Damage Calculations

This page lists all the applicable damage formulas for a single fleet. Special cases like Combined Fleets and Land-Based Air Squadrons have their own adjustments to the standard damage formulas. Please see those pages for further details.

Please note that all formulas between [math]\displaystyle{ \lfloor \ \rfloor }[/math] or marked with [math]\displaystyle{ \downarrow }[/math] are rounded down.

• For example, [math]\displaystyle{ \lfloor 4.2 \rfloor = 4 }[/math].
• [math]\displaystyle{ 4.2 \times_\downarrow 1.5 = \lfloor 4.2 \times 1.5 \rfloor = \lfloor 6.3 \rfloor = 6 }[/math], but [math]\displaystyle{ 4.2 \times_\downarrow 1 = 4.2 }[/math] (by definition, [math]\displaystyle{ \times_\downarrow }[/math] is then a non-commutative non-associative operator, it is assumed to be left-associative with lower priority than the usual multiplication operator).

Damage Formula

[math]\displaystyle{ \text{Damage} = \biggl \lfloor \biggl ( \lfloor \text{Atk}_\text{cap} \rfloor \times \text{Mod}_\text{spotting} \times_\downarrow \text{Mod}_\text{AP} \times \text{Mod}_\text{CVCI} \times_\downarrow \text{Crit} \times \text{Mod}_\text{post} - \text{DEF} \biggr ) \times \text{Ammo} \biggr \rfloor }[/math]

• [math]\displaystyle{ \text{Atk}_\text{cap} }[/math] is the Cap Adjusted Attack Power
• [math]\displaystyle{ \text{Mod}_\text{spotting} }[/math] is the bonus from artillery spotting.
• [math]\displaystyle{ \text{Mod}_\text{CVCI} }[/math] is the bonus from carrier cut-ins.
• [math]\displaystyle{ \text{Mod}_\text{AP} }[/math] is the bonus from having an AP shell equipped, if applicable.
• [math]\displaystyle{ \text{Mod}_\text{post} }[/math] is any remaining post-cap modifiers that are applicable.
• [math]\displaystyle{ \text{Crit} }[/math] is the critical strike modifier.
• [math]\displaystyle{ \text{Ammo} }[/math] is the remaining ammunition modifier.
• [math]\displaystyle{ \text{DEF} }[/math] is the defensive power of the target.

Where, Cap Adjusted Attack Power is Basic Attack Power that has been adjusted by applying the damage cap. This only applies if the calculated pre-cap attack power is above the damage cap.

[math]\displaystyle{ \text{Atk}_\text{cap} = \text{Cap} + \sqrt{\left ( \text{Atk}_\text{base} \times \text{Mod}_\text{pre}\right)-\text{Cap}} }[/math]

• [math]\displaystyle{ \text{Cap} }[/math] is the damage cap relevant to the phase.
• [math]\displaystyle{ \text{Atk}_\text{base} }[/math] is the basic attack power of the relevant attack.
• [math]\displaystyle{ \text{Mod}_\text{pre} }[/math] is any pre-cap modifiers that are applicable.

Defense Power

[math]\displaystyle{ \text{DEF} = \left( \text{Armor} \times 0.7 + \text{Armor}_\text{rand} \times 0.6 \right) - \text{Pen} }[/math]

• [math]\displaystyle{ \text{Armor} }[/math] is the armor of the target including all equipment and upgrade bonuses.
• [math]\displaystyle{ \text{Armor}_\text{rand} }[/math] is a random number between [math]\displaystyle{ 0 }[/math] and [math]\displaystyle{ \lfloor\text{Armor}\rfloor - 1 }[/math]
  • Note that it is inclusive, meaning it can also output [math]\displaystyle{ 0 }[/math] and [math]\displaystyle{ \lfloor\text{Armor}\rfloor - 1 }[/math]
• [math]\displaystyle{ \text{Pen} }[/math] is any applicable armor penetration mechanic:
  • See ASW for details on ASW armor penetration,
  • Some debuffs may include armor penetration.

Therefore, the maximum armor value [math]\displaystyle{ \text{Armor} \times 1.3 - 0.6 }[/math] and the minimum armor value is [math]\displaystyle{ \text{Armor} \times 0.7 }[/math]. This makes the maximum defensive power a target can have is 1.3x armor and the lowest is 0.7x armor.

