Roof Pitch to Degrees: Chart and Formula
To convert a roof pitch to degrees, take the arctangent of rise ÷ run: degrees = arctan(rise ÷ 12). A 4/12 roof is 18.4°, 6/12 is 26.6°, 8/12 is 33.7° and 12/12 is exactly 45°.
Roof pitch to degrees chart
| Pitch | Degrees | Grade | Pitch factor |
|---|---|---|---|
| 1/12 | 4.8° | 8% | 1.003 |
| 2/12 | 9.5° | 17% | 1.014 |
| 3/12 | 14.0° | 25% | 1.031 |
| 4/12 | 18.4° | 33% | 1.054 |
| 5/12 | 22.6° | 42% | 1.083 |
| 6/12 | 26.6° | 50% | 1.118 |
| 7/12 | 30.3° | 58% | 1.158 |
| 8/12 | 33.7° | 67% | 1.202 |
| 9/12 | 36.9° | 75% | 1.250 |
| 10/12 | 39.8° | 83% | 1.302 |
| 11/12 | 42.5° | 92% | 1.357 |
| 12/12 | 45.0° | 100% | 1.414 |
| 14/12 | 49.4° | 117% | 1.537 |
| 16/12 | 53.1° | 133% | 1.667 |
| 18/12 | 56.3° | 150% | 1.803 |
| 24/12 | 63.4° | 200% | 2.236 |
Grade is rise ÷ run as a percentage. The pitch factor turns a flat footprint into real roof area; see the roof pitch multiplier.
Pitch to degrees formula
degrees = arctan(rise ÷ run)
Pitch is written as rise over a 12-inch run, so for a 6/12 roof: 6 ÷ 12 = 0.5, and arctan(0.5) = 26.57°. On a phone calculator, turn it sideways for the scientific keys, make sure it's in degrees (not radians), enter 0.5 and press tan⁻¹.
If you measured a run other than 12 inches, divide first. A 3 inch rise over a 6 inch run is 0.5, the same 6/12 pitch.
Degrees to roof pitch
rise per 12 = 12 × tan(degrees)
| Degrees | Pitch |
|---|---|
| 15° | 3.2/12 |
| 20° | 4.4/12 |
| 25° | 5.6/12 |
| 30° | 6.9/12 |
| 35° | 8.4/12 |
| 40° | 10.1/12 |
| 45° | 12/12 |
What the numbers mean for roofing
- Under 2/12 (about 9.5°): too flat for shingles. These roofs need a low-slope system such as membrane or rolled roofing.
- 2/12 to 4/12: asphalt shingles are allowed under the International Residential Code, but only with a double layer of underlayment.
- 4/12 to 9/12: the range most houses fall in. Standard shingle installation, and walkable for most roofers.
- Over 9/12 (about 37°): steep. Expect roof jacks, harnesses and a higher labor price.
Don't know your pitch yet? See how to measure roof pitch.
Questions
What is a 4/12 roof pitch in degrees?
18.4 degrees. The roof rises 4 inches for every 12 inches of horizontal run, a 33% grade.
What is a 6/12 roof pitch in degrees?
26.6 degrees, a 50% grade. It's one of the most common pitches on houses in North America.
What is a 12/12 roof pitch?
A 45 degree roof: it rises 12 inches for every 12 inches of run, so the rise equals the run. Its pitch factor is 1.414.
How do I convert degrees to roof pitch?
Multiply 12 by the tangent of the angle. 30 degrees is 12 × tan(30°) = 6.9, so about a 7/12 pitch.