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# Damage Formula

$\text{Damage} = \left [ \left [ \left [ \text{Atk}_\text{cap} \times \text{Mod}_\text{post}\right]\times \text{Crit}\right]-\text{DEF}\right]\times \text{Ammo}$

Where, Cap Adjusted Attack Power is Basic Attack Power that has been adjusted by applying the damage cap.

$\text{Atk}_\text{cap} = \text{Cap} + \sqrt{\left [ \text{Atk}_\text{basic} \times \text{Mod}_\text{pre}\right]-\text{Cap}}$

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

Important Notes

• Pre- and post-cap multipliers are multiplicative.
• Results are rounded down to the nearest whole number. I.e. 4.2 → 4.

# Defense Power

$\text{DEF} = \left[ \text{Armour} \times 0.7 + \text{Armour}_\text{rand} \times 0.6 \right] - \text{Debuff}$

• $\text{Armour}$ is the armour of the target.
• $\text{Armour}_\text{rand}$ is a random number between 0 and $\text{Armour} - 1$

TTherefore, the maximum damage percentage dealt by overkill protection is $\text{HP}_\text{current} \times 1.3 - 0.6$ and the minimum percentage dealt is $\text{HP}_\text{current} \times 0.7$. his makes the maximum defensive power a target can have is 1.3x armour and the lowest is 0.7x armour.

# 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.

Important Notes

• $\text{FP}$ is the firepower of the ship including equipment.
• $\text{TRP}$ is the torpedo power of the ship including equipment or plane.
• $\text{ASW}$ is the anti-submarine power of the ship or equipment.
• $\text{DB}$ is the dive bombing power of the plane.
• $\bigstar$ is the upgrade bonus of the equipment.

## Airstrike

This applies to both jet assaults and airstrikes.

$\text{Bombing Power} = \text{Type} \times \left[ \left[ \left[ \text{DB}\ OR\ \text{TRP} + \bigstar \right] \times \sqrt{\text{Count}_\text{Plane}}\right] + 25\right]$

• $\text{Type}$ is a multiplier based on the type of the plane. See below for details.
• $\text{Count}_\text{Plane}$ is the number of planes performing the attack.
Type Multiplier Notes
Torpedo Bombers 0.8x or 1.5x The multiplier is chosen randomly. The chance is roughly 50%.
Dive Bombers

Seaplane Bombers
Fighter Bombers

1.0x
Jets

(During jet assault)

1.0x
Jets

(During normal bombing)

0.7071x

Important Notes

• Bombing power is calculated independently for each equipment slot on the carrier.
• The firepower of the carrier does not affect bombing power.
• 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.

## Surface Shelling

$\text{Shelling Power} = \text{FP} + \bigstar + 5$

Important 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

$\text{Power}_\text{carrier} = \left[ \text{FP} + \text{TRP} + \bigstar + \left[ \text{DB} \times 1.3 \right] \times 1.5 \right] + 55$

Important Notes

• Slot sizes and the number of remaining aircraft does not affect carrier attack power during shelling.
• 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.
• 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.

Brief: Understanding the Carrier Formula

• Dive and Torpedo groups contribute, respectively, twice (1.95) and 1.5 times their dive bomb and torpedo stats towards shelling power
• 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)
• Planes are not shot down when a carrier participates in shelling

## Torpedo Attacks

$\text{Torpedo Power} = \text{TRP} + \bigstar + 5$

Important 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

$\text{ASW Power} = \left[ \sqrt{\text{ASW}_\text{ship}} \times 2 + \text{ASW}_\text{equip} \times 1.5 + \bigstar + \text{Type}_\text{ship} \right] \times \text{Mod}_\text{synergy}$

