1: | = | ||

Rise:Run | Degrees |

What angles do 1:6, 1:7, 1:8 correspond to?

Dovetails angles are often specified as a Rise:Run ratio, for example 1:7. This corresponds to the angle of a line that covers a vertical distance of 7 cm (or inches, or whatever unit you prefer) and deflects horizontally by 1 cm (or inches, or whatever unit you prefer).

Here are the angles that these rise:run ratios correspond to:

Rise:Run | Angle |
---|---|

1:1 | 45.00 |

1:2 | 26.57 |

1:3 | 18.43 |

1:4 | 14.04 |

1:5 | 11.31 |

1:6 | 9.46 |

1:7 | 8.13 |

1:8 | 7.13 |

1:9 | 6.34 |

1:10 | 5.71 |

1:11 | 5.19 |

1:12 | 4.76 |

In case you are wondering, the formula to calculate the angle from a rise:run ratio is this:

```
arctan(rise/run)
```

If you want to do this in a spreadsheet, use this:

```
=DEGREES(ATAN(rise/run))
```

And here’s the opposite table from a few suitable angles to the corresponding rise:run, if you were wondering:

Angle (degrees) | Rise:Run |
---|---|

5 | 1:11.43 |

6 | 1:9.51 |

7 | 1:8.14 |

8 | 1:7.12 |

9 | 1:6.31 |

10 | 1:5.67 |

11 | 1:5.14 |

12 | 1:4.70 |

13 | 1:4.33 |

14 | 1:4.01 |

15 | 1:3.73 |

16 | 1:3.49 |

17 | 1:3.27 |

18 | 1:3.08 |

19 | 1:2.90 |

20 | 1:2.75 |

The formula to go from an angle to Rise:Run is this:

```
Rise = 1
Run = 1/tan(angle)
```

In case you are wondering what “the correct” angle is - there is no consensus whatsoever. Answers vary greatly depending on who you ask, but everything I have ever seen is between 1:4 (about 14 degrees) and 1:8 (about 7 degrees).