## Main FormulaEdit

$ \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 PowerEdit

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 confirmed for both secondary and machine gun improvements.

For the **Opening Airstrike**:

$ \hat{F} = M_{type} \left ( P_{p} \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
- $ 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).

- For Dive Bombers and Seaplane Bombers:
- $ 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 ) $

- Applicable
**Night Aircraft**include Swordfish variants, Zero Fighter Model 62 (Fighter-bomber / Iwai Squadron) and Night Planes. **Night Planes**(purple icon) are limited to F6F-3N, F6F-5N, and TBM-3D.- $ F_{p} $ is the plane's firepower stat
- $ T_{p} $ is the plane's torpedo stat
- $ A_{p} $ is the plane's ASW stat
- $ D_{p} $ is the plane's dive bombing stat
- $ \bigstar_{p} $ is the plane's improvement level
- $ M_{p} $ is the plane's calculated night multiplier
- $ N $ is the current plane count (slot size) of that slot
- $ K_{a} $ is the first Night Plane modifier; becomes
**3**if the plane is a Night Plane, and is 0 otherwise. - $ K_{b} $ is the second Night Plane modifier; becomes
**0.45**if the plane is a Night Plane, and is**0.3**otherwise.

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 Akashi's Improvement Arsenal page for effects given by upgraded equipment.
- 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 ModifiersEdit

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

- Anti-Installation Attack Modifier
- Formation Modifier (see "Damage modifier")
- Engagement Modifier
- Health Modifier
- Night Special Attack Modifier
- Light Cruiser Fit Bonus

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.
- The WG42 (Wurfgerät 42) adds at least 75 Attack Power, exact number depend on amount of WG42 equipped, see WG42's page. In the event both are present, this is added after the Type 3 Shell's effects, but before the sum is multiplied by the other modifiers.
- 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 ModifierEdit

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 BonusEdit

*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.

- Applicable Twin Gun Mounts: 15.2cm Twin Gun Mount, 15.2cm Twin Gun Mount Kai, 14cm Twin Gun Mount
- Applicable Single Gun Mounts: 15.2cm Single Gun Mount, 14cm Single Gun Mount
- Not Applicable Guns: All the 15.5cm and 20.3cm guns, OTO 152mm Triple Rapid Fire Gun Mount, 15cm Twin Secondary Gun Mount, etc.

## Attack Power CapEdit

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 ASW (Anti-Submarine) attacks**150**for Others (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 ModifiersEdit

In damage calculation, Post-cap modifiers apply* after the cap*, but

*. Thus they are very effective approach to boost your damage output (esp. against heavy armor enemies).*

**before enemy armor reduction**Currently, the post-cap modifiers are from:

- Artillery Spotting (aka. Day time special attacks)
- Critical Damage and Aircraft Proficiency
- Contact (Opening air strike)
- AP Shell (against certain targets)
- PT Imp Pack (unconfirmed)

#### 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 ModifierEdit

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.

#### ContactEdit

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 ShellEdit

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).

## Remaining Ammo ModifierEdit

Remaining Ammunition | Modifier |
---|---|

5 to 10 bars | 100% |

4 bars | 80% |

3 bars | 60% |

2 bars | 40% |

1 bar | 20% |

0 bars | Scratch Damage |

- In general, two bars of will be used in Day Battle for all ships, regardless of whether they attack or not.
- The Remaining Ammo Modifier affects all phases, including the opening Aerial Combat Phase.
- When entering night battle, the Remaining Ammo Modifier on a vessel remains same as the previous day battle. One bar of is used for all ships in Night Battle, regardless of whether they attack or not.
- Because most battles will consume 2 bars of ammunition each, try to engage the boss before the 5th battle, or else achieving victory becomes unlikely (but not impossible).
- When attempting to defeat boss nodes, avoid night battles and whirlpools on the way.
- Whirlpools will decrease either or bars of your sorted fleet, which can be disadvantageous in long sorties. Equipping one or more ships with RADAR can help reduce losses taken from these.
- Only one RADAR is required per ship. Equipping multiple RADAR to the same ship will not reduce the penalty further.
- The max reduction typically occurs at 3 ships with RADAR. In events special caveats such as only RADAR in the main fleet of a Combined Fleet being considered can exist.

- Whirlpools will decrease either or bars of your sorted fleet, which can be disadvantageous in long sorties. Equipping one or more ships with RADAR can help reduce losses taken from these.
- Submarine-only nodes on limited-time event maps do not consume ammo in Day or Night Battle.
- Hayasui with Underway Replenishment can temporarily resupply ammo/fuel when players choose to use the item.
- Ammo/Fuel reduced in Air Raid nodes are reduced. Read Events/Mechanics for details.

## Player Ship Protection MechanismsEdit

$ \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.

- 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.

- Damage taken cannot reduce HP below 1.

## See AlsoEdit

- WikiWiki section on damage calculation
- ja.kancolle.wikia pages:
- Online calculator (explanations)