Damage

Damage Formula

(
  (
    (
        + (Base Damage + "Buff" Weapon Damage) * Combo Bonus * Impact Zone Bonus
        + Gear "+N Weapon Damage"|"N Magical Damage"
        + Divine Strike Damage
    )
    * (1 + Power Bonus)
    + "Additional" Damage
  )
  * (Hit Location Multiplier)
  * (1 - Damage Reduction * (1 - Penetration))
  * (1 - Projectile Reduction)
)
* Projectile Falloff
+ True Damage

Base Damage

The displayed damage of a weapon, skill, or spell. For example: Rondel Dagger's 18 Weapon Damage, Rupture's 20 Physical Damage, Lightning Strike's 30 Magical Damage, or Judgement's 25 Magical Damage.

"Buff" Weapon Damage

The damage added from the perks Slayer, War Song, and Rapier Mastery. This stat is multiplied by Impact Zone Bonus and Combo Bonus. It essentially acts like a modification to your weapon's base damage.

Gear "+N Weapon Damage"

The damage added by the "+ Weapon Damage" affix on gear (formally "Physical Weapon Damage Add"). This stat benefits from Power Bonus. This stat will only apply to direct attacks from weaponry, and will not apply to skills such as Rupture, Caltrops, Achilles Strike, and so on. This is a Physical stat, and so will not add to sources of Magical Damage. This stat is different from "Buff" Weapon Damage, in that it will not be multiplied by your Impact Zone Bonus or your Combo Bonus. This stat is influenced by Attribute Bonus Ratio.

Gear "N Magical Damage"

The damage added by the "Magical Damage" stat on the Magic Staff, Spellbook, and Crystal Ball. This damage benefits from Power Bonus. This damage will apply to all sources of Magical Damage, and will do so multiple times per spell, if the spell has multiple damage sources. Examples include each hit of Magic Missile, or Zap's direct hit and DoT portions. This is a Magical stat, and so will not add to sources of Physical Damage. This stat is influenced by Attribute Bonus Ratio.

Divine Strike Damage

The damage added by the Cleric buff "Divine Strike". This stat benefits from Power Bonus. Unlike Weapon Damage, this stat will apply to both weapon attacks, and indirect sources of Physical Damage, such as Rupture, Caltrops, and Achilles Strike. This is a Physical stat, and so will not add to sources of Magical Damage. This stat is influenced by Attribute Bonus Ratio.

Impact Zone Bonus

A multiplier enforced when hitting with the "sour spots" of certain weapons. See Weapons for each weapon's exact multipliers.

Combo Bonus

A multiplier enforced when hitting with the latter hits of certain weapons' combos. See Weapons for each weapon's exact multipliers.

Power Bonus

A multiplier that affects all damage types listed so far. This can be of the Physical or Magical variety, and each will only apply to its respective damage type (Physical Power Bonus will not apply to Zap, for example). This value can be positive or negative, and is influenced by gear or by the player's Attributes. This stat is influenced by Attribute Bonus Ratio. Physical Damage Bonus is included (modifies Physical Power stat).

"Additional" Damage

The damage added by specific Perks or by the "Additional Physical/Magical Damage" affix on gear. This can be of the Physical or Magical variety, and each will only apply to its respective damage type (Additional Physical Damage will not apply to Zap, for example). This stat does not benefit from Power Bonus. This stat will apply to any instance of its respective type of damage, and will do so multiple times per skill if applicable. Examples include Achilles Strike's individual movement damage ticks (Physical), or each hit of Magic Missile (Magical). This stat is influenced by Attribute Bonus Ratio.

Hit Location Multiplier

A multiplier enforced when hitting the head or the limbs with certain attacks. The multipliers:

Head: 150%
Body: 100%
Arms: 80%
Legs: 60%
Feet/Hand: 50%

Area of Effect and Damage over Time sources are not affected by this multiplier.

