Damage Formula

General Formula for Damage

$$\text{DMG} = (\Sigma(\text{Base DMG} \times \text{BaseDMGMultiplier}) + \text{AdditiveBaseDMGBonus}) \\ \times (1 + \text{DMGBonus} - \text{DMGReduction} {\text{Target}}) \\ \times \text{CRIT} \times \text{EnemyDefMult} \times \text{EnemyResMult} \\ \times \text{AmplifyingReaction} + \text{TransformativeReaction} + \text{Proc} \\$$

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

Base Damage

$$\text{Base DMG} = \begin{cases} \text{Talent\%} \times \text{ATK} & \text{if, Talent scales with ATK} \\ \text{Talent\%} \times \text{DEF} & \text{if, Talent scales with DEF} \\ \text{Talent\%} \times \text{Max HP} & \text{if, Talent scales with Max HP} \\ \text{Talent\%} \times \text{EM} & \text{if, Talent scales with EM} \end{cases}$$ $$\text{ATK} = (\text{AttackCharacter} + \text{AttackWeapon}) \times (1 + \text{AttackBonus}) + \text{FlatAttack}$$ $$\text{DEF} = \text{DefenseCharacter} \times (1 + \text{DefenseBonus}) + \text{FlatDefense}$$ $$\text{Max HP} = \text{HealthCharacter} \times (1 + \text{HealthBonus}) + \text{FlatHealth}$$

Formula Variable	Explanation
Talent%	The scaling percentage of the Talent.
AttackCharacter	Character's Base ATK.
AttackWeapon	Weapon's Base ATK.
AttackBonus	Sum of all percentage-based ATK Bonuses from weapons, artifacts, and other sources.
FlatAttack	Sum of all non-percentage-based ATK Bonuses from artifacts, and other sources.
DefenseCharacter	Character's Base DEF.
DefenseBonus	Sum of all percentage-based defense bonuses from artifacts, weapons, and other sources.
HealthCharacter	Character's Base HP.
HealthBonus	Sum of all percentage-based HP bonuses from artifacts, weapons, and other sources
EM	Sum of all Elemental Mastery from ascension stat, weapons, artifacts, and other sources.
AdditiveBaseDMGBonus	Extra damage from sources such as Zhongli's A4 or Additive Reactions.
DMGBonus	Sum of all percentage damage increases from goblets, weapons, set bonuses and other buffs. Excludes Xingqiu's C4 and Yoimiya's Elemental Skill.
BaseDMGMultiplier	Applies to certain character Talents only. See the Special Multiplier section for full details.

Additive Base DMG Sources

Talents and Constellations

Talents:

• Arataki Itto's Bloodline of the Crimson Oni (A4)
• Cyno's Authority Over the Nine Bows (A4)
• Faruzan's Lost Wisdom of the Seven Caverns (A4)
• Gorou's A Favor Repaid (A4)
• Kuki Shinobu's Heart's Repose (A4)
• Layla's Sweet Slumber Undisturbed (A4)
• Sangonomiya Kokomi's Nereid's Ascension (Elemental Burst)
• Sangonomiya Kokomi's Song of Pearls (A4)
• Shenhe's Spring Spirit Summoning (Elemental Skill) Icy Quills
• Thoma's Flaming Assault (A4)
• Yun Jin's Cliffbreaker's Banner (Elemental Burst)
• Yun Jin's Breaking Conventions (A4)
• Zhongli's Dominance of Earth (A4)

Constellations:

• Albedo's Opening of Phanerozoic (C2)
• Hu Tao's Ominous Rainfall (C2)
• Layla's Starry Illumination (C4)
• Sayu's Sleep O'Clock (C6)
• Wanderer's Shoban: Ostentatious Plumage (C1)

Weapons

• Cinnabar Spindle's Spotless Heart
• Everlasting Moonglow's Byakuya Kougetsu
• Hunter's Path's At the End of the Beast-Paths
• Light of Foliar Incision's Whitemoon Bristle
• Redhorn Stonethresher's Gokadaiou Otogibanashi