Note:

• The range of armor values is uniformly distributed, every armor roll has the same chance of occurring.

Basic Attack Power Formulas

The following formulas only apply to single fleets. Please see Combined Fleet, Land-Based Air Squadron and Support Expeditions for more details.

Notes:

• [math]\displaystyle{ \text{FP} }[/math] is the firepower of the ship including equipment.
• [math]\displaystyle{ \text{TP} }[/math] is the torpedo of the ship including equipment or the torpedo of a plane.
• [math]\displaystyle{ \text{ASW} }[/math] is the anti-submarine of the ship or equipment.
• [math]\displaystyle{ \text{DB} }[/math] is the dive bombing of the plane.
• [math]\displaystyle{ \bigstar }[/math] is the upgrade bonus of the equipment.
  • See Improvement or Akashi List for upgrade bonus values.
• [math]\displaystyle{ \text{Plane}_\text{Count} }[/math] is the remaining amount of planes in a slot, performing the attack.

Airstrike

This applies to both jet assaults, airstrikes, and LBAS.

[math]\displaystyle{ \text{Airstrike Power} = \text{Type} \times \biggl( \left( \text{DB or TP} + \bigstar \right) \times \sqrt{\text{Plane}_\text{Count}} + 25 \biggr) }[/math]

• [math]\displaystyle{ \text{Type} }[/math] is a multiplier based on the type of the plane. See below for details.

Type		Multiplier	Notes
	Torpedo Bombers	0.8x or 1.5x	The multiplier is chosen randomly. The chance is roughly 50%.
Bomber	Dive Bombers Seaplane Bombers	1.0x
	Jets (During jet assault)	1.0x
	Jets (During normal bombing)	0.7071x

Notes:

• Airstrike power is calculated independently for each equipment slot on the carrier.
• The firepower of the carrier does not affect airstrike power.
• Torpedo Stat from fit does not contribute to airstrike damage
• The power is calculated after the air combat and anti-air fire phases which means bombers getting shot down will affect the final calculation.
• It is not affected by engagement, formation or damage states.
• It is affected by contact.
• For LBAS, the stat used when calculating attack power varies based on the target. Please see LBAS for more details.

Surface Shelling

[math]\displaystyle{ \text{Shelling Power} = \text{FP} + \bigstar + 5 }[/math]

Notes:

• The caliber of the gun does not affect damage.
• Abyssal installations that are not equipped with a plane that has a torpedo or dive bombing stat will use the surface shelling formula for calculating damage.

Carrier Attacks

[math]\displaystyle{ \text{Power}_\text{carrier} = \bigl\lfloor \left( \text{FP} + \left(\text{TP} + \bigstar \right) + \lfloor \text{DB} \times 1.3 \rfloor + \bigstar \right) \times 1.5 \bigr\rfloor + 55 }[/math]

Notes:

• Dive and Torpedo groups contribute, respectively, 1.95 and 1.5 times their dive bomb and torpedo stats towards shelling power
• Torpedo Stat from fit does not contribute to shelling damage
• If a carrier is not equipped with any torpedo or dive bombers, she will not participate in shelling.
  • This also applies if they have lost all bombers during the aerial combat phase.
  • But even if an air group has had all its planes shot down, it will still contribute towards carrier shelling power (if the CV is still capable of attacking).
• Remember that there are potentially two sources of [math]\displaystyle{ \bigstar }[/math] bonuses.
  • Torpedo bomber upgrades to the torpedo stat.
  • Secondary and machine gun upgrades to the firepower stat.
• Slot sizes and the number of remaining aircraft do not affect carrier attack power during shelling.
• Carriers have the easiest time hitting the damage cap. This makes them very powerful assets for the fleet.
• Abyssal installations equipped with a plane that has a torpedo or dive bombing stat will use the carrier formula for determining shelling damage.
• Planes are not shot down when a carrier participates in shelling

Torpedo Attacks

[math]\displaystyle{ \text{Torpedo Power} = \text{TP} + \bigstar + 5 }[/math]

Notes:

• Submarines and Abyssal installations cannot be targeted by torpedoes.
  • If the only available targets are submarines or installations, the attack will trigger but always miss.
• A ship must have a base torpedo stat of more than 0 to perform torpedo attacks.