For on-hit damaging effects there are some exceptions:

Cleric's Smite does NOT benefit
Barbarian's Achilles Strike does NOT benefit
Rogue's Poisoned Weapon does NOT benefit
Warlock's Blow of Corruption does benefit
Wizard's Ignite and the Ignite's burn does benefit

The headshot reduction stat reduces this additively if the target hitbox is a head, while Ranger's Sharpshooter increases it. For example, targeting the head with the Sharpshooter perk against a player with 20% Headshot reduction results in 1.5 + .1 - .2 = 1.4x headshot multiplier

Damage Reduction

A defensive multiplier based on the opponent's Damage Reduction stat. Physical Damage Reduction applies to Physical Damage sources, such as weapon hits, Rupture, Achilles Strike, and so on. Magical Damage Reduction applies to Magical Damage sources, such as Zap, Explosive Bottles, Poison Weapon, and so on.

Penetration

A modifier for Damage Reduction that can be acquired from certain weapons, or from the "Armor Penetration" or "Magical Penetration" affixes on gear. This stat multiplies with their Damage Reduction %, not their Armor Rating/Magic Resist Rating.

% Damage Reduced = Target's Damage Reduction * (1 - Attacker's Pen)

This then multiplies the damage an enemy takes with this new reduction by (1 - Target's Modified Damage Reduction) Or, combined Damage Multiplier = 1 - Target's Damage Reduction * (1 - Attacker's Pen)

This modifier cannot bring Damage Reduction below 0% meaning there is no functional benefit to exceeding 100% Penetration
This modifier also does nothing if the target's Damage Reduction % is 0% or less.
Using these limitations, the above formula can be expanded to the following: (note that for brevity, Damage Reduction is written as DR and Penetration is written as Pen.

max((1-DR*(1-min(Pen,1))),1-DR)

Projectile Reduction

A defensive multiplier that can be acquired from Plate Armor, or the Projectile Resistance Perk for Fighter. This influences damage done by Projectiles, including but not limited to Arrows, Bolts, Throwables, and selectively applies to some Magical Damage sources and not to others. Sources that are influenced include: Ice Bolt, Magic Missile, and Fireball (Direct Hit).

Projectile Falloff

Damage multiplier to gravity affected projectiles, currently including arrows shot by Recurve Bow, Survival Bow, Longbow, Hand Crossbow, Crossbow, Windlass Crossbow as well as throwables, like Drum's, Throwing Knife, Francisca Axe, but not Torches. The multiplier depends on the air time of the projectile, is different for each source, and can be found in the mentioned pages.

True Damage

The damage added by the "True Physical Damage" or "True Magical Damage" affixes on gear. Each will only apply to its respective damage type (True Magical Damage will not apply to an Arming Sword, for example). This damage is mostly unaffected by any other multipliers, and is added at the end of all calculations. This stat is influenced by Attribute Bonus Ratio.
Cleric's Perseverance Perk is effectively "negative True Damage", however it seems to not reduce damage if that damage would be reduced below 1. For example, 1 stack of Rogue's Poison Weapon tends to deal less than 1 damage per second, and so Perseverance will not reduce it.

Damage/Healing over Time

Rather than calculating the value per hit, they calculate the total damage/healing, and then divide by the number of damaging/healing ticks, which is usually the same as the number of seconds.

Additionally, nearly all Damage over times have 50% Attribute Bonus Ratio rather than 100%, making damage increases only half as effective
Example: Rogue's Rupture skill does 20 physical damage over 5 seconds, or 4 damage a second. If they attain +5 additional physical damage this becomes 22.5 damage over 5 seconds, or 4.5 a second.

The number of damaging ticks is affected by the receiving player's Buff/Debuff Duration, and is rounded down to the nearest integer. This strictly affects how long the DoT lasts, and not the damage per tick of the DoT
Sources like Ray of Darkness, Din of Darkness, Torture Mastery, and movement based abilities like Achilles Strike and Earthquake are not Damage/Heal over times, rather, bonuses apply per-hit to these like normal.
Sources like Locusts' Swarm and Explosive lanterns fire only deal damage while inside the area and are also not damage over times

Formulas

Note, "Value" refers to either Damage or Healing

Base # of Ticks = Base duration/Interval length

Total duration = Base # of Ticks * (1 + Debuff Duration%)

Total ticks = floor(Total duration)

Total Value = Base Value/Base Ticks * Total ticks

Value per interval = Total value / Base Ticks

Value per second = Value per interval / Interval length

Since nearly all Damage/Healing over times have an Interval length of 1 second, these can be simplified to:

Total Duration = Base Duration * (1 + Debuff Duration)

Total Value = Base Value / Base Duration * floor(Total Duration)

Value per second = Total Value / Base Duration

Examples

Example 1: Rogue's Rupture

Rogue's Rupture which normally does 20 damage, with -17% Physical Power Bonus% and +10 additional physical damage will instead deal 23.3 damage due to having a 50% Attribute Bonus Ratio.

