Roof pitch formulas
- Pitch to degrees: angle = arctan(rise ÷ 12)
- Degrees to pitch: rise = 12 × tan(angle)
- Percent slope: slope % = rise ÷ run × 100 = tan(angle) × 100
- Rafter multiplier: √(1 + (rise ÷ 12)²). Multiply the run by it to get the rafter length (before overhang)
Roof pitch chart
| Pitch | Degrees | Percent | Multiplier |
|---|---|---|---|
| 1/12 | 4.76° (≈ 5°) | 8.3% | 1.003 |
| 2/12 | 9.46° (≈ 9°) | 16.7% | 1.014 |
| 3/12 | 14.04° (≈ 14°) | 25% | 1.031 |
| 4/12 | 18.43° (≈ 18°) | 33.3% | 1.054 |
| 5/12 | 22.62° (≈ 23°) | 41.7% | 1.083 |
| 6/12 | 26.57° (≈ 27°) | 50% | 1.118 |
| 7/12 | 30.26° (≈ 30°) | 58.3% | 1.158 |
| 8/12 | 33.69° (≈ 34°) | 66.7% | 1.202 |
| 9/12 | 36.87° (≈ 37°) | 75% | 1.25 |
| 10/12 | 39.81° (≈ 40°) | 83.3% | 1.302 |
| 11/12 | 42.51° (≈ 43°) | 91.7% | 1.357 |
| 12/12 | 45° (≈ 45°) | 100% | 1.414 |
| 13/12 | 47.29° (≈ 47°) | 108.3% | 1.474 |
| 14/12 | 49.4° (≈ 49°) | 116.7% | 1.537 |
| 15/12 | 51.34° (≈ 51°) | 125% | 1.601 |
| 16/12 | 53.13° (≈ 53°) | 133.3% | 1.667 |
| 17/12 | 54.78° (≈ 55°) | 141.7% | 1.734 |
| 18/12 | 56.31° (≈ 56°) | 150% | 1.803 |
| 19/12 | 57.72° (≈ 58°) | 158.3% | 1.873 |
| 20/12 | 59.04° (≈ 59°) | 166.7% | 1.944 |
| 21/12 | 60.26° (≈ 60°) | 175% | 2.016 |
| 22/12 | 61.39° (≈ 61°) | 183.3% | 2.088 |
| 23/12 | 62.45° (≈ 62°) | 191.7% | 2.162 |
| 24/12 | 63.43° (≈ 63°) | 200% | 2.236 |
Common roof pitches in the US
- Low slope (under 4/12, below about 18°): porches, additions, modern homes and commercial buildings. Needs extra underlayment or membrane roofing.
- Conventional (4/12 to 9/12, 18° to 37°): the majority of American houses. 4/12, 5/12 and 6/12 are typical for ranch houses; 7/12 to 9/12 for two-story colonials.
- Steep (10/12 and up, 40°+): Victorians, Tudors, A-frames and snowy regions. Roofers need fall protection and roof jacks.
Also handy: set a miter saw for rafters or trim with the miter angle calculator, or measure an existing roof with the phone angle finder.
Frequently asked questions
How do I convert roof pitch to degrees?
Divide the rise by the run and take the arctangent: degrees = arctan(rise ÷ 12). For a 6/12 pitch, arctan(6 ÷ 12) = arctan(0.5) = 26.57°.
What is a 4/12 roof pitch in degrees?
A 4/12 pitch is 18.43°, or a 33.3% slope. It is one of the most common pitches for ranch-style homes in the US.
What pitch is a 45 degree roof?
A 45° roof is a 12/12 pitch: it rises 12 inches for every 12 inches of run, which is a 100% slope.
What is the minimum roof pitch for asphalt shingles?
Most shingle manufacturers and the International Residential Code allow asphalt shingles down to a 2/12 pitch (9.46°), but pitches from 2/12 up to 4/12 require a double layer of underlayment. Below 2/12 you need a low-slope roofing system such as a membrane.
How do I measure my roof pitch?
Place a level on a rafter or the roof deck, mark 12 inches along it from the roof, and measure straight down (or up) to the roof: that distance is the rise. Or lay your phone on the roof or a rafter and read the pitch directly with the phone angle finder. From the ground, