-369\right|,370 \le L_{uckGrade}<374:3.521+0.003\left|L_{uckGrade}-370\right|,374 \le L_{uckGrade}<375:3.533+0.002\left|L_{uckGrade}-374\right|,375 \le L_{uckGrade}<377:3.535+0.003\left|L_{uckGrade}-375\right|,377 \le L_{uckGrade}<378:3.541+0.002\left|L_{uckGrade}-377\right|,378 \le L_{uckGrade}<380:3.543+0.003\left|L_{uckGrade}-378\right|,380 \le L_{uckGrade}<381:3.549+0.002\left|L_{uckGrade}-380\right|,381 \le L_{uckGrade}<382:3.551+0.003\left|L_{uckGrade}-381\right|,382 \le L_{uckGrade}<383:3.554+0.002\left|L_{uckGrade}-382\right|,383 \le L_{uckGrade}<384:3.556+0.003\left|L_{uckGrade}-383\right|,384 \le L_{uckGrade}<385:3.559+0.002\left|L_{uckGrade}-384\right|,385 \le L_{uckGrade}<386:3.561+0.003\left|L_{uckGrade}-385\right|,386 \le L_{uckGrade}<387:3.564+0.002\left|L_{uckGrade}-386\right|,387 \le L_{uckGrade}<388:3.566+0.003\left|L_{uckGrade}-387\right|,388 \le L_{uckGrade}<389:3.569+0.002\left|L_{uckGrade}-388\right|,389 \le L_{uckGrade}<390:3.571+0.003\left|L_{uckGrade}-389\right|,390 \le L_{uckGrade}<392:3.574+0.002\left|L_{uckGrade}-390\right|,392 \le L_{uckGrade}<393:3.578+0.003\left|L_{uckGrade}-392\right|,393 \le L_{uckGrade}<396:3.581+0.002\left|L_{uckGrade}-393\right|,396 \le L_{uckGrade}<397:3.587+0.003\left|L_{uckGrade}-396\right|,397 \le L_{uckGrade}<401:3.59+0.002\left|L_{uckGrade}-397\right|,401 \le L_{uckGrade}<402:3.598+0.003\left|L_{uckGrade}-401\right|,402 \le L_{uckGrade}<414:3.601+0.002\left|L_{uckGrade}-402\right|,414 \le L_{uckGrade}<415:3.625+0.001\left|L_{uckGrade}-414\right|,415 \le L_{uckGrade}<419:3.626+0.002\left|L_{uckGrade}-415\right|,419 \le L_{uckGrade}<420:3.634+0.001\left|L_{uckGrade}-419\right|,420 \le L_{uckGrade}<423:3.635+0.002\left|L_{uckGrade}-420\right|,423 \le L_{uckGrade}<424:3.641+0.001\left|L_{uckGrade}-423\right|,424 \le L_{uckGrade}<425:3.642+0.002\left|L_{uckGrade}-424\right|,425 \le L_{uckGrade}<426:3.644+0.001\left|L_{uckGrade}-425\right|,426 \le L_{uckGrade}<428:3.645+0.002\left|L_{uckGrade}-426\right|,428 \le L_{uckGrade}<429:3.649+0.001\left|L_{uckGrade}-428\right|,429 \le L_{uckGrade}<430:3.65+0.002\left|L_{uckGrade}-429\right|,430 \le L_{uckGrade}<431:3.652+0.001\left|L_{uckGrade}-430\right|,431 \le L_{uckGrade}<432:3.653+0.002\left|L_{uckGrade}-431\right|,432 \le L_{uckGrade}<433:3.655+0.001\left|L_{uckGrade}-432\right|,433 \le L_{uckGrade}<434:3.656+0.002\left|L_{uckGrade}-433\right|,434 \le L_{uckGrade}<436:3.658+0.001\left|L_{uckGrade}-434\right|,436 \le L_{uckGrade}<437:3.66+0.002\left|L_{uckGrade}-436\right|,437 \le L_{uckGrade}<438:3.662+0.001\left|L_{uckGrade}-437\right|,438 \le L_{uckGrade}<439:3.663+0.002\left|L_{uckGrade}-438\right|,439 \le L_{uckGrade}<442:3.665+0.001\left|L_{uckGrade}-439\right|,442 \le L_{uckGrade}<443:3.668+0.002\left|L_{uckGrade}-442\right|,443 \le L_{uckGrade}<447:3.67+0.001\left|L_{uckGrade}-443\right|,447 \le L_{uckGrade}<448:3.674+0.002\left|L_{uckGrade}-447\right|,448 \le L_{uckGrade}<461:3.676+0.001\left|L_{uckGrade}-448\right|,461 \le L_{uckGrade}<462:3.689+0\left|L_{uckGrade}-461\right|,462 \le L_{uckGrade}<466:3.689+0.001\left|L_{uckGrade}-462\right|,466 \le L_{uckGrade}<467:3.693+0\left|L_{uckGrade}-466\right|,467 \le L_{uckGrade}<469:3.693+0.001\left|L_{uckGrade}-467\right|,469 \le L_{uckGrade}<470:3.695+0\left|L_{uckGrade}-469\right|,470 \le L_{uckGrade}<472:3.695+0.001\left|L_{uckGrade}-470\right|,472 \le L_{uckGrade}<473:3.697+0\left|L_{uckGrade}-472\right|,473 \le L_{uckGrade}<474:3.697+0.001\left|L_{uckGrade}-473\right|,474 \le L_{uckGrade}<475:3.698+0\left|L_{uckGrade}-474\right|,475 \le L_{uckGrade}<476:3.698+0.001\left|L_{uckGrade}-475\right|,476 \le L_{uckGrade}<477:3.699+0\left|L_{uckGrade}-476\right|,477 \le L_{uckGrade}<478:3.699+0.001\left|L_{uckGrade}-477\right|,478 \le L_{uckGrade}<479:3.7+0\left|L_{uckGrade}-478\right|,479 \le L_{uckGrade}<480:3.7+0.001\left|L_{uckGrade}-479\right|,480 \le L_{uckGrade}<481:3.701+0\left|L_{uckGrade}-480\right|,481 \le L_{uckGrade}<482:3.701+0.001\left|L_{uckGrade}-481\right|,482 \le L_{uckGrade}<484:3.702+0\left|L_{uckGrade}-482\right|,484 \le L_{uckGrade}<485:3.702+0.001\left|L_{uckGrade}-484\right|,485 \le L_{uckGrade}<487:3.703+0\left|L_{uckGrade}-485\right|,487 \le L_{uckGrade}<488:3.703+0.001\left|L_{uckGrade}-487\right|,488 \le L_{uckGrade}<491:3.704+0\left|L_{uckGrade}-488\right|,491 \le L_{uckGrade}<492:3.704+0.001\left|L_{uckGrade}-491\right|,492 \le L_{uckGrade}<500:3.705+0\left|L_{uckGrade}-492\right|\right\}