• $\text{Type}_\text{ship}$ is a constant depending on the type of the ship performing the attack. See below for details.
• $\text{Mod}_\text{synergy}$ is the synergy multiplier bonus from using certain combinations of ASW equips. See below for details.
Ship Type Constant
Constant Ship Types
13 Destroyer Escorts, Destroyers, Light Cruisers, Oilers (without seaplane bombers, torpedo bombers or rotary-wing aircraft equiped)
8 Aviation Cruisers, Aviation Battleships, Seaplane Tenders, Light Carriers, Landing Ships, Oilers (with seaplane bombers, torpedo bombers or rotary-wing aircraft equiped)
ASW Synergy Bonus
Equipment Combination Bonus
Depth Charge + Depth Charge Projector + Sonar 1.4375x
Depth Charge Projector + Sonar 1.15x
Depth Charge + Sonar 1.15x
Depth Charge + Depth Charge Projector 1.1x

Understanding the ASW Formula

• When contributing to ASW power, Base ASW is square rooted, while equipment ASW is multiplied by 1.5
• ASW equipment is therefore the primary source of ASW damage, with base ASW playing a very minor role
• However, base ASW is the primary determinant of whether a ship can reach 100 total ASW to perform opening ASW attacks
• Submarines cannot take more than scratch damage at night (and therefore cannot be sunk)
• The exception to this rule is when a battle starts at night, or when in a combined fleet
• It is possible to perform opening ASW attacks when certain conditions are achieved. For more details, please see Opening Anti-Submarine Warfare.
• As performing an opening attack effectively doubles your damage output, reaching this OASW threshold is in general more important than tacking on additional synergy

## Surface Night Battle

$\text{Night Battle Power} = \text{FP} + \text{TRP} + \bigstar + \text{Contact}_\text{NB}$

• $\text{Contact}_\text{NB}$ is the Night Battle Contact constant of +5 if triggered.

Important Notes

• Night battle is unaffected by engagement.
• If a night battle special attack is evaded, chip damage is applied instead.
• Graf Zeppelin, Base Saratoga, Taiyou Kai Ni, 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 not counted.
• This also means any upgrade bonuses to torpedo power is ignored.

## Carrier Night Cut-In

$\text{Night Battle Power}_\text{carrier} = \text{FP}_\text{ship} + \text{FP}_\text{night plane} + \text{TRP}_\text{night plane} + \text{DB}_\text{night plane} + \sum{\text{Night Plane Bonus}}$

Where:

$\text{Night Plane Bonus} = \mathrm{A} \times \text{Count}_\text{plane} + \mathrm{B} \times \left[ \text{FP}_\text{night plane} + \text{TRP}_\text{night plane} + \text{DB}_\text{night plane} + \text{ASW}_\text{night plane} \right] \times \sqrt{\text{Count}_\text{plane}} + \sqrt{\bigstar}$

Important 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.
• If the carrier night attack is evaded, it deals chip damage instead.
• Unlike daytime carrier attacks, it is possible to attack even if no bombers are equipped.
• You still need night fighters to trigger the attack.
• Like daytime carrier attacks, carriers are unable to attack if moderately damaged or worse.
• Armoured 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 (includes upgrade bonuses from night capable planes).
• This means any other stats and upgrade bonuses from equipment like guns and non-night capable planes are ignored.

## Anti-Installation Attacks

$\text{Anti-Installation Power} = \text{Atk} \times \text{Mod}_\text{A} + \text{Mod}_\text{B}$