Anti-Submarine Warfare

For more information on this topic, see Anti-Submarine Warfare.

The stats used to calculate damage against submarines is the ASW.

• When contributing to ASW power, Base ASW is square rooted, while equipment ASW is multiplied by 1.5.
  • Anti-submarine weaponry is therefore the primary source of ASW damage, with the base ship ASW playing a very minor role damage-wise.
  • However, base ship ASW is the primary determinant of whether a ship can reach 100 total ASW to perform "Opening ASW" (OASW) attacks.
• Unlike shelling, ASW damage is capped at 170.

ASW attacks have different modifiers gained from Formations,

• Line Abreast is the main ASW formation, with a 1.3x damage modifier,
• Cruising Formation 1 is the main ASW formation for Combined Fleets, with a 1.3x damage modifier.

Anti-Submarine Formula
[math]\displaystyle{ \text{Atk}_\text{base ASW} = \left( 2\sqrt{\text{ASW}_\text{ship} } + 1.5\text{ASW}_\text{equip} + \bigstar + \text{Type}_\text{ship} \right) \times \text{Mod}_\text{synergy} }[/math] With [math]\displaystyle{ \text{Type}_\text{ship} }[/math] a constant depending on the type of the ship performing the attack. See below for details. Ship Type Constant Ship Types [math]\displaystyle{ \text{Type}_\text{ship} }[/math] Coastal Defense Ships (DE) Destroyers (DD) Light Cruisers (CL/CT) Oilers (AO) (without carrier bomber) 13 Aviation Cruisers (CAV) Aviation Battleships (BBV) Seaplane Tenders (AV) Light Carriers (CVL) Landing Ships (LHA) Oilers (AO) (with carrier bomber) 8 [math]\displaystyle{ \text{Mod}_\text{synergy} }[/math] the synergy multiplier bonus from using certain combinations of ASW equips (see below).
Notes The bonuses do not stack, meaning only the highest possible bonus applies. The exception is the depth charge penetration detailed above. Multiple equipments of the same type still only apply the bonus once. There is an accuracy bonus as well but it is small. Stacking sonars will give a bigger accuracy bonus.

Surface Night Battle

[math]\displaystyle{ \text{Night Battle Power} = \text{FP} + \text{TP} + \bigstar + \text{Mod}_\text{contact} }[/math]

• [math]\displaystyle{ \text{Mod}_\text{contact} }[/math] is the Night Battle Contact if Night Recon is triggered:
  • 5 for the Type 98 Night Recon,
  • 7 for the Type 0 Night Recon & Loire 130M.

Notes:

• Night battle is unaffected by engagement.
  • Exceptions are ASW for night battle nodes and Special Attacks.
• If a night battle special attack is evaded, scratch damage is applied instead.
• Graf Zeppelin, Base Saratoga, Taiyou Kai Ni, Shinyou Kai Ni, Kaga Kai Ni Go, and Ark Royal (with Swordfish) use the surface night battle formula if they are not performing a carrier night attack.
• In night battle versus Abyssal installations, the torpedo stat is ignored.
  • This also means any upgrade bonuses to torpedo power is ignored.

Carrier Night Air Attacks

[math]\displaystyle{ \text{Night Battle Power}_\text{carrier} = \text{FP}_\text{ship} + \sum_\text{All Night Planes} \text{FP}_\text{night plane} + \text{TP}_\text{night plane} + \text{DB}_\text{night plane} + \text{Night Plane Bonus} }[/math]

Where:

[math]\displaystyle{ \text{Night Plane Bonus} = \mathrm{A} \times \text{Plane}_\text{Count} + \mathrm{B} \times \left( \text{FP}_\text{night plane} + \text{TP}_\text{night plane} + \text{DB}_\text{night plane} + \text{ASW}_\text{night plane} \right) \times \sqrt{\text{Plane}_\text{Count}} + \sqrt{\bigstar} }[/math]

• [math]\displaystyle{ \mathrm{A} }[/math] is:
  • 3 for night planes,
  • 0 for Swordfish
    
    , Zero FB Iwai and Suisei Photobomb.
• [math]\displaystyle{ \mathrm{B} }[/math] is:
  • 0.45 for night planes,
  • 0.3 for Swordfish
    
    , Zero FB Iwai and Suisei Photobomb.

Notes:

• Carriers must be equipped with a Night Operation Aviation Personnel or Night Operation Aviation Personnel + Skilled Deckhands in addition to night attack capable planes in order to perform carrier night attacks. Night Carriers (CVN) are CV/CVL capable of Carrier Night Air Attacks without needing a NOAP
  .
• If the carrier night attack is evaded, it deals scratch damage instead.
• Unlike daytime carrier attacks, it is possible to attack even if no bombers are equipped.
  • Night fighters are still needed to trigger the attack.
• Like daytime carrier attacks, carriers are unable to attack if moderately damaged or worse.
  • Armored carriers are only disabled at heavy damage.
  • Carriers that can use the night battle shelling formula will use that instead if moderately damaged.
• The formula only takes into account the base stats of the carrier and night attack capable planes equipped.
  • The hidden upgrade bonus to stats is not taken into account.
  • This means any other stats and upgrade bonuses from equipment like guns and non-night capable planes are ignored.
  • This also means that visible Torpedo Stat Fit Bonus from Planes is also ignored
• Certain carriers (see here) are capable of performing night attacks but they are not carrier night air attacks and are just normal shelling attacks. Please see Carrier Night Attacks for more details.

Anti-Installation Attacks

See the Anti-Installation page.

Attack Power Corrections

After calculating the basic attack power of the attack being made, it is then adjusted based on various factors. Attack power modifiers can be split into pre- and post-cap modifiers. Post-cap modifiers are more powerful to have because they aren't reduced by the cap.

Attack Power Cap

The attack power cap varies depending on the phase of combat it is in.

• Support, ASW, Airstrike, LBAS - 170
• Opening and closing torpedo - 180
• Day shelling - 220
• Night battle - 360

Notes:

• Any excess firepower above this cap is square rooted. Please see the damage formula for how it is applied.
• It is still worth aiming to go above the attack power cap because some pre-cap modifiers can severely reduce the attack power.

Pre-cap Modifiers

Engagement

For more details on engagement, please see Engagement Form.

Form	Damage Modifier	Chance	Chance with Saiun
Parallel Engagement 同航戦 (Doukousen, 同航戦?)	100%	45%	45%
Head-on Engagement 反航戦 (Hankousen, 反航戦?)	80%	30%	40%
Crossing the T (Advantage) T字戦有利 (T Ji-sen Yuuri, T字戦有利?)	120%	15%	15%
Crossing the T (Disadvantage) T字戦不利 (T Ji-sen Furi, T字戦不利?)	60%	10%	0%

• All engagement forms affect both sides equally, including crossing the T (Advantage or Disadvantage).
• Night battle and aerial combat are not affected by engagement.
  • The exception to this are ASW and Special Attacks.
• OASW and opening torpedoes are affected by engagement even though it is only displayed after those phases.
• Equipping a Saiun
  
  effectively makes what would have been Crossing the T (Disadvantage) become Head-on engagement.

Notes:

• It is useful in some situations to not take the Saiun in order to get Crossing the T (Disadvantage). This is because it can also hamper the enemy from damaging the fleet.

Formation

For more details on formation, please see Formation Selection.

Formation Attack Power Modifiers
Formation	Shelling	Torpedo	ASW	Night Battle
Line Ahead 単縦陣 (Tanjuu-jin, 単縦陣?)	100%	100%	60%	100%
Double Line 複縦陣 (Fukujuu-jin, 複縦陣?)	80%	80%	80%	100%
Diamond 輪形陣 (Rinkei-jin, 輪形陣?)	70%	70%	120%	100%
Echelon 梯形陣 (Teikei-jin, 梯形陣?)	75%	60%	110%	100%
Line Abreast 単横陣 (Tan'ou-jin, 単横陣?)	60%	60%	130%	100%
Vanguard 警戒陣 (Keikai-jin, 警戒陣?)	50%	100%	100%	50%
	100%	100%	60%	100%

Damage State

Damage State	Shelling	Torpedo	ASW
Lightly Damaged (小破)	100%	100%	100%
Moderately Damaged (中破)	70%	80%	70%
Heavily Damaged (大破)	40%	0%	40%

Notes:

• Damage state does not affect aerial combat.
  • It will affect carrier attacks in the shelling phase.