Artifacts

• Echoes of an Offering's 4-Piece Set Bonus

Reactions

• Aggravate
• Spread

Critical Hits

$$\text{CRIT} = \begin{cases} 1 + \text{CRITDamage} & \text{if, CRIT} \\ 1 & \text{otherwise} \end{cases}$$ $$\text{AverageCrit} = 1 + \text{clamp}\{0\%, \text{CRITRate}, 100\% \} \times \text{CRITDamage}$$

Formula Variable	Explanation
CRITRate	The total CRIT Rate, including the 5% base CRIT Rate and bonuses from weapons, artifacts, etc.
CRITDamage	The total CRIT DMG, including the 50% base CRIT DMG and bonuses from weapons, artifacts, etc.

Enemy Defense

$$\text{EnemyDefMult} = \frac {\text{Level}_{\text{Character}} + 100} {(\text{Level}_{\text{Character}} + 100) + (\text{Level}_{\text{Enemy}} + 100) \times (1 - \text{DefReduction}) \times (1 - \text{DefIgnore})}$$

Formula Variable	Explanation
LevelCharacter	The player character's level.
LevelEnemy	The enemy's level.
DefReduction	The total defense (but not resistance) reduction from various defense reduction effects.
DefIgnore	The total defense ignore from effects from certain constellations.

• DefReduction is hard capped at 90%

Defense Ignore Sources

Constellations

• Raiden Shogun's Steelbreaker (C2)
• Yae Miko's Forbidden Art: Daisesshou (C6)

Defense Reduction Sources

Talents and Constellations

Talents:

• Lisa's Static Electricity Field (A4): 15%

Constellations:

• Kamisato Ayaka's Ebb and Flow (C4): 30%
• Klee's Explosive Frags (C2): 23%
• Nahida's The Root of All Fullness (C2): 30%
• Razor's Bite (C4): 15%

Enemy Resistance

$$\text{EnemyResMult} = \begin{cases} 1 - \frac{\text{Resistance}}{2} & \text{if, } \text{Resistance} \lt 0 \\ 1 - \text{Resistance} & \text{if, } 0 \le \text{Resistance} \lt 0.75 \\ \frac{1}{4 \times \text{Resistance} + 1} & \text{if, } \text{Resistance} \ge 0.75 \end{cases}$$ $$\text{Resistance} = \text{BaseResistance} - \text{ResistanceReduction}$$

Formula Variable	Explanation
BaseResistance	The enemy's base resistance to the Element of the attack being used. Enemy Resistances database contains all enemy base Elemental resistances.
ResistanceReduction	The total resistance reduction of the relevant Element from effects such as Superconduct and Viridescent Venerer.

Base DMG Multiplier

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

$$\text{BaseDMGMultiplier} = \begin{cases} 2 & \text{if, World-Shaker triggered} \\ 1.5 & \text{if, Evilsoother triggered} \\ \text{Talent \%} & \text{if, Niwabi Fire-Dance or Hanega: Song of the Wind triggered} \\ 1 & \text{otherwise} \end{cases}$$

Formula Variable	Explanation
World-Shaker	Electro Traveler's Constellation 6 ability applies a 2 buff to some attacks of their Elemental Burst.
Hanega: Song of the Wind	Wanderer's Elemental Skill applies a scaling buff to his Normal Attacks.
Evilsoother	Xingqiu’s Constellation 4 ability applies a 1.5 buff to his Elemental Skill.
Niwabi Fire-Dance	Yoimiya's Elemental Skill applies a scaling buff to her Normal Attacks.

Amplifying Reaction

Equals to $1$ if no amplifying reaction is triggered, otherwise:

$$\text{AmplifyingReaction} = \text{ReactionMultiplier} \times \biggl(1 + \frac{2.78 \times \text{EM}}{1400 + \text{EM}} + \text{ReactionBonus}\biggr)$$ $$\text{ReactionMultiplier} = \begin{cases} 2 & \text{if, triggering Vaporize with {\color{4688ff}Hydro} or Melt with {\color{f68f9a}Pyro}}\\ 1.5 & \text{if, triggering Vaporize with {\color{f68f9a}Pyro} or Melt with {\color{7ba4d3}Cryo}}\end{cases}$$

Formula Variable	Explanation
EM	The character's total Elemental Mastery.
ReactionBonus	Reaction damage bonuses such as the Crimson Witch 4-Piece set bonus and from Mona's C1 (for Vaporize).

Transformative Reaction

$$\begin{align*} \text{TransformativeReactions} = & \ \text{ReactionMultiplier} \times \text{LevelMultiplier} \times \biggl(1 + \frac{16 \times \text{EM}}{2000 + \text{EM}} + \text{ReactionBonus} \biggr) \\ & \times \text{EnemyResistanceMultiplier} \end{align*}$$ $$\text{ReactionMultiplier} = \begin{cases} 3 & \text{if, triggering {\color{fd9e0d}Burgeon} and {\color{df96fe}Hyperbloom}}\\ 2 & \text{if, triggering {\color{cd7b8d}Overloaded} and {\color{00eb50}Bloom}}\\ 1.5 & \text{if, triggering Shattered}\\ 1.2 \times \text{ECTriggers} & \text{if, triggering {\color{df96fe}Electro-Charged}}\\ 0.6 & \text{if, triggering {\color{5bcba3}Swirl}}\\ 0.5 & \text{if, triggering {\color{b1aeff}Superconduct}}\\ 0.25 & \text{if, triggering {\color{fd9e0d}Burning}}\\ 0 & \text{otherwise} \end{cases}$$

Formula Variable	Explanation
ECTriggers	The number of times Electro-Charged triggers, and depends on the Elemental Gauge strength of the Hydro and Electro Elements applied to the enemy.
EM	The character's total Elemental Mastery.
ReactionBonus	Includes reaction damage bonuses from the 4-Piece set bonuses of Thundering Fury and Viridescent Venerer, Mona's C1, and Nilou's A4.
LevelMultiplier	Player level multiplier at Lv. : 1446.85 Enemy/environment level multiplier at Lv. : 1202.81
EnemyResistanceMultiplier	Uses 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

$$\text{AdditiveReaction} = \text{ReactionMultiplier} \times \text{LevelMultiplier} \times \biggl(1 + \frac{5 \times \text{EM}}{1200 + \text{EM}} + \text{ReactionBonus}\biggr)$$ $$\text{ReactionMultiplier} = \begin{cases} 1.25 \ \text{if, triggering {\color{00eb50}Spread}}\\ 1.15 \ \text{if, triggering {\color{df96fe}Aggravate}} \end{cases}$$

Formula Variable	Explanation
EM	The character's total Elemental Mastery.
ReactionBonus	Includes reaction damage bonus from 4-Piece set bonus of Thundering Fury.
LevelMultiplier	Player 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

• Anemo Traveler's Slitting Wind (A1)
• Chongyun's Ice Unleashed (C1)
• Collei's Through Hill and Copse (C2)
• Collei's Forest of Falling Arrows (C6)
• Fischl's Stellar Predator (A1)
• Fischl's Undone Be Thy Sinful Hex (A4)
• Fischl's Gaze of the Deep (C1)
• Fischl's Her Pilgrimage of Bleak (C4)
• Fischl's Evernight Raven (C6)
• Geo Traveler's Frenzied Rockslide (A4)
• Kamisato Ayato's Boundless Origin (C6)
• Razor's Lupus Fulguris (C6)
• Tighnari's Karma Adjudged From the Leaden Fruit (C6)
• Xiangling's Oil Meets Fire (C2)

Weapons

• Bows
  • Skyward Harp
  • The Viridescent Hunt

• Claymores
  • Debate Club
  • Luxurious Sea-Lord
  • Prototype Archaic
  • Skyward Pride
  • Snow-Tombed Starsilver

• Polearms
  • Crescent Pike
  • Dragonspine Spear
  • Halberd
  • Skyward Spine

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:

• Sucrose's Mollis Favonius (A4): EM share
• Kaedehara Kazuha's Poetics of Fuubutsu (A4): DMG% buff
• Electro Traveler's Resounding Roar (A4): Energy Recharge buff

Evidence Vault

📄️ Damage Formula

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