Total damage (before debuff duration) = 20 * (1-.17 * .5)+10 * .5 = 23.3

Rupture lasts 5s and deals damage in 1s intervals, so against a Bard with 25% longer Debuff duration, it will instead deal 27.96 damage

Base ticks = 5/1 = 5 ticks

Total duration = 5 * (1 + .25) = 6.25s

Total Damage = 23.3/5 * floor(6.25) = 27.96 damage

Damage per second = 27.96/5 = 5.592 damage per second

Example 2: Wizard's Zap's Burn

Zap's Burn deals damage with a 1s interval and lasts only 1s total, meaning any negative debuff duration, even -1%, will make it have 0 ticks and deal 0 damage due to rounding.
On the contrary, it would require at least 100% debuff duration% on the target to get an extra tick from Zap.

Example 3: Healing Potion

See Healing#Healing_Potion

Rounding

Damage/Health: All sources of damage/healing can do decimal amounts, and therefore you can have decimal health. Damage text that is displayed when you hit a dummy is always rounded down. Health on players' details page is always rounded up.
Details page: Currently all details round up, but some to the nearest integer, and some to the nearest tenth. Wizard's Sage and Warlock's Malice can give decimal knowledge/will, although their displays round up to an integer. Expect all decimal stats to have a margin of error of +/- .1, and integer stats to have a margin of error of +/- 1.
Memory Capacity is both rounded up to the nearest integer in the details page and in reality. +1% Memory Capacity will always equate to at least +1 Memory Capacity
Buffs/Debuffs: Durations are not rounded and last their exact amount. However, durations that perform an action in intervals, like Damage/Healing over Time, are rounded down to the nearest integer, resulting in thresholds that players may want to take advantage of. In other words, increases must be greater than its interval length, which is usually 1 second.

Total Ticks = floor(Base Duration * (1 + Bonus Duration))

Examples

A 5s buff with 19% bonus duration will have

floor(5 seconds * (1 + .19)) = 5 ticks

A 5s buff with 20% bonus duration, however, will have

floor(5 seconds * (1 + .2)) = 6 ticks

A 5s buff with -1% bonus duration will have

floor(5 seconds * (1 + -.01)) = 4 ticks

Notes

For statuses that can stack their damaging effect several times over, like Rogue's Poisoned Weapon, the stacks multiply the damage dealt at the very end. They do not multiply the base damage. This means that each stack benefits from flat bonuses just the same as the first stack.

Rogue's Weakpoint Attack's debuff multiplies the victim's Armor Rating directly. Because Armor Rating to Damage Reduction follows a variable curve, it is very difficult to predict how much this will influence damage.

Attribute Bonus Ratio

- "Attribute Bonus Ratio" is a hidden modifier present on a variety of spells, items, and skills. It will modify any sources of personal bonus damage/healing/shields/whatever else, based on its multiplier.

What does this include?

Power Bonus (Magical and Physical)
Magical Damage (From Spellbooks, Staves, and Crystal Balls)
Divine Strike's special Physical Damage buff
Additional Damage (Magical and Physical)
True Damage (Magical and Physical)
Weapon Damage (There is currently nothing implemented in the game with Attribute Bonus Ratio that can also benefit from standard Weapon Damage)
+Magical/Physical Healing

What does this not include?

Location Bonus
Enemy Damage Reduction
Projectile Reduction
Combo Multiplier
Weapon Impact Zone Multiplier
Attributes (common misconception)
Casting Speed
Projectile Speed
Vampirism

This can be summarized as Attribute Bonus Ratio affects all flat bonuses, as well as Power Bonus (Physical and Magical).

- Here's an example using default Warlock's Curse of Pain damage over time (not the direct hit). Curse of Pain has a base of 10 damage over 8 seconds, the default Magic Staff grants 5 Magical Damage, and Warlock's default Magic Power Bonus is 24%.