Night Battle Special Attacks

For more details please see Night Special Attacks.

Gun Fit Bonuses

Unlike the other pre-cap bonuses, this is just an additive firepower bonus added for light cruisers and Italian heavy cruisers when equipped with certain guns. The bonus is minor, please refer to Hidden Fit Bonuses for more details.

Post-cap Modifiers

Aerial Contact

For more details please see Aerial Combat.

During aerial combat, there is a chance for the ships to trigger Contact. When it is triggered, the is a bonus multiplier applied to airstrike damage depending on the accuracy of the plane that triggered contact.

Accuracy	Damage Modifier
0	112%
1	112%
2	117%
3+	120%

Artillery Spotting

For more details, please see Artillery Spotting

Attack Type	Prerequisites	Post-cap Damage Modifier	Accuracy Modifier	Hits	Notes
Main Zuiun Cut-in (Zuiun CI)		1.35	?	1	Ise-class Kai Ni only
Main Suisei Cut-in (Suisei CI)		1.3	?	1
Main AP Shell Cut-in (APCI)		1.5	1.2	1
Secondary AP Shell Cut-in (Sec APCI)		1.3	1.3	1
Secondary Radar Cut-in (Radar CI)		1.2	1.5	1
Secondary Cut-in (Sec CI)		1.1	1.3	1
Double Attack (DA)		1.2	1.1	2

Carrier Cut-In Attacks

For more details, please see Carrier Cut-In Attacks.

Attack Type	Prerequisites	Post-cap Damage Modifier	Accuracy Modifier	Hits
Fighter-Bomber-Attacker (FBA)		1.25	1.2~1.3?	1
Bomber-Bomber-Attacker (BBA)		1.2	1.2~1.3?	1
Bomber-Attacker (BA)		1.15	1.2~1.3?	1

Armor-Piercing Modifier

During day combat, certain enemy ships take extra damage from AP Shells

.

Type	Modifier
	1.08
	1.10
	1.15
	1.15

• It is inadvisable to run any of the other setups beyond the most basic Gun+AP. This is because the other setups will interfere with artillery spotting and cost the better attack bonuses.
• The bonus applies when attacking battleships (including aviation), heavy cruisers (including aviation), carriers, and installations.
  • It also applies to demon, princess, water demon, and imp enemies that are classified as one of the above. This means that destroyer, light cruiser seaplane tender, and air-defense bosses are exempt.

Anti-Installation Equipment Modifiers

See the Anti-Installation page.

Critical Strikes

For more details on how critical chance is calculated, please see Accuracy, Evasion and Criticals.

Normal Criticals

Attack Type	Modifier
Normal	100%
Critical	150%

Plane Proficiency Critical Modifier

Carriers get a bonus critical modifier when equipped with high proficiency planes. This modifier is multiplicative with the normal critical modifier. For more details, please see Plane Proficiency

• For Carrier Attacks, they gain a 1.2 critical bonus multiplier for a ❱❱ plane in the top slot and an additional 0.1 for every other ❱❱ plane.
  • For example, a carrier with two max proficiency planes (with one in the top slot) would get a critical bonus of: (1.2 + 0.1) x 1.5 = 1.95.
• For Carrier Cut-In Attacks, they gain a 1.106 bonus when a ❱❱ plane is selected to participate in the attack and an additional +0.15 if one of the selected planes is in the top slot.

Ammunition Modifier

The damage of the fleet is reduced once their ammunition falls below 50%. This modifier cannot go above 1. The formula use to determine this is:

[math]\displaystyle{ \text{Ammo} = \dfrac{\text{Remaining Ammo %}}{50} }[/math]

Remaining Ammo	Ammo Modifier	Notes
>50%	100%
40~49%	80%	4th Battle
30~39%	60%
20~29%	40%	5th Battle
10-19%	20%
0%	0%	6th Battle

• The battle number indicated in the notes assumes only normal surface engagements. Engaging in night battles and other special engagements can change that number.
• Whatever ammunition modifier applies in day battle carries over to night battle.
• Maelstroms that reduce ammunition also count towards this modifier.
• Using AO equipped with Underway Replenishment is a way to medigate ammo penalties.
• The ammunition modifier affects aerial battle.
• Once a ship hits 0% ammo, all attacks become scratch damage.
• Scratch damage is unaffected by the ammunition modifier.
• Debuffs are affected by the ammunition modifier.

