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Damage Formula

General Formula for Damage

Damage=((BaseDamage×SpecialMultiplier)+FlatDamage)×(1+DamageBonusDamageReduction)×CRIT×EnemyDefMult×EnemyResMult×AmplifyingReaction+TransformativeReaction+Proc\text{Damage} = ((\text{BaseDamage} \times \text{SpecialMultiplier}) + \text{FlatDamage}) \\ \times (1 + \text{DamageBonus} - \text{DamageReduction}) \\ \times \text{CRIT} \times \text{EnemyDefMult} \times \text{EnemyResMult} \times \text{AmplifyingReaction} \\ + \text{TransformativeReaction} + \text{Proc}

See the sections below for the breakdown of each individual part of the formula.

Base Damage

BaseDamage={Talent%×ATKif, Talent scales with ATKTalent%×DEFif, Talent scales with DEFTalent%×Max HPif, Talent scales with Max HPTalent%×EMif, Talent scales with EM\text{BaseDamage} = \begin{cases} \text{Talent\%} \times \text{ATK} & \text{if, Talent scales with ATK} \\ \text{Talent\%} \times \text{DEF} & \text{if, Talent scales with DEF} \\ \text{Talent\%} \times \text{Max HP} & \text{if, Talent scales with Max HP} \\ \text{Talent\%} \times \text{EM} & \text{if, Talent scales with EM} \end{cases}
ATK=(AttackCharacter+AttackWeapon)×(1+AttackBonus)+FlatAttack\text{ATK} = (\text{AttackCharacter} + \text{AttackWeapon}) \times (1 + \text{AttackBonus}) + \text{FlatAttack}
DEF=DefenseCharacter×(1+DefenseBonus)+FlatDefense\text{DEF} = \text{DefenseCharacter} \times (1 + \text{DefenseBonus}) + \text{FlatDefense}
Max HP=HealthCharacter×(1+HealthBonus)+FlatHealth\text{Max HP} = \text{HealthCharacter} \times (1 + \text{HealthBonus}) + \text{FlatHealth}
Formula VariableExplanation
Talent%The scaling percentage of the Talent.
AttackCharacterCharacter's Base ATK.
AttackWeaponWeapon's Base ATK.
AttackBonusSum of all percentage-based ATK Bonuses from weapons, artifacts, and other sources.
FlatAttackSum of all non-percentage-based ATK Bonuses from artifacts, and other sources.
DefenseCharacterCharacter's Base DEF.
DefenseBonusSum of all percentage-based defense bonuses from artifacts, weapons, and other sources.
HealthCharacterCharacter's Base HP.
HealthBonusSum of all percentage-based HP bonuses from artifacts, weapons, and other sources
EMSum of all Elemental Mastery from ascension stat, weapons, artifacts, and other sources.
FlatDamageExtra damage from sources such as Zhongli's A4 or Additive Reactions.
DamageBonusSum of all percentage damage increases from goblets, weapons, set bonuses and other buffs. Excludes Xingqiu's C4 and Yoimiya's Elemental Skill.
SpecialMultiplierApplies to certain character Talents only. See the Special Multiplier section for full details.

Flat Damage Sources

Talents and Constellations
Weapons
Reactions

Critical Hits

CRIT={1+CRITDamageif, CRIT1otherwise\text{CRIT} = \begin{cases} 1 + \text{CRITDamage} & \text{if, CRIT} \\ 1 & \text{otherwise} \end{cases}
AverageCrit=1+clamp{0%,CRITRate,100%}×CRITDamage\text{AverageCrit} = 1 + \text{clamp}\{0\%, \text{CRITRate}, 100\% \} \times \text{CRITDamage}
Formula VariableExplanation
CRITRateThe total CRIT Rate, including the 5% base CRIT Rate and bonuses from weapons, artifacts, etc.
CRITDamageThe total CRIT DMG, including the 50% base CRIT DMG and bonuses from weapons, artifacts, etc.

