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## Main Formula Edit

$\text{Damage Value} = \bigg \lfloor \left ( \left \lfloor \operatorname{cap} \left ( \hat{F} \cdot M_{pre} \right ) \cdot C \right \rfloor \cdot M_{post} - \hat{A} \right ) \cdot R \bigg \rfloor$

Where:

• $\hat{F}$ is Basic Attack Power.
• $M_{pre}$ is the combination of Pre-Cap Modifiers.
• $M_{post}$ is the combination of Post-Cap Modifiers.
• $C$ is the Critical Hit modifier. Assumes a value of 1.5 if the attack is a Critical Hit, and is 1 otherwise.
• $\operatorname{cap}$ is the soft cap to attack power.
• $\hat{A}$ is Defense Power.
• $R$ is the remaining ammo penalty:
• $R = \begin{cases} 2R_{s}, & \text{ if } R_{s} < 0.5 \\ 1, & \text{ otherwise } \end{cases}$
• $R_{s}$ is the ship's current ammo percentage (1 bar = 10% = 0.1)
• $\left \lfloor x \right \rfloor$ is the floor function; that is, the rounding down of input $x$

Defense Power is calculated as follows:

$\hat{A} = 0.7 A_t + 0.6 \big ( \text{random} \in \left [ 0 , \left \lfloor A_t \right \rfloor - 1 \right ] \big ) - D$

Where:

• $A_{t}$ is the sum of the defending ship's displayed armor stat and all improvements to armor.
• The random number function outputs an integer value between 0 and $\left \lfloor A_{t} \right \rfloor - 1$ (inclusive, uniformly distributed).
• $D$ is the Depth Charge Rack armor penetration effect. See Anti-Submarine Warfare for details.

If Damage Value is less than 1, it becomes scratch damage, and the following formula is applied instead:

$\text{Damage Value} = \Big \lfloor 0.06 H_t + 0.08 \big ( \text{random} \in \left [ 0 , H_t - 1 \right ] \big ) \Big \rfloor$

Where:

• $H_{t}$ is the target's current HP.
• The random number function outputs an integer value between 0 and $H_{t} - 1$ (inclusive, uniformly distributed).

## Basic Attack Power Edit

For Shelling:

$\hat{F} = F_{s} + F_{\bigstar} + C_{f} + 5$

• $F_{s}$ is the ship's firepower stat
• $F_{\bigstar}$ is the sum of all improvements to shelling damage
• $C_{f}$ is the Combined Fleet factor

For Torpedo:

$\hat{F} = T_{s} + T_{\bigstar} + 5$

• $T_{s}$ is the ship's torpedo stat
• $T_{\bigstar}$ is the sum of all improvements to torpedo damage

For Carrier Shelling:

$\hat{F} = 55 + \big \lfloor 1.5 \left ( F_{s} + T_{s} + \left \lfloor 1.3 D_{s} \right \rfloor + F_{\bigstar} + C_{f} \right ) \big \rfloor$

• $D_{s}$ is the ship's dive bombing stat
• $F_{\bigstar}$ is the sum of improvements to carrier shelling. It is confirmed for secondary and machine gun improvements, and also torpedo bomber improvements (0.2 per star).

For the Opening Airstrike:

$\hat{F} = M_{type} \left ( ( P_{p} + P_{\bigstar} ) \sqrt{N} + K_{f} \right )$

• $N$ is the current plane count (slot size) of a given slot
• $P_{p}$ is the plane's dive bombing or torpedo stat
• $P_{\bigstar}$ is the plane's improvement bonus to airstrike damage:
• $P_{\bigstar} = \begin{cases} 0.2 \bigstar, & \text{ for Torpedo Bombers, Seaplane Bombers } \\ 0, & \text{ for Dive Bombers } \end{cases}$
• $M_{type}$ is the Plane Scaling modifier:
• For Dive Bombers and Seaplane Bombers: 1
• For Torpedo Bombers: 0.8 or 1.5; one value is picked at random (~50% chance of each).
• $K_{f}$ is the airstrike damage constant. Varies according to which type of fleet is being targeted:
• Against Single Fleets, or Player Combined Fleets: $K_{f} = 25$
• Against an Abyssal Main Fleet: $K_{f} = 15$
• Against an Abyssal Escort Fleet: $K_{f} = 5$

For Anti-Submarine Warfare:

$\hat{F} = \left ( 2 \sqrt{A_{s}} + A_{\bigstar} + 1.5 E_{asw} + C_{t} \right ) \cdot S_{asw} \left ( 1 + S_{a} + S_{b} \right )$