Miscellaneous Damage Modifiers

Scratch Damage

If a special attack is evaded, the target's armor cannot be penetrated, or the ammo count hits 0; attacks will deal "scratch damage" instead, also called "chip damage".

• Scratch damage is dealt as a percentage of remaining HP calculated using the following formula:

[math]\displaystyle{ \text{scratch} = \text{HP}_\text{current} \times 0.06 + \text{HP}_\text{rand} \times 0.08 }[/math]

• [math]\displaystyle{ \text{HP}_\text{current} }[/math] is the current HP of the target.
• [math]\displaystyle{ \text{HP}_\text{rand} }[/math] is a random HP number between 0 and [math]\displaystyle{ \text{HP}_\text{current} - 1 }[/math]

Therefore the maximum possible scratch damage [math]\displaystyle{ \text{HP}_\text{current} \times 0.14 - 0.08 }[/math] and the minimum damage is [math]\displaystyle{ \text{HP}_\text{current} \times 0.06 }[/math]. Meaning scratch damage is generally between 6-14% of current HP.

• If the target's HP is low, it is possible for the result of the formula to return a result of 0. Remember that all formulas are rounded down.
  • This means the target's HP cannot be reduced to 0 by scratch damage.

Historical Bonus

On almost every Event map, as well as some regular maps (7-4 so far), certain ships, types of ships, equipment, or types of equipment will bring bonuses.

• Those bonuses are most of the time raw damages multipliers, and sometimes, accuracy bonuses.
• Bonuses are independent to each ship, so only the ships with any historical bonus or ships equipped with historical equipment will be affected.
• Bonuses may be applicable to some part of a map only, such as specific phases of nodes.

This mechanic is here to encourage the use of "historically significant fleets and setups".

• By nature, historical bonuses are arbitrary, so refer to each individual map to see what bonuses are applicable.

Debuffs

Debuffs are a special case that only applies during events. Certain event maps have debuff mechanics that require meeting certain conditions to trigger them. Debuffs can be either a reduction to the enemy's armor or a post-cap damage modifier for the fleet.

Notes:

• Debuffs are affected by the remaining ammo modifier.

Overkill Protection

When a ship in the fleet takes more damage than her current HP, she will take a percentage of her current HP in damage instead.

• The ship must be the flagship OR
• The ship must not be heavily damaged nor red morale at the start of the battle.
  • If the ship has red morale, she will just have her HP reduced to 1.

[math]\displaystyle{ \text{Overkill} = \text{HP}_\text{current} \times 0.5 + \text{HP}_\text{rand} \times 0.3 }[/math]

• [math]\displaystyle{ \text{HP}_\text{current} }[/math] is the current HP of the ship.
• [math]\displaystyle{ \text{HP}_\text{rand} }[/math] is a random HP number between 0 and [math]\displaystyle{ \text{HP}_\text{current} - 1 }[/math]

Therefore, the maximum damage from overkill protection is [math]\displaystyle{ \text{HP}_\text{current} \times 0.8 - 0.3 }[/math] and the minimum damage is [math]\displaystyle{ \text{HP}_\text{current} \times 0.5 }[/math]. Meaning overkill protection will take off between 50-80% of the ship's current HP.

Important Information

• In general:
  • Overkill protection is most applicable to DDs.
    • The most pronounced effects of overkill protection occur at low HP
    • It is also the primary means of surviving a hit they fail to evade
    • For example, a 32HP DD has a 15.5% chance of being heavily damage by a BB hime, while a 31 HP DD has just a 6.5% chance
    • This has great implications when marrying ships, 36 HP has one of the highest chances of a taiha
  • Odd numbered HP is better when overkill protection is triggered. This is because the damage calculations round down, reducing the likelihood of being knocked down to heavy damage.
  • This mechanism is most applicable to ships at full HP. Once a ship starts taking damage, the utility of overkill protection diminishes
• As a rule, ships with HP that is divisible by 4 have worse survivability.