Enemy Defense

EnemyDefMult=LevelCharacter+100(LevelCharacter+100)+(LevelEnemy+100)×(1DefReduction)×(1DefIgnore)\text{EnemyDefMult} = \frac {\text{Level}_{\text{Character}} + 100} {(\text{Level}_{\text{Character}} + 100) + (\text{Level}_{\text{Enemy}} + 100) \times (1 - \text{DefReduction}) \times (1 - \text{DefIgnore})}
Formula VariableExplanation
LevelCharacterThe player character's level.
LevelEnemyThe enemy's level.
DefReductionThe total defense (but not resistance) reduction from various defense reduction effects.
DefIgnoreThe total defense ignore from effects such as Raiden Shogun's C2 or Yae Miko's C6.
  • DefReduction is hard capped at 90%

Defense Reduction Sources

Enemy Resistance

EnemyResMult={1Resistance2if, Resistance<01Resistanceif, 0Resistance<0.7514×Resistance+1if, Resistance0.75\text{EnemyResMult} = \begin{cases} 1 - \frac{\text{Resistance}}{2} & \text{if, } \text{Resistance} \lt 0 \\ 1 - \text{Resistance} & \text{if, } 0 \le \text{Resistance} \lt 0.75 \\ \frac{1}{4 \times \text{Resistance} + 1} & \text{if, } \text{Resistance} \ge 0.75 \end{cases}
Resistance=BaseResistanceResistanceReduction\text{Resistance} = \text{BaseResistance} - \text{ResistanceReduction}
Formula VariableExplanation
BaseResistanceThe enemy's base resistance to the Element of the attack being used. Enemy Resistances database contains all enemy base Elemental resistances.
ResistanceReductionThe total resistance reduction of the relevant Element from effects such as Superconduct and Viridescent Venerer.

Special Multiplier

Unlike other bonuses, these are directly multiplicative with base Talent scaling. They can be considered a multiplier of the Talent motion value.

SpecialMultiplier={1.5if, Evilsoother triggeredTalent %if, Frozen Wilds or Niwabi Fire-Dance triggered1otherwise\text{SpecialMultiplier} = \begin{cases} 1.5 & \text{if, Evilsoother triggered} \\ \text{Talent \%} & \text{if, Frozen Wilds or Niwabi Fire-Dance triggered} \\ 1 & \text{otherwise} \end{cases}
Formula VariableExplanation
EvilsootherXingqiu’s Constellation 4 ability applies a 1.5 buff to his Elemental Skill.
Frozen WildsAloy's Elemental Skill applies a buff to her Normal Attacks depending on the amount of Coil stacks.
Niwabi Fire-DanceYoimiya's Elemental Skill applies a scaling buff to her Normal Attacks.

Amplifying Reaction

AmplifyingReaction=ReactionMultiplier×(1+2.78×EM1400+EM+ReactionBonus)\text{AmplifyingReaction} = \text{ReactionMultiplier} \times \biggl(1 + \frac{2.78 \times \text{EM}}{1400 + \text{EM}} + \text{ReactionBonus}\biggr)
ReactionMultiplier={2if, triggering Vaporize with Hydro or Melt with Pyro1.5if, triggering Vaporize with Pyro or Melt with Cryo1otherwise\text{ReactionMultiplier} = \begin{cases} 2 & \text{if, triggering Vaporize with {\color{4688ff}Hydro} or Melt with {\color{f68f9a}Pyro}}\\ 1.5 & \text{if, triggering Vaporize with {\color{f68f9a}Pyro} or Melt with {\color{7ba4d3}Cryo}}\\ 1 & \text{otherwise} \end{cases}
Formula VariableExplanation
EMThe character's total Elemental Mastery.
ReactionBonusReaction damage bonuses such as the Crimson Witch 4-Piece set bonus and from Mona's C1 (for Vaporize).

