# Health of Cogs

Cogs have certain amount of **health** that depend on their level and are determined by certain mathematic formulas. The table below shows the health of every existing Cog level.

Level | Health |
---|---|

Level 1 | 6 |

Level 2 | 12 |

Level 3 | 20 |

Level 4 | 30 |

Level 5 | 42 |

Level 6 | 56 |

Level 7 | 72 |

Level 8 | 90 |

Level 9 | 110 |

Level 10 | 132 |

Level 11 | 156 |

Level 12 | 196 |

Level 13 | 224 |

Level 14 | 254 |

Level 15 | 286 |

Level 16 | 320 |

Level 17 | 356 |

Level 18 | 394 |

Level 19 | 434 |

Level 20 | 476 |

## Formulas

### Level 1-11 Cogs

The formula for health of Cogs from levels 1 to 11 can be:

`f(x) = x`

^{2}+ 3x + 2

or in a simplified way:

`f(x) = (x + 1) * (x + 2)`

where *x* is the Cog's level and *f(x)* is a function that returns the Cog's health value.

For example, the formula works in the following method to determine the health of level 4 Cogs.

`f(4) = (4 + 1) * (4 + 2)`

`f(4) = (5) * (6)`

`f(4) = 30`

### Level 12+ Cogs

Level 12 Cogs previously had a 10% boost in health, putting them at 200. As of the 3.0.0 update that was released on December 3, 2021, which introduced balancing changes, level 12+ Cogs now have a unique formula to determine their health.^{[1]}

The formula for health of level 12+ Cogs can be:

`f(x) = x`

^{2}+ 3x + 16

which is the same as the formula for levels 1 through 11, but has an increase of 14 units in Y value for every unit of X. Unlike the former formula, it has no roots.

The simplified formula can also be represented as:

`f(x) = (x + 1) * (x + 2) + 14`

For example, the formula works in the following method to determine the health of level 16 Cogs.

`f(16) = (16 + 1) * (16 + 2) + 14`

`f(16) = 17 * 18 + 14`

`f(16) = 306 + 14`

`f(16) = 320`