- Without Attribute Bonus Ratio, the damage calculation would look as follows:

( 10 + 5 ) * (1 + 0.24) = 18.6 dmg over 8s

- However, with Attribute Bonus Ratio of 50%, we must halve the +5 Magical Damage and the 24% Magic Power Bonus.

( 10 + 2.5 ) * (1 + 0.12) = 14 dmg over 8s

- 14 damage over 8 seconds then equates to 1.75 damage dealt every second.

What sources of damage are affected by this?

All attribute bonus scalars can now be found in the class/unique specific pages.

Additional vs True

Difference

Using the formula, the difference between Additional Physical/Magical and True Physical/Magical can be summarized as follows:

Additional damage:

Scales with Hit Location Multiplier which can be both a good and a bad thing
Reduced by Damage Reductions
Reduced by Projectile Damage Falloff if its a gravity-affected projectile
Generally better against enemies with lower damage reduction, and when headshots can be hit easily/consistently.

True damage:

Unaffected by Hit Location Multiplier which can be both a good and a bad thing
Unaffected by Damage Reductions
Unaffected by Projectile Damage Falloff
Generally better against enemies with higher damage reduction, or when some sources of your damage cannot headshot, or when headshotting is difficult, or when using gravity-affected projectiles

On a particular hit, True damage is always better than Additional damage when it cannot headshot (Damage over Time / Area of Effect).

Additional is substantially better in PvE for physical hits as most Monsters have negative Physical Damage Reduction, and headshots are very consistent.

Note that neither of these benefit from Physical/Magic Power Bonus.

Formula

To determine exactly which is better with your specific stats and by how much, use the following formula:

(1 - Damage Reduction after Penetration) * (Hit Location Multiplier) * (Damage Falloff)

For non-gravity affected projectiles, Damage Falloff can be left out.

If the resulting number is greater than 1, Add is better.

If the resulting number is less than 1, True is better.

Examples

Example 1

Scenario: Headshot against slightly above average damage reduction

For example, against an enemy with 33.33% Damage Reduction (after Penetration) with a headshot (1.5x Hit Location Multiplier) (not projectile):

(1 - .3333) * 1.5 = 1x

In this scenario, True gives exactly the same amount of damage as Additional.

Example 2

Scenario: Low damage reduction with a Damage over Time

Against an enemy with 20% Damage Reduction when using a Damage over Time (1x Hit Location Multiplier) (not projectile):

(1 - .2) * 1 = 0.8x

In this scenario, Additional gives 80% of the damage that True gives. In other words, Additional gives 20% less damage than True does.

Example 3

Scenario: No damage reduction, hitting limb

Against an enemy with 0% Damage Reduction and the damage hits a Hand (0.5x Hit Location Multiplier) (not projectile):

(1 - 0) * 0.5 = 0.5x

In this scenario, Additional gives 50% of the damage that True gives. In other words, Additional gives 50% less damage than True does.

Example 4

Scenario: PvE with a headshot

Against an enemy with -22% Damage Reduction and the damage hits the head (1.5x Hit Location Multiplier) (not projectile):

(1 - -.22) * 1.5 = 1.83

In this scenario, Additional gives 183% of the damage that True gives. In other words, Additional gives 83% more damage than True does.

Example 5

Scenario: Gravity-affected Projectile

Against an enemy with 10% Damage Reduction and an *arrow* hits their arm (0.5x Hit Location Multiplier) after being in the air for half a second with a Recurve Bow (0.7x Damage Falloff)

(1 - .1) * 0.5 * 0.7 = 0.315

In this scenario, Additional gives 31.5% of the damage that True gives. In other words, Additional gives 68.5% less damage than True does.

Example 6

Scenario: Realistic PvP

Lastly, for a more realistic example, you can guess what your average Hit Location Multiplier is. If you never hit the head, and sometimes you hit limbs/arms/feet, your average may be 0.9x.

Against an enemy with 20% Damage Reduction:

(1 - .2) * 0.9 = 0.72x

In this scenario, Additional gives 72% of the damage that True gives. In other words, Additional gives 28% less damage than True does.

Video Guides

Note that Hit Location Multiplier is outdated in this video.