Transformative Reaction

TransformativeReactions= ReactionMultiplier×LevelMultiplier×(1+16×EM2000+EM+ReactionBonus)×EnemyResistanceMultiplier\begin{align*} \text{TransformativeReactions} = & \ \text{ReactionMultiplier} \times \text{LevelMultiplier} \times \biggl(1 + \frac{16 \times \text{EM}}{2000 + \text{EM}} + \text{ReactionBonus} \biggr) \\ & \times \text{EnemyResistanceMultiplier} \end{align*}
ReactionMultiplier={3if, triggering Burgeon and Hyperbloom2if, triggering Overloaded and Bloom1.5if, triggering Shattered1.2×ECTriggersif, triggering Electro-Charged0.6if, triggering Swirl0.5if, triggering Superconduct0.25if, triggering Burning0otherwise\text{ReactionMultiplier} = \begin{cases} 3 & \text{if, triggering {\color{fd9e0d}Burgeon} and {\color{df96fe}Hyperbloom}}\\ 2 & \text{if, triggering {\color{cd7b8d}Overloaded} and {\color{00eb50}Bloom}}\\ 1.5 & \text{if, triggering Shattered}\\ 1.2 \times \text{ECTriggers} & \text{if, triggering {\color{df96fe}Electro-Charged}}\\ 0.6 & \text{if, triggering {\color{5bcba3}Swirl}}\\ 0.5 & \text{if, triggering {\color{b1aeff}Superconduct}}\\ 0.25 & \text{if, triggering {\color{fd9e0d}Burning}}\\ 0 & \text{otherwise} \end{cases}
Formula VariableExplanation
ECTriggersThe number of times Electro-Charged triggers, and depends on the Elemental Gauge strength of the Hydro and Electro Elements applied to the enemy.
EMThe character's total Elemental Mastery.
ReactionBonusIncludes reaction damage bonuses from the 4-Piece set bonuses of Thundering Fury and Viridescent Venerer, Mona's C1, and Nilou's A4.
LevelMultiplierPlayer level multiplier at Lv. : 1446.85
Enemy/environment level multiplier at Lv. : 1202.81
EnemyResistanceMultiplierUses the Enemy Resistance formula above, but for the Element of the Transformative Reaction (Pyro for Overloaded, Physical for Shattered, Electro for Electro-Charged, Cryo for Superconduct, the Element being Swirled for Swirl, and Dendro for Bloom, Bugeon, and Hyperbloom).

Additive Reaction

AdditiveReaction=ReactionMultiplier×LevelMultiplier×(1+5×EM1200+EM+ReactionBonus)\text{AdditiveReaction} = \text{ReactionMultiplier} \times \text{LevelMultiplier} \times \biggl(1 + \frac{5 \times \text{EM}}{1200 + \text{EM}} + \text{ReactionBonus}\biggr)
ReactionMultiplier={1.25 if, triggering Spread1.15 if, triggering Aggravate\text{ReactionMultiplier} = \begin{cases} 1.25 \ \text{if, triggering {\color{00eb50}Spread}}\\ 1.15 \ \text{if, triggering {\color{df96fe}Aggravate}} \end{cases}
Formula VariableExplanation
EMThe character's total Elemental Mastery.
ReactionBonusIncludes reaction damage bonus from 4-Piece set bonus of Thundering Fury.
LevelMultiplierPlayer level multiplier at Lv. : 1446.85
Enemy/environment level multiplier at Lv. : 1202.81

Proc

The damage dealt by weapon and ability procs when they trigger, such as Prototype Archaic or Xiangling's constellation 2. This is dealt as a separate instance of damage from the attack that triggered it.

To calculate this damage, substitute the proc percentage (e.g. 240% for Prototype Archaic R1) for Talent in the damage formula. Note that weapon proc effects always deal Physical damage, and are therefore affected by Physical damage bonuses and Physical resistance, even if an Elemental attack is used to trigger them.

Proc Damage Sources

Characters
Weapons

Additional Notes

Any effect that scales off of a certain stat will not count any buffs that also scale themselves off of someone else's stat in their calculation.

"In order to avoid infinite stacking of in-game bonuses, when an effect confers one attribute as a certain percentage of another attribute, this effect will not then factor into calculations of other similar percentage-based effects." - HoYoverse

Examples of such buffs:

Evidence Vault

📄️ Damage Formula

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