# Damage

## Contents

## Overview

In Factorio, entities have health, can die/be destroyed, and have resistances. *Damage* is defined as the concept of lowering an entity's health by using an attack, such as a gun firing at it, or a biter chewing on it. An entity's resistances will define exactly how much damage the entity will take off of an arbitrary attack.

The character's maximum health is 250 (without energy shields). Other entities' health values are listed in their individual entries.

## Achievements

The concept of damage is directly connected to the following achievements:

Run Forrest, runDestroy 100 trees by impact. |

PyromaniacDestroy 10k trees with fire. |

SteamrolledDestroy 10 spawners by impact. |

GolemSurvive a hit of 500 damage or more. |

Watch your stepGet killed by a moving locomotive. |

## Damage types

Damage type | Used by |
---|---|

Physical | Bullets (regular/piercing/uranium), shotgun (regular/piercing), biters, axe (iron/steel), defender robots |

Impact | Collision (of train/car) |

Fire | Flamethrower |

Acid | Worm Turrets, Spitters |

Poison | Poison capsule |

Explosion | Rockets, Explosive Rockets, Grenade, Cluster grenade |

Laser | Laser turrets, distractor/destroyer robots, personal laser defense |

### Piercing power

Piercing power is present with Tank ammunition and piercing shotgun shells. It determines how many HP of enemies can a projectile damage before it is no longer able to travel further. To penetrate an enemy, the enemy has to be killed by the projectile, and the damage dealt for the kill must be less than current piercing power.[1] The damage dealt also decreases piercing power. For example, shooting medium biters with 75 health with a cannon shell of 300 piercing power means that the shell will pierce through 4 medium biters, killing them, and still destroy/damage one more target.

## Resistance

Resistance has two aspects:

### Decrease, or "flat" resistance

Decrease resistance decreases the damage by specified number as long as the resulting damage wouldn't be less than 1. If the result damage would be less than 1, an alternate formula is used. Let R denote the flat resistance value, D the incoming damage, and M the modified damage, after accounting for flat resistance. Then

if R+1<D

`M=D-R`

otherwise if D>1

`M=1/(R-D+2)`

otherwise

`M=1/(R+1)`

.

If flat resistance matches or exceeds the raw damage, then modified damage is asymptotic towards 0, as shown by following example table:

Damage | Flat Resistance | Modified damage (with 0% resistance) |
---|---|---|

5 | 0 | 5 |

5 | 1 | 4 |

5 | 2 | 3 |

5 | 3 | 2 |

5 | 4 | 1 |

5 | 5 | 1/2 |

5 | 6 | 1/3 |

5 | 7 | 1/4 |

5 | 8 | 1/5 |

... | ... | ... |

### Percentile resistance

Percentile resistance reduces the damage by the specified percent. It is applied *after* flat/decrease resistances when both are present and thus changes the 'modified damage' value above, decreasing it by the specified percentage. If the value is 100%, the entity is immune to the damage. This is the only way to have an entity immune to a type of damage, as flat reduction cannot reduce damage beneath 1.

As an example, an entity with 25% resistance to physical damage hit with a bullet dealing 100 physical damage would take 75 damage instead of 100.

The formula used for percentage resistance to damage is as follows:

Let M denote the flat-resistance-modified starter damage, and let P denote the percentage resistance (in decimal form, so 25%=0.25), and let F denote final damage.

`F = M * (1 - P)`

In Factorio, resistances are displayed in the UI as follows:

Decrease resistance/Percent resistance (Damage type)

So, an entity that displays 10/20% resistance to fire has 10 flat resistance and 20% percentile resistance to fire. If the aforementioned entity were to take 30 fire damage, they would instead take 16 damage, after resistances were applied.

The formula used for the above:

16^{final damage} = (30^{initial raw damage} - 10^{flat resist}) * 0.8^{20% resistance}

## Combined formulas

Let D denote the raw incoming damage (of applicable type), R denoted the flat resistance value (against damage of the applicable type), P the percentage resistance (against damage of the same type) in decimal form (e.g. 20%=0.2), and let F denote the final damage (of applicable type) dealt to the target.

### If R+1<D

F = (D - R) * (1 - P)

### otherwise if D>1

F = (1 - P) / (R-D+2)

### otherwise

F = (1 - P) / (R+1)