Arknights Calculations

I don't like navigating the Arknights wiki, so I'm collecting numbers information like this onto a single page here for easy personal reference instead. When I find the time I'll also cook up a simple calculator to do this kind of math with.

Damage formula

a = Final outgoing damage
b = Initial atk stat
x1 = Sum of all percent atk buffs
x2 = Atk inspiration
y = Final damage multiplier(s)

A percent atk buff is any buff that says it increases attack by a percentage. A final damage modifier says it deals a certain percentage of damage. An operator can have multiple final damage multipliers, for example from a skill + a talent + a module, which all stack multiplicatively.

The outgoing damage is reduced by the target's defensive stats depending on damage type. Defensive stats cannot be lower than 0, and the amount of damage done after the target's defensive stats are applied is always at least 5% of the outgoing damage.

Physical damage

Physical damage is reduced by the target's defense, which reduces the damage by a flat number.

Final damage = [a − (d − if) × (1 − ip)] × (amp × red)
d = [(def + fb) × (1 + pb) − fd] × (1 − pd)

a = Outgoing damage
if = Flat def ignore
ip = Percent def ignore
amp = Sum of all physical damage amplification debuffs
red = Sum of all physical damage reductions

d = Final def stat
def = Target's base def including any stage-specific modifiers like challenge mode buffs
fb = Sum of flat def buffs
pb = Sum of all percent def buffs
fd = Sum of flat def debuffs
pd = Product of all percent def debuffs

Flat defense debuffs from enemies like acid slugs are applied to the base def before any modifiers.

Arts damage

Arts damage is reduced by the target's resistance, which reduces the damage by a percentage.

Final damage = [a × (1 − (r − if) × (1 − ip)/100] × (amp × red)
r = [(res + fb) × (1 + pb) − fd] × (1 − pd)

a = Outgoing damage
if = Flat res ignore
ip = Percent res ignore
amp = Sum of all Arts damage amplifications
red = Sum of all Arts damage reductions

r = Final res stat
res = Target's base res including any stage specific modifiers like challenge mode buffs
fb = Sum of flat res buffs
pb = Sum of percent res buffs
fd = Sum of flat res debuffs
pd = Sum of percent res debuffs

Attack interval

a = 100 ÷ (100 + x/b + y)

a = final attack interval.
b = base attack interval.
x = sum of all base aspd modifiers.
y = flat attack interval modifier.

All aspd buffs and debuffs are additive. Flat interval modifiers are only found in operators' personal skills and cannot be stacked.

Elemental injury

Normal and elite enemies and friendly units need 1000 elemental injury to trigger burst, and bosses need 2000. Take note of whether your source of elemental injury deals it as a percentage of the operator's attack, or as a percentage of their damage done.

Elemental injury is reduced by a percentage based on the target's Effect Resistance. Elemental Damage is a damage type that can only be inflicted on targets under elemental injury burst, and is reduced by a percentage based on Elemental RES.