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Damage Calculations
This page lists all the applicable damage formulas for a single fleet. Special cases like Combined Fleets and LandBased 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 noncommutative nonassociative operator, it is assumed to be leftassociative 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]
With:
 [math]\displaystyle{ \text{Atk}_\text{cap} }[/math] the Cap Adjusted Attack Power,
 [math]\displaystyle{ \text{Mod}_\text{spotting} }[/math] the bonus from artillery spotting,
 [math]\displaystyle{ \text{Mod}_\text{CVCI} }[/math] the bonus from carrier cutins,
 [math]\displaystyle{ \text{Mod}_\text{AP} }[/math] the bonus from an AP shells,
 [math]\displaystyle{ \text{Mod}_\text{post} }[/math] any remaining postcap modifiers that are applicable,
 [math]\displaystyle{ \text{Crit} }[/math] the critical strike modifier,
 [math]\displaystyle{ \text{Ammo} }[/math] the remaining ammunition modifier,
 [math]\displaystyle{ \text{DEF} }[/math] 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 precap 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 precap 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:
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, LandBased 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 antisubmarine 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 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 antiair 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]
Torpedo Attacks only include the Opening Torpedo Salvo and Closing Torpedo Salvo.
 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.
AntiSubmarine Warfare
 For more information on this topic, see AntiSubmarine 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.
 Antisubmarine weaponry is therefore the primary source of ASW damage, with the base ship ASW playing a very minor role damagewise.
 However, base ship ASW is the primary determinant of whether a ship can reach 100 total ASW to perform "Opening ASW" (OASW) attacks.
 Unlike sheeling, 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.
AntiSubmarine  

Precap:
With:

ASW Damage Synergy  

Small Small Sonars  
Large Large Sonars  
DCP Depth Charge Projectors (DCP)  AP AP  
DCR Depth Charge (Racks) (DCR)  AP AP AP AP AP  
Other ASW Mortars  
ASW Damage Modifiers: [math]\displaystyle{ \text{Mod}_\text{synergy} = {Mod}_\text{1} \times {Mod}_\text{2} }[/math]  
[math]\displaystyle{ {Mod}_\text{1} }[/math]  + (Any Sonar + Any Depth Charge) 
1.15 
[math]\displaystyle{ {Mod}_\text{2} }[/math]  DCP + DCR and NO Small  1.1 
Small + DCP + DCR  1.25  
Examples  
[math]\displaystyle{ \text{Mod}_\text{synergy} }[/math]  Small + DCP + DCR  1.4375[math]\displaystyle{ 1.15 \times 1.25 }[/math] 
Large + DCP + DCR  1.265[math]\displaystyle{ 1.15 \times 1.1 }[/math]  
Armor Penetration  
Indepentant of synergies, some equipment provides additional armor penetration to ASW attacks.
The flat armor penetration value is calculated as follows:

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, Taiyouclass 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 NOAP or NOAP+ in addition to "Night Planes", in order to perform carrier night attacks.
 Night Carriers (CVN) are CV/CVL capable of Carrier Night Air Attacks without needing a NOAP
.
 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 Improvement stats are not taken into account.
 This means any other stats and upgrade bonuses from equipment like guns and nonnightcapable planes are ignored.
 This also means that any Visible Bonus from Planes is also ignored.
 The Visible Bonuses given by the SDP+ are whoever counted here.
 The Improvement stats are not taken into account.
 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.
AntiInstallation Attacks
Installations differ from regular enemy warships, as they are immune to certain attack elements like the torpedo stat, but are extremely weak against specialized gears.
 See the AntiInstallation page for more details.
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 postcap modifiers. Postcap 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.
Attack Type  Cap 

LBAS  170 
Support Expeditions  
ASW  
Airstrike  
Opening Torpedo Salvo  180 
Closing Torpedo Salvo  
Day shelling  220 
Night battle  360 
 Notes
 Any excess attack power above this cap is squarerooted. See the damage formula for how it is applied.
 It is still worth aiming to go above the attack power cap because some precap modifiers can severely reduce the attack power.
Precap Modifiers
Engagement
See Engagement for more details.
Form  Damage Modifier  Chance  Chance with Saiun 

Parallel Engagement 同航戦 (Doukousen^{?}) 
100%  45%  45% 
Headon Engagement 反航戦 (Hankousen^{?}) 
80%  30%  40% 
Crossing the T (Advantage) T字戦有利 (T Jisen Yuuri^{?}) 
120%  15%  15% 
Crossing the T (Disadvantage) T字戦不利 (T Jisen 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 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 Headon 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
See Formation for more details.
Formation Attack Power Modifiers  

Formation  Shelling  Torpedo  ASW  Night Battle 
Line Ahead 単縦陣 (Tanjuujin^{?}) 
100%  100%  60%  100% 
Double Line 複縦陣 (Fukujuujin^{?}) 
80%  80%  80%  100% 
Diamond 輪形陣 (Rinkeijin^{?}) 
70%  70%  120%  100% 
Echelon 梯形陣 (Teikeijin^{?}) 
75%  60%  110%  100% 
Line Abreast 単横陣 (Tan'oujin^{?}) 
60%  60%  130%  100% 
Vanguard^{[1]} 警戒陣 (Keikaijin^{?}) 
50%  100%  100%  50% 
100%  100%  60%  100% 
 ↑ The direct translation of "Keikai" is "alert".
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
Night CutIns will apply extra modifiers if triggered.
 See Night CutIn for more details.
Hidden Fit Bonuses
Unlike the other precap bonuses, this is just a minor additive firepower bonus added for some ships (mostly cruisers) when equipped with certain guns.
 See Hidden Fit Bonuses for more details.
Postcap 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  Postcap Damage Modifier 
Accuracy Modifier 
Hits  Notes 

Main Zuiun Cutin (Zuiun CI) 
1.35  ?  1  Iseclass Kai Ni only  
Main Suisei Cutin (Suisei CI) 
1.3  ?  1  
Main AP Shell Cutin (APCI) 
1.5  1.2  1  
Secondary AP Shell Cutin (Sec APCI) 
1.3  1.3  1  
Secondary Radar Cutin (Radar CI) 
1.2  1.5  1  
Secondary Cutin (Sec CI) 
1.1  1.3  1  
Double Attack (DA) 
1.2  1.1  2 
Carrier CutIn Attacks
For more details, please see Carrier CutIn Attacks.
Attack Type  Prerequisites  Postcap Damage Modifier 
Accuracy Modifier 
Hits 

FighterBomberAttacker (FBA) 
1.25  1.2~1.3?  1  
BomberBomberAttacker (BBA) 
1.2  1.2~1.3?  1  
BomberAttacker (BA) 
1.15  1.2~1.3?  1 
ArmorPiercing Modifier
During day combat, certain enemy ships take extra damage from AP Shells
.
 The bonus only applies against BB, FBB, BBV, CA, CAV, CV, and CVL.
 This include Installations.
 This means that this bonus does not apply against CL, CLT, DD, and AV.
Type  Modifier 

1.08  
1.10  
1.15  
1.15 
 Note
 It is unadvisable to run any of the other setups beyond the most basic Gun+AP, as the other setups will interfere with artillery spotting and give worse bonuses.
AntiInstallation Equipment Modifiers
See the AntiInstallation 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 CutIn 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 
1019%  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 614% 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 (74 & 75 so far), certain ships, types of ships, equipment, or types of equipment will bring bonuses.
 Those bonuses are most of the time raw damage 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 postcap 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 5080% 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
 Overkill protection is most applicable to DDs.
 As a rule, ships with HP that is divisible by 4 have worse survivability.
Other Information