• $\text{Atk}$ is the basic attack power of shelling, carrier attacks, night battle or carrier night attacks with the torpedo stat ignored.
• $\text{Mod}_\text{A}$ are the multiplicative anti-installation bonuses. See below for details.
• $\text{Mod}_\text{B}$ are the additive anti-installation bonuses. See below for details
Multiplicative Bonuses
Equipment Name Artillery Imp Isolated Island Demon Soft-Skinned[1]
Single Multiple Single Multiple Single Multiple
Anti-Aircraft Shells - 1.75 2.5
Armour-Piercing Shells 1.85 - -
WG42 (Wurfgerät 42) 1.6 2.72 1.4 2.1 1.3 1.82
Shipborne Model Type 4 20cm Anti-ground Rocket Launcher 1.5 2.7 1.3 2.145 1.25 1.875
Mortars 1.3 1.95 1.2 1.68 1.2 1.56
Landing Crafts 1.8 1.8 1.4
Toku Daihatsu-class Landing Craft 1.15 1.15 1.15
Daihatsu-class Landing Craft (Type 89 Medium Tanks & Marines) 1.5 2.1 1.2 1.68 1.5 1.95
Toku Daihatsu Landing Craft + 11th Tank Regiment 1.8 1.8 1.8
Landing Craft Upgrade Bonus $1 + \dfrac{\left( \text{Average Landing Craft}\ \bigstar \right)}{50}$
Type 2 Ka-Mi Tank 2.4 3.24 2.4 3.24 1.5 1.8
Tank Upgrade Bonus $1 + \dfrac{\left( \text{Average Landing Craft}\ \bigstar \right)}{30}$
Dive Bombers[2] 1.4 1.4 -
Seaplane Bombers
1.5 - 1.2
Destroyers
1.4 - -
1. Only certain dive bombers are able to attack installations in shelling.
Equipment Name Number Equipped
1 2 3 4
WG42 (Wurfgerät 42) 75 110 140 160
Shipborne Model Type 4 20cm Anti-ground Rocket Launcher 55 115 ?? ??
Type 2 12cm Mortar Kai 30 55 75 ??
Type 2 12cm Mortar Kai (Concentrated Deployment) 60 110 ?? ??
Toku Daihatsu Landing Craft + 11th Tank Regiment 25 - - -
Submarines 30
• Question marks indicate values that haven't been tested.

Important Notes

• For the Toku Daihatsu, T98+Marines and 11th Tank Regiment, they get both the regular Daihatsu bonus and their own special bonus.
• All multipliers used in determining anti-installation power are pre-cap.
• The amount of multipliers available make even low firepower ships like destroyers viable anti-installation ships.

# 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, opening and closing torpedo - 150
• Day shelling - 180
• Night battle - 300

Important 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 your attack power.

## Pre-cap Modifiers

### Engagement

For more details on engagement, please see Engagement Form.

Form Damage Modifier Chance Chance with Saiun
Parallel Engagement

100% 45% 45%

80% 30% 40%
T字戦有利 (T Ji-sen Yuuri?)
120% 15% 15%
T字戦不利 (T Ji-sen Furi?)
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 night battle nodes.
• 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.

Important 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 hamper the enemy from damaging your fleet as much as it hampers yours.

### Formation

For more details on formation, please see Formation Selection.

Formation Attack Power Modifiers
Formation Shelling Torpedo Anti-Submarine Night Battle

100% 100% 60% 100%
Double Line

80% 80% 80% 100%
Diamond

70% 70% 120% 100%
Echelon

75% 60% 110% 100%
Line Abreast

60% 60% 130% 100%
Vanguard[1]

50% 100% 100% 50%
100% 100% 60% 100%
1. The direct translation of "Keikai" is "alert".

### Damage State

Damage State Shelling Torpedo Anti-Submarine
Lightly Damaged

(小破)

100% 100% 100%
Moderately Damaged

(中破)

70% 80% 70%
Heavily Damaged

(大破)

40% 0% 40%

Important 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 Battle Special Attacks.

Attack Type Number of Equipment Multiplier No. of Attacks Notes
Main Gun
Secondary Gun
Torpedo
Skilled Lookout
Destroyer Lookout
- - 1 1 1 - 120% 1 Destroyers only.

