Formulas
Degrees = arctan(rise / 12) x 180 / π
Rise = 12 x tan(degrees)
Rise = 12 x tan(degrees)
Example: 7/12 gives arctan(0.5833) = 30.26°. And 35° gives 12 x tan(35°) = 8.4, close to 8.5/12.
Pitch to degrees table
| Pitch | Degrees | Percent | Factor | Extra area |
|---|---|---|---|---|
| 1/12 | 4.76° | 8.3% | 1.003 | 0.3% |
| 2/12 | 9.46° | 16.7% | 1.014 | 1.4% |
| 3/12 | 14.04° | 25.0% | 1.031 | 3.1% |
| 4/12 | 18.43° | 33.3% | 1.054 | 5.4% |
| 5/12 | 22.62° | 41.7% | 1.083 | 8.3% |
| 6/12 | 26.57° | 50.0% | 1.118 | 11.8% |
| 7/12 | 30.26° | 58.3% | 1.158 | 15.8% |
| 8/12 | 33.69° | 66.7% | 1.202 | 20.2% |
| 9/12 | 36.87° | 75.0% | 1.250 | 25.0% |
| 10/12 | 39.81° | 83.3% | 1.302 | 30.2% |
| 11/12 | 42.51° | 91.7% | 1.357 | 35.7% |
| 12/12 | 45.00° | 100.0% | 1.414 | 41.4% |
| 14/12 | 49.40° | 116.7% | 1.537 | 53.7% |
| 16/12 | 53.13° | 133.3% | 1.667 | 66.7% |
| 18/12 | 56.31° | 150.0% | 1.803 | 80.3% |
| 20/12 | 59.04° | 166.7% | 1.944 | 94.4% |
| 24/12 | 63.43° | 200.0% | 2.236 | 123.6% |
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Degrees to pitch table
| Degrees | Rise per 12 | Nearest pitch |
|---|---|---|
| 5° | 1.05 | 1/12 |
| 10° | 2.12 | 2/12 |
| 15° | 3.22 | 3/12 |
| 20° | 4.37 | 4.5/12 |
| 22.5° | 4.97 | 5/12 |
| 25° | 5.60 | 5.5/12 |
| 30° | 6.93 | 7/12 |
| 35° | 8.40 | 8.5/12 |
| 40° | 10.07 | 10/12 |
| 45° | 12.00 | 12/12 |
| 50° | 14.30 | 14.5/12 |
| 60° | 20.78 | 21/12 |
Sources and further reading
- 2021 International Residential Code, Chapter 9: Roof Assemblies
- 2021 International Residential Code, Chapter 8: Roof-Ceiling Construction
- National Roofing Contractors Association (NRCA)
Frequently asked questions
How do I convert pitch to degrees?
Divide rise by 12, take the arctangent and convert radians to degrees. 6/12 is 26.57 degrees.
What pitch is 30 degrees?
About 6.93/12, usually rounded to 7/12.
What pitch is 20 degrees?
About 4.37/12.