See Example for how to use.

Probabilities from Luck

To calculate the drop rate at X Luck there are three steps.

1. For each Luck Grade's Drop Rate apply the corresponding Luck Scalar.
   
2. Find the dot product between the Luck Scalar vector at X Luck and the Base Rate.
   (This is the same as adding up each term from the first step.)
   
3. For each term in the first step divide by the dot product from the second step to get the new drop rate at X Luck.

The table below is the Drop Rate table of Quest Drops.

Every monster with a quest drop uses the Drop Rate table.
However, depending on the monster's Loot Drop Table, many of the Luck Grade rates will be associated with dropping nothing.

And in other instances, like Demon Centaur, a Luck Grade's rate may be split between two Loot Drops.
This will not affect the calculations below, but they will determine an individual item's probability.

Luck Grade	Drop Rate
Junk	220
Poor	250
Common	200
Uncommon	150
Rare	100
Epic	50
Legendary	20
Unique	10

Click expand to see the calculations for 0 and 250 Luck.

Drop Rate tables generally sum to a power of ten. Since the Luck Scalars are simply 1 at 0 Luck, the probability calculation is trivial.

Using the Luck Scalars at 0 Luck, the dot product is

$\color {White}{\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}1.000\cdot {\textbf {220}}}+{\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}1.000\cdot {\textbf {250}}}+{\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}1.000\cdot {\textbf {200}}}+{\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {150}}}+{\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}1.000\cdot {\textbf {100}}}+{\color [rgb]{0.6784313725490196,0.35294117647058826,1}1.000\cdot {\textbf {50}}}+{\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}1.000\cdot {\textbf {20}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}1.000\cdot {\textbf {10}}}={\color {violet}1000}$