Destroyer Mixed

1 - 1 - 1 - 130% 1 Destroyers only
Special Destroyer Mixed
1[2] - 1 - 1 - 162.5% 1 Destroyers only
Torpedo/Torpedo/Torpedo
Submarine Torpedo
- - 2[3][4] - - 1 175% 2 Submarines only
Torpedo/Torpedo/Torpedo
Torpedo
- - 2 - - - 150% 2
Main/Main/Main
Gun
3 - - - - - 200% 1
Main/Main/Secondary
Mixed Gun
2 1 - - - - 175% 1
Main/Torpedo/Torpedo
Mixed Torpedo
1 - 1 - - - 130% 2
Double Attack 2 - - - - 120% 2
1. Special cut in for the 12.7cm Twin Mount Type-D Kai 2.
2. Only applies to the Late Model Bow Torpedo Mount (6 Tubes) and Skilled SONAR Personnel + Late Model Bow Torpedo Mount (6 Tubes). |style="text-align: center; border-style: solid; border-width: 1px; width:10%;"| - |style="text-align: center; border-style: solid; border-width: 1px; width:10%;"| - |style="text-align: center; border-style: solid; border-width: 1px; width:10%;"| - |style="text-align: center; border-style: solid; border-width: 1px; width:2.5%;"| 160% |style="text-align: center; border-style: solid; border-width: 1px; width:2.5%;"| 2 |style="text-align: center; border-style: solid; border-width: 1px; width:15%;"| Submarines only |- |style="text-align: center; border-style: solid; border-width: 1px; width:10%;"| Torpedo/Torpedo/Sub RADAR
Submarine Radar |style="text-align: center; border-style: solid; border-width: 1px; width:10%;"| - |style="text-align: center; border-style: solid; border-width: 1px; width:10%;"| - |style="text-align: center; border-style: solid; border-width: 1px; width:10%;"| 1
3. As above.

### Carrier Night Attacks

For more details please see Carrier Night Attacks.

Type Modifier Notes
Cut-In 2x Night Fighter

1x Night Bomber

1.25
1x Night Fighter

1x Night Bomber

1.2
3x Night Fighter 1.18
2x Night Fighter

Other

Night Fighter

Night Bomber
Other

Night Fighter

2x Other

Normal Attack 1.0

### 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 the gun 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 your 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 Bonus
0 112%
0 112%
2 117%
3 120%

### Artillery Spotting

For more details, please see Artillery Spotting

Type Modifier Notes
Cut-In 2x Main Gun

Armour-Piercing Shell

1.5
Main Gun

Secondary Gun
Armour-Piercing Shell

1.3
Main Gun

Secondary Gun

1.2
Main Gun

Secondary Gun

1.1
Double Attack 1.2x2
Normal Attack 1.0

### Carrier Cut-In Attacks

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

Type Modifier Notes
Cut-In Fighter

Dive Bomber
Torpedo Bomber

1.25
2x Dive Bomber

Torpedo Bomber Armour-Piercing Shell

1.2
Dive Bomber

Torpedo Bomber

1.15
Normal Attack 1.0

### Armour-Piercing Modifier

During day combat, certain enemy ships take extra damage from armour-piercing shells.

Type Modifier
Main Gun

Armour-Piercing Shell

1.08
Main Gun

Armour-Piercing Shell

1.10
Main Gun

Secondary Gun
Armour-Piercing Shell

1.15
Main Gun

Secondary Gun
Armour-Piercing Shell

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 you 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

Multiplicative Bonuses
Equipment Name Supply Depot Princess
Single Multiple
Anti-Aircraft Shells -
Armour-Piercing Shells -
WG42 (Wurfgerät 42) 1.25 1.625
Shipborne Model Type 4 20cm Anti-ground Rocket Launcher 1.2 1.68
Mortars 1.15 1.38
Landing Crafts 1.7
Toku Daihatsu-class Landing Craft 1.2
Daihatsu-class Landing Craft (Type 89 Medium Tanks & Marines) 1.3 2.08
Toku Daihatsu Landing Craft + 11th Tank Regiment -
Landing Craft Upgrade Bonus $1 + \dfrac{\left( \text{Average Landing Craft}\ \bigstar \right)}{50}$
Type 2 Ka-Mi Tank 1.7 2.55
Tank Upgrade Bonus $1 + \dfrac{\left( \text{Average Landing Craft}\ \bigstar \right)}{30}$
Dive Bombers[1] -
Seaplane Bombers
-
Destroyers
-
1. Only certain dive bombers are able to attack installations in shelling.