• $A_{s}$ is the ship's naked ASW stat (no equipment ASW is considered)
• $A_{\bigstar}$ is the sum of all improvements to ASW damage
• $E_{asw}$ is the sum of the displayed ASW stat of the ship's equipment. Recon Seaplanes are not considered.
• $C_{t}$ is the ASW type constant:
• If Sonar or Depth Charge (DD, CL): 13
• If aircraft-based (AV, CVL, CAV, BBV): 8
• $S_{asw}$ is the basic synergy modifier for ASW. Becomes 1.15 if the ship is equipped with a Sonar and Depth Charge Projector pair; assume 1 otherwise.
• $S_{a}$ is a secondary synergy modifier. Becomes 0.15 if the ship is equipped with a Sonar and Depth Charge Rack pair; assume 0 otherwise.
• $S_{b}$ is a secondary synergy modifier. Becomes 0.1 if the ship is equipped with a Depth Charge Projector and Depth Charge Rack pair; assume 0 otherwise.

Additionally, equipping a Depth Charge Rack will incur an additional armor penetration effect when executing ASW attacks, denoted as $D$ in the Defense Power formula. It is calculated as follows:

$D = \sqrt{D_{asw} - 2} + C_{ship}$

• $D_{asw}$ is the Depth Charge Rack's displayed ASW value
• $C_{ship}$ is the Ship Type constant; becomes 1 if the ship equipping the Depth Charge Rack is a DE, and is 0 otherwise.

For Night Battle:

$\hat{F} = F_{s} + T_{s} + N_{\bigstar} + C_{r}$

• $N_{\bigstar}$ is the sum of all improvements to night battle damage
• $C_{r}$ is the Night Contact bonus; 5 if Night Scout has activated, 0 otherwise

For Night Battle (Aerial Attack):

$\hat{F} = F_{s} + \sum^{\text{Night Aircraft}} F_{p} + T_{p} + M_{p} \sqrt{N} + NK_{a} + \sqrt{\bigstar_{p}}$

$M_{p} = K_{b} \left( F_{p} + T_{p} + A_{p} + D_{p} \right )$

Notes:

• Multiple SONAR/Depth charges do not boost the ASW Bonus (i.e. 2 of each still makes the bonus 1.15)
• In KanColle Kai abyssal ships with non-zero ASW stat (not counting equipment) have an ASW constant of 13. This takes precedence over ship classification. Currently, it is confirmed that Re Elite exhibits this behavior.
• Please read Combined Fleet page for combined fleet factor in combined fleets.
• During Night Battle, the basic attack power of anti-submarine warfare can be treat as zero, with the exception of in Combined Fleet maps and Night Battle nodes.
• Carriers utilize the Night Battle formula unless one of the following:
• Saratoga Mk.II (uses Aerial Attack formula)
• Equipped with night operation aviation personnel (uses Aerial Attack formula)
• Ark Royal equipped with Swordfish and not equipped with night operation aviation personnel (uses normal night battle formula, but ignores all equipment besides Swordfish).

### Pre-Cap Modifiers Edit

These are the factors directly applied to your ship's attack power.

Effects from the modifiers are multiplied/added cumulatively.

#### Anti-Installation Attack Modifier Edit

Main article: Installation Type
• The Type 3 Shell multiplies Attack Power by 2.5 against soft-skinned installations
• The WG42 (Wurfgerät 42) adds a flat bonus and possibly an additional modifier depending on the installation and number equipped.
• Landing Crafts give varying bonuses against installations.

Note also that against installations, only firepower is taken into account; in night battle, even though attack power is normally the sum of firepower and Torpedo, for installations specifically the Torpedo stat is disregarded.

#### Ship's Health Modifier Edit

Damage Shelling/ASW Torpedo
Minor damage (小破 Shouha) or less 100% 100%
Moderate damage (中破 Chuuha) 70% 80%
Heavy damage (大破 Taiha) 40% 0%

These modifiers do not affect Aerial Combat.

#### Night Special Attack Modifier Edit

Certain Equipment setups have a chance to trigger special attacks at night, giving boost to both attack power and accuracy. This stage is usually the most rewarding / dangerous because both sides have drastically increased attack power.

The ship must be able to participate in the night battle in order to trigger the special attacks.

#### Light Cruiser Fit Bonus Edit

Main article: Overweight Penalty and Fit Gun Bonus

a few points would be added for CL's attack power after all pre-cap firepower but before the cap if they used fit guns.