Luck Grade	Drop Probability at 0 Luck
Junk	$\color {White}{\frac {\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}1.000\cdot {\textbf {220}}}{\color {violet}1000}}=22\%$
Poor	$\color {White}{\frac {\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}1.000\cdot {\textbf {250}}}{\color {violet}1000}}=25\%$
Common	$\color {White}{\frac {\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}1.000\cdot {\textbf {200}}}{\color {violet}1000}}=20\%$
Uncommon	$\color {White}{\frac {\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {150}}}{\color {violet}1000}}=15\%$
Rare	$\color {White}{\frac {\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}1.000\cdot {\textbf {100}}}{\color {violet}1000}}=10\%$
Epic	$\color {White}{\frac {\color [rgb]{0.6784313725490196,0.35294117647058826,1}1.000\cdot {\textbf {50}}}{\color {violet}1000}}=5\%$
Legendary	$\color {White}{\frac {\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}1.000\cdot {\textbf {20}}}{\color {violet}1000}}=2\%$
Unique	$\color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}1.000\cdot {\textbf {10}}}{\color {violet}1000}}=1\%$

Using the Luck Scalars at 250 Luck, the dot product is

$\color {White}{\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.750\cdot {\textbf {220}}}+{\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.750\cdot {\textbf {250}}}+{\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.875\cdot {\textbf {200}}}+{\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {150}}}+{\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}2.878\cdot {\textbf {100}}}+{\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.125\cdot {\textbf {50}}}+{\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}3.441\cdot {\textbf {20}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}3.535\cdot {\textbf {10}}}={\color {violet}1227.42}$

Luck Grade	Drop Probability at 250 Luck
Junk	$\color {White}{\frac {\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.750\cdot {\textbf {220}}}{\color {violet}1227.42}}=13.443\%$
Poor	$\color {White}{\frac {\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.750\cdot {\textbf {250}}}{\color {violet}1227.42}}=15.276\%$
Common	$\color {White}{\frac {\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.875\cdot {\textbf {200}}}{\color {violet}1227.42}}=14.258\%$
Uncommon	$\color {White}{\frac {\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {150}}}{\color {violet}1227.42}}=12.221\%$
Rare	$\color {White}{\frac {\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}2.878\cdot {\textbf {100}}}{\color {violet}1227.42}}=23.448\%$
Epic	$\color {White}{\frac {\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.125\cdot {\textbf {50}}}{\color {violet}1227.42}}=12.868\%$
Legendary	$\color {White}{\frac {\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}3.441\cdot {\textbf {20}}}{\color {violet}1227.42}}=5.607\%$
Unique	$\color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}3.535\cdot {\textbf {10}}}{\color {violet}1227.42}}=2.880\%$

Using the Luck Scalars at 500 Luck, the dot product is

$\color {White}{\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.500\cdot {\textbf {220}}}+{\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.500\cdot {\textbf {250}}}+{\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.750\cdot {\textbf {200}}}+{\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {150}}}+{\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}3.505\cdot {\textbf {100}}}+{\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.881\cdot {\textbf {50}}}+{\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}4.257\cdot {\textbf {20}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}4.382\cdot {\textbf {10}}}={\color {violet}1208.51}$

Luck Grade	Drop Probability at 500 Luck
Junk	$\color {White}{\frac {\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.500\cdot {\textbf {220}}}{\color {violet}1208.51}}=9.102\%$
Poor	$\color {White}{\frac {\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.500\cdot {\textbf {250}}}{\color {violet}1208.51}}=10.343\%$
Common	$\color {White}{\frac {\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.750\cdot {\textbf {200}}}{\color {violet}1208.51}}=12.412\%$
Uncommon	$\color {White}{\frac {\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {150}}}{\color {violet}1208.51}}=12.412\%$
Rare	$\color {White}{\frac {\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}3.505\cdot {\textbf {100}}}{\color {violet}1208.51}}=29.003\%$
Epic	$\color {White}{\frac {\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.881\cdot {\textbf {50}}}{\color {violet}1208.51}}=16.057\%$
Legendary	$\color {White}{\frac {\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}4.257\cdot {\textbf {20}}}{\color {violet}1208.51}}=7.045\%$
Unique	$\color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}4.382\cdot {\textbf {10}}}{\color {violet}1208.51}}=3.626\%$

The table below is the Drop Rate table of the Gold Coin Chest.

The Loot Drop table is rather simple. At Luck Grade 0, "Junk", you get nothing. At Luck Grade 2, "Common", you get 1x Gold Coin Chest.

Notice that despite the Gold Coin Chest's item rarity being unique, its Luck Grade is actually Common.
Item Rarity does not equal Luck Grade, despite the two being equal for most items.

Luck Grade	Drop Rate
Junk	99900
Poor	0
Common	100
Uncommon	0
Rare	0
Epic	0
Legendary	0
Unique	0

Click expand to see the calculations for 0 and 250 Luck.

Using the Luck Scalars at 0 Luck, the dot product is

$\color {White}{\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}1.000\cdot {\textbf {99900}}}+{\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}1.000\cdot {\textbf {100}}}+{\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.6784313725490196,0.35294117647058826,1}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}1.000\cdot {\textbf {0}}}={\color {violet}100000}$

Luck Grade	Drop Probability at 0 Luck
Junk	$\color {White}{\frac {\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}1.000\cdot {\textbf {99900}}}{\color {violet}100000}}=99.9\%$
Poor	$\color {White}{\frac {\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%$
Common	$\color {White}{\frac {\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}1.000\cdot {\textbf {100}}}{\color {violet}100000}}=0.1\%$
Uncommon	$\color {White}{\frac {\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%$
Rare	$\color {White}{\frac {\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%$
Epic	$\color {White}{\frac {\color [rgb]{0.6784313725490196,0.35294117647058826,1}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%$
Legendary	$\color {White}{\frac {\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%$
Unique	$\color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%$

Using the Luck Scalars at 250 Luck, the dot product is

$\color {White}{\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.750\cdot {\textbf {99900}}}+{\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.750\cdot {\textbf {0}}}+{\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.875\cdot {\textbf {100}}}+{\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}2.878\cdot {\textbf {0}}}+{\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.159\cdot {\textbf {0}}}+{\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}3.441\cdot {\textbf {0}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}3.535\cdot {\textbf {0}}}={\color {violet}75012.5}$

Luck Grade	Drop Probability at 250 Luck
Junk	$\color {White}{\frac {\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.750\cdot {\textbf {99900}}}{\color {violet}75012.5}}=99.883\%$
Poor	$\color {White}{\frac {\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.750\cdot {\textbf {0}}}{\color {violet}75012.5}}=0\%$
Common	$\color {White}{\frac {\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.875\cdot {\textbf {100}}}{\color {violet}75012.5}}=0.117\%$
Uncommon	$\color {White}{\frac {\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {0}}}{\color {violet}75012.5}}=0\%$
Rare	$\color {White}{\frac {\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}2.878\cdot {\textbf {0}}}{\color {violet}75012.5}}=0\%$
Epic	$\color {White}{\frac {\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.159\cdot {\textbf {0}}}{\color {violet}75012.5}}=0\%$
Legendary	$\color {White}{\frac {\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}3.441\cdot {\textbf {0}}}{\color {violet}75012.5}}=0\%$
Unique	$\color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}3.535\cdot {\textbf {0}}}{\color {violet}75012.5}}=0\%$

Using the Luck Scalars at 500 Luck, the dot product is

$\color {White}{\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.500\cdot {\textbf {99900}}}+{\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.500\cdot {\textbf {0}}}+{\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.750\cdot {\textbf {100}}}+{\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}3.505\cdot {\textbf {0}}}+{\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.881\cdot {\textbf {0}}}+{\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}4.257\cdot {\textbf {0}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}4.382\cdot {\textbf {0}}}={\color {violet}50025}$

Luck Grade	Drop Probability at 500 Luck
Junk	$\color {White}{\frac {\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.500\cdot {\textbf {99900}}}{\color {violet}50025}}=99.850\%$
Poor	$\color {White}{\frac {\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.500\cdot {\textbf {0}}}{\color {violet}50025}}=0\%$
Common	$\color {White}{\frac {\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.750\cdot {\textbf {100}}}{\color {violet}50025}}=0.150\%$
Uncommon	$\color {White}{\frac {\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {0}}}{\color {violet}50025}}=0\%$
Rare	$\color {White}{\frac {\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}3.505\cdot {\textbf {0}}}{\color {violet}50025}}=0\%$
Epic	$\color {White}{\frac {\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.881\cdot {\textbf {0}}}{\color {violet}50025}}=0\%$
Legendary	$\color {White}{\frac {\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}4.257\cdot {\textbf {0}}}{\color {violet}50025}}=0\%$
Unique	$\color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}4.382\cdot {\textbf {0}}}{\color {violet}50025}}=0\%$

It's worth noting that you can calculate probability at X Luck from either the Drop Rate table or the Drop Probability at 0 Luck table.
Using the Drop Probability at 0 Luck table works because the Luck Scalars are all 1 and you have to normalize regardless of using the Drop Rate or the Probability at 0 Luck.

The wiki does not display the Drop Rate tables themselves, however it does show the alternative.