Important Notes

• Carrier-based dive bombers, seaplane bombers and land-based attack aircraft have further multiplicative and additive post-cap bonuses versus certain installations.
• Artillery Imp - 1.55x
• Isolated Island Demon - 1.7x
• Supply Depot Princess - +100
• For the Toku Daihatsu, T98+Marines and 11th Tank Regiment, they get both the regular Daihatsu bonus and their own special bonus.
• The amount of multipliers available make even low firepower ships like destroyers viable anti-installation ships.

# 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

Carrier Attack Modifier $\text{Mod}_\text{CVAtk} = 1 + \text{Count}_\text{equipped} \times 0.1 + 0.1\text{(If max proficiency plane in first slot)}$

• $\text{Count}_\text{equipped}$ is the number of max proficiency planes equipped.
• This means a carrier with two maxed proficiency planes equipped in the top two slots, it will have a 1.3x bonus. This makes her total critical strike modifier 1.95x (1.5 x 1.3).
• This also applies to carrier night attacks.
• Unlike other carrier night attacks formulas, non-night capable planes are taken into account for calculating the proficiency critical bonus.

Carrier Cut-In Attacks $\text{Mod}_\text{CVCI} = 1.016 + 0.15\text{(If the plane in the first slot participates in the attack)}$

• The average skill level of all planes is taken into account when calculating the modifier. The 1.106 value assumes all planes equipped are of max proficiency.
• If you have multiple aircraft of the same type equipped, the plane in the first slot will always take priority.

# Ammunition Modifier

The damage of your fleet is reduced once their ammunition falls below 50%. The formula use to determine this is:

$\text{Ammo} = \dfrac{\text{Remaining Ammo %}}{50}$

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 battle 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.
• The low ammo penalty can be counteracted with the Maritime Resupply item. Please see the page for more details.
• The ammunition modifier affects aerial battle.
• Once you hit 0% ammo, all attacks become chip damage.
• Chip damage is unaffected by the ammunition modifier.
• Debuffs are affected by the ammunition modifier.

# Miscellaneous Damage Modifiers

## Chip Damage

In the event that a special attack is evaded, you are unable to penetrate the target's armour or your ammunition hits 0; attacks will deal chip damage instead. Chip damage is dealt as a percentage of remaining HP calculated using the following formula:

$\text{Chip %} = \text{HP}_\text{current} \times 0.06 + \text{HP}_\text{rand} \times 0.08$

• $\text{HP}_\text{current}$ is the current HP of the target.
• $\text{HP}_\text{rand}$ is a random HP number between 0 and $\text{HP}_\text{current} - 1$

Therefore the maximum damage percentage dealt by overkill protection is $\text{HP}_\text{current} \times 0.14 - 0.08$ and the minimum percentage dealt is $\text{HP}_\text{current} \times 0.06$. Meaning chip damage is generally between 6-14%.

• 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 chip damage.

## Debuffs

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

Important Notes

• Debuffs are affected by the remaining ammo modifier.

# Overkill Protection

When a ship in your 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 and red morale at the start of the battle.
• If the ship has red morale, she will just have her HP reduced to 1.

$\text{Chip %} = \text{HP}_\text{current} \times 0.5 + \text{HP}_\text{rand} \times 0.3$

• $\text{HP}_\text{current}$ is the current HP of your ship.
• $\text{HP}_\text{rand}$ is a random HP number between 0 and $\text{HP}_\text{current} - 1$

Therefore, the maximum damage percentage dealt by overkill protection is $\text{HP}_\text{current} \times 0.8 - 0.3$ and the minimum percentage dealt is $\text{HP}_\text{current} \times 0.5$. Meaning overkill protection will take off between 50-80% of your ship's remaining 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.