## Attack Power Cap Edit

Applies after the pre-cap modifiers. This is a soft limit on your effective attack power. It is given by:

$\operatorname{cap} \left ( x \right ) = \begin{cases} \left \lfloor S + \sqrt{x - S} \right \rfloor, & \text{if } x > S \\ \left \lfloor x \right \rfloor, & \text{otherwise} \end{cases}$

Where:

• $x$is the input of the function; or in other words, the value of Basic Attack Power multiplied by all Pre-Cap Modifiers.
• $S$is the attack power cap, represented by different thresholds according to the type of attack:
• 180 for Day Battle Shelling
• 300 for Night Battle
• 150 for Others (ASW, support shelling, aerial attack, torpedo attack, etc.)

Daytime Shelling Attack Cap (180) often makes it important to utilize Artillery Spotting since they boost your attack power after the cap, Night Combat can be very dangerous and/or rewarding due to having a very high cap (300) and the inclusion of torpedo to firepower for the basic attack power calculation.

## Post-Cap Modifiers Edit

In damage calculation, Post-cap modifiers apply after the cap, but before enemy armor reduction. Thus they are very effective approach to boost your damage output (esp. against heavy armor enemies).

Currently, the post-cap modifiers are from:

#### Artillery Spotting Edit

Certain equipment setups provide a chance to trigger special attacks during day battle, giving boost to both attack power and accuracy. The damage modifiers are applied after the cap (180), thus very effective against heavy armor targets. Note that the ship requires at least 1 seaplane on board to perform Artillery Spotting.

#### Critical Modifier Edit

Most forms of attack (Torpedo, Shelling, Anti-Submarine, Preemptive Bombing) have a chance to crit the target. The damage modifier applies after the cap.

Attack Type Modifier
Normal Attack 100%
Critical Hit 150%

It should be noted that the critical message always appears when damage dealt is greater than or equal to 40, regardless of whether the 150% modifier was applied or not. On the other hand, the critical message will never appear when damage dealt is less than or equal to 14, even if the 150% modifier was applied.

Critical damage rate seems to depend on accuracy.

Aircraft Proficiency boost Critical Hit Modifier.

#### Contact Edit

Contact takes place during the Aerial Combat bombing phase, and applies to the bombing damage of all allied planes.  For activation conditions, rate and additional details, see Aerial Combat.

The damage increase depends on the +accuracy bonus of the squadron performing contact.

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

#### AP Shell Edit

Damage against certain targets increases when both large-caliber main guns and AP shells are equipped.

This modifier works against the following enemy classes:

• Battleships (including Fast Battleships and Aviation Battleships)
• Heavy Cruisers
• Standard Carriers
• Demons and Princesses (including land installations)
• Floating Fortresses (Escort Fortress and Floating Fortress)
Type Modifier
Main + Main + AP Shell + Seaplane 108%
Main + Main + AP Shell + AA gun 108%
Main + Main + AP Shell + Radar 110%
Main + Main + Secondary + AP Shell 115%
Main + Secondary + AP Shell + Radar 114~115%?
Main + Secondary + AP Shell + Seaplane 115~116%?

Notes

• The AP shell and seaplane used in the tests were Type 91 AP Shell and Type 0 Observation Seaplane.
• Numbers for the setups involving secondary guns are not confirmed yet, but believed to be near.
• Has not been tested against Light Cruiser Demon and Destroyer Princess at the moment.
• Has not been tested against Armored Carriers and Aviation Cruisers as of 02/06/2015.
• Detailed tests are still ongoing. Values differ slightly from test to test (source). Current values are taken off wikiwiki.
• Exercise caution as this modifier works for enemy ships as well (practice matches and special enemies with Deteriorate AP Shell equipped).

## Player Ship Protection Mechanisms Edit

$\text{Damage Value} = \left \lfloor \frac{H_{t}}{2} + 0.3 \big ( \text{rand} \in \left [ 0 , H_{t} - 1 \right ] \big ) \right \rfloor$ While the above formulas and statements are generally true for damage taken by a player's ships, there are additional limits that apply to friendly units only. These protection mechanisms are important for game balance and to protect your fleet from sinking.

• For ships entering battle at chuuha (orange) or higher HP:
• Damage taken cannot reduce HP below 1.
• Any further hits will become misses.
• For flagships, as well as ships with 20 morale or more (i.e. not red face):
• If damage taken exceeds a ship's current HP, then instead of taking full damage, the damage of the current attack is limited to 50%-79% (rounded down) of current HP.
• For multi-hit attacks, such as night battle torpedo cut-in attacks, each hit is calculated separately.
• This can occasionally help ships avoid taiha (red HP), because it narrows the range of damage where it is possible to be hit into taiha.
• For ships with at full HP and an odd HP total, it is occasionally possible to stop damage at lightly damaged.

## See Also Edit

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