# Roof Pitch Calculator

## Calculate the Pitch of a Roof

Enter the rise and run of the roof or the angle in degrees to calculate the pitch. Learn more about finding the rise and run of the angle below.

## How to Find the Pitch of a Roof

Homes and other buildings have roofs with slopes ranging from no slope or flat to very steep slopes. Roof pitch is expressed as rise over a 12 inch run, for example 4/12. Finding the pitch of a roof can be done by finding the rise and run, or converted from the angle if it is known. See the chart below for some examples of common roof pitches.

### Measure the Rise and Run From the Roof

One method to find the pitch is to climb on the roof and measure the rise for a 12″ run. You’ll need a level that is 12″ or longer and a tape measure. On the roof, hold the level perfectly level, and measure the height from the roof to the level 12 inches away from where the level touches the surfase, this will be the rise. For example, if the level is 4″ above the roof at a point 12″ away from where the level is touching the surface then the pitch is 4/12.

### Measure the Rise and Run From the Attic

Another method to find the roof pitch is to go into the attic and measure the rise for a 12″ run of the roof rafters, which allows finding the pitch without going on the roof. From the attic, hold a level perfectly level and touching a rafter at one end. Measure the distance from the level to the rafter 12 inches away from where the level touches the rafter.

### Measure the Total Rise and Total Run to Find the Pitch

If you know the total height of the peak and the width of the roof you can also find the pitch with a little math. For example, if the peak is 4 feet and the total roof with is 20 feet, the total rise is 4 feet, or 48 inches. The total run is the distance from the peak to the edge of the roof, which in this case is the total width divided in half, which is equal to 10 feet or 120 inches. Since pitch is expressed as a rise over a 12 inch run, divide the run by 12 to get the multiplier, in this case 120/12 = 10. Now, divide the run by the multiplier to get the pitch, eg. 48/10 = 4.8. The pitch of this roof is 4.8/12. The calculator above can handle much of this math.

### Convert Angle in Degrees to Roof Pitch

If you know the angle of the roof in degrees you can find the roof pitch by converting the angle in degrees to a slope, then finding the rise by multiplying the slope by 12. First, find the slope by finding the tangent of the degrees, eg. slope = tan(degrees). Then multiply the slope by 12 to get the rise. The pitch is the rise/12.

For example, if the angle of a roof is 35°:

tan(35) = 0.70020754

0.70020754 × 12 = 8.40249048

Pitch = 8.4/12

## Finding the Angle of a Roof in Degrees

To find the angle of a roof in degrees convert the pitch to a slope, then convert to degrees by finding the arc tangent of the slope. First, convert the pitch to a slope. To do this simply convert the rise and run as a fraction to a decimal form, eg. rise/run = rise ÷ run = slope. Next, find the degrees by finding the arc tangent of the slope, eg. degrees = atan(slope).

For example, if the pitch of the roof is 4/12:

4/12 = 4 ÷ 12 = .333

atan(.333) = 18.41775837

Angle = 18.4°

## Common Roof Pitches and Equivalent Grade, Degree, and Radian Angles

Pitch | Grade (slope) | Degrees | Radians |
---|---|---|---|

1/12 | 8.3% | 4.8° | 0.1 |

2/12 | 16.7% | 9.5° | 0.2 |

3/12 | 25% | 14° | 0.2 |

4/12 | 33.3% | 18.4° | 0.3 |

5/12 | 41.7% | 22.6° | 0.4 |

6/12 | 50% | 26.6° | 0.5 |

7/12 | 58.3% | 30.3° | 0.5 |

8/12 | 66.7% | 33.7° | 0.6 |

9/12 | 75% | 36.9° | 0.6 |

10/12 | 83.3% | 39.8° | 0.7 |

11/12 | 91.7% | 42.5° | 0.7 |

12/12 | 100% | 45° | 0.8 |

13/12 | 108.3% | 47.3° | 0.8 |

14/12 | 116.7% | 49.4° | 0.9 |

15/12 | 125% | 51.3° | 0.9 |

16/12 | 133.3% | 53.1° | 0.9 |

17/12 | 141.7% | 54.8° | 1 |

18/12 | 150% | 56.3° | 1 |

19/12 | 158.3% | 57.7° | 1 |

20/12 | 166.7% | 59° | 1 |

21/12 | 175% | 60.3° | 1.1 |

22/12 | 183.3% | 61.4° | 1.1 |

23/12 | 191.7% | 62.4° | 1.1 |

24/12 | 200% | 63.4° | 1.1 |

## Additional Roofing Resources

The calculator above can find the pitch given a known rise and run or an angle in degrees. See our roofing material calculator to estimate the amount of shingles and other materials needed to install a roof. Consider requesting free roofing estimates to learn more about the cost of a replacing or repairing roof in your area. Learn how much it costs to install a new roof.

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