Knowing Is Half the Battle!
(the other half is the battle with Sanity)
In this reference document we will present what are generally believed to be the damage formulas for Arknights in a concise format and offer links to more indepth information and examples of the formulas presented. The formulas presented here are not of my creation. They were shared with me by Kawa and, to my knowledge, come from the RIHQ Discord. My goal is to share them in a concise format, explain what they mean, and list Operators that have relevant abilities. I am not a mathematical genius, in fact numbers frighten me, so if you find any errors in my calculations or conclusions, please contact me via Discord.
Attacks Per Second Formula
Where,

Attack_Interval = Operators Base Attack Interval, the measure of how long it takes to do one attack (Seconds per Attack)

Attack_Interval_Modifer = Change to Base Attack Interval applied by the Operator’s own Skill. Will say modifies “Attack Interval”.

Attack_Speed_Modifiers = the summation of all +ASPD modifiers
For more details on what these variables mean and how to find them, see our detailed article:

First, Increase/decrease the normal Attack Interval by any Attack Interval change from an active Skill.

Second, increase the attacking rate by a percentage equal to the summation of all the ASPD buffs.

Angelina  Talent  Accelerator Field

Silence  Talent  Booster Injection

The Attack Interval modifier is a flat increase/decrease to the attack interval. Thus, any given value change will have a larger effect on faster attackers than slower ones.

Attack Speed increases are percentile, and thus represent an equal percent increase in damage for any Operator.
Final_ATK (Attack Modifiers)
Where,

Base_Attack = ATK stat of the Operator

Base_ATK_Buff = the summation of all ATK percentage increases

Sora_SK2_Buff = the ATK added by Sora’s Skill 2

Attack_Multiplier_Buff = ATK percentage increase or decrease associated with any Talents or Skills that say things like “Increases ATK to X%” or “ X% of ATK”. Multiple buffs of this type are multiplicative with each other.
For more details on what these variables mean and how to find them, see our detailed article:

Start with Base ATK.

Apply any Base ATK buffs (ATK % with a +).

Add the ATK from Sora’s Skill 2 if it applies

Apply the ATK multiplier buff (ATK % without a +)

Sora  Skill 2  Hymn of Battle  (Note: Sora’s Skill 2 has a unique application in the Final_ATK formula)

Zima  Skill 2  Ursus’s Roar

Castle3  Talent  Tactical Configuration 1

Dobermann  Talent  Starter Instructor

Gavial  Talent  Battlefield Medic

Exusiai  Talent  Angel’s Blessing

Siege  Talent  King of Beasts

Eyjafjalla  Talent  Pyrobreath

Skadi  Talent  Abyssal Predator

Warfarin  Skill  Unstable Plasma

Swire  Talent  Melee Combat Guidance

Sametype Base ATK buffs are additive with each other, where ATK multiplier buffs are multiplicative with each other and Base ATK buffs. This means, all else equal, additional ATK Multiplier buffs will provide better overall performance than additional Base ATK buffs because of the nature of diminishing relative gain of additive buffs.

Sora’s Skill 2 is additive with base ATK buffs, but multiplicative with ATK multiplier buffs. Thus, in general, she will be more effective at improving the latter.
Phys_Damage Formula
Where,

Final_Attack = as described in section above

Defense = the target’s Defense value

Flat_Def_Down = any flat (nonpercentage) reduction to Defense. Note: Flat_Def_Down is listed ingame as a negative number, which is why in the formula it is added to Defense and not subtracted from it. For more details, see the detailed Damage formula article linked below.

Scaling_Def_Down = total Defense reduction percentages applied by debuffs

Phys_Dmg_Taken_Up = abilities that increase Physical damage take

Minimum Physical Damage is 5% of Final_Attack.
For more details on what these variables mean and how to find them, see our detailed article:

Start with the Defense of the enemy target.

Subtract the flat Defense debuffs.

Multiply by the percentage Defense debuffs.

Subtract the result from the Operator’s buffed ATK stat.

Multiply by Physical damage up modifiers

Meteor  Skill  Armor Breaker

Meteor  Skill  Armor Breaker  Spread

Pramanix  Skill  Natural Deterrent

Franka  Talent  Thermite Blade

Franka  Skill  Vorpal Edge

Indra  Skill  ArmorCrusher

Nightmare  Skill  Night Phantom

Cliffheart  Skill  Binding Chains
 Meteorite  Skill  High Explosive Shell
 Ifrit  Skill  Pyroclasm
Included with Arts_Damage Takeaways below.
Arts_Damage Formula
Where,

Final_Attack = as described in section above

Resistance = the target’s Resistance value

Flat_Res_Down = any flat (nonpercentage) reduction to Resistance. Note: Flat_Res_Down is listed ingame as a negative number, which is why in the formula it is added to Resistance and not subtracted from it. For more details, see the detailed Damage formula article linked below.

Scaling_Res_Down = total Resistance reduction percentages applied by debuffs

Arts_Dmg_Taken_Up = abilities that increase Arts damage taken
For more details on what these variables mean and how to find them, see our detailed article:

Start with the Resistance of the enemy target.

Subtract the flat Resistance debuffs.

Multiply by the percentage Resistance debuffs.

Turn what is remaining into a resistance percentage.

Reduce the buffed attack by the resistance percentage.

Multiply by Arts Damage Up modifiers.

Pramanix  Skill  Natural Deterrent

Haze  Talent  Black Mist

Eyjafjalla  Skill  Ignition

Ifrit  Talent  Spiritual Dissolution

Nightmare  Skill  Night Phantom

Cliffheart  Talent  Binding Chains
 Ifrit  Skill  Scorched Earth
 Saria  Skill  Calcification

Skyfire  Talent  Arts Sniper

Physical Damage is a straight subtraction of modified Defense from modified Attack.

Arts damage is the modified ATK reduced by the modified Resistance as a percentage.

Percentage Defense or Resistance reduction modifiers won’t increase damage much against low Defense or Resistance enemies, but become more effective as Defense or Resistance increases.

Flat Defense reduction is basically +damage.

Flat Defense or Resistance reduction will be relatively more effective than percent Defense or Resistance reduction at low Defense or Resistance levels, and less at higher levels.

Percentage Defense or Resistance down debuffs and Physical or Arts Damage Taken Increases are multiplicative to each other, which means each one you add makes all the others more effective.

The higher the ATK amount, the more effective a given percent increase will be.

If ATK is less than Defense, increasing ATK may not result in a damage improvement if the resulting ATK is still less than Defense. Not so for Arts Damage, as a % increase in Attack creates a % increase in damage.

Percentage increases in ATK or decreases in DEF may result in higher or lower corresponding damage increase percentage, depending on actual values, where for Arts damage, percentage increases in ATK or decreases to RES lead to similar changes in damage
Total DPS and HPS

For Arts Damage attacker: Attacks_Per_Second * Arts_Damage

For Physical Damage attacker: Attacks_Per_Second * Phys_Damage

For healer: Attacks_Per_Second * Arts_Damage

(healing is Medic damage to friendly Operators

Where

Attacks_Per_Second = as shown in Section above.

Arts_Damage = as shown in Section above.

Phys_Damage = as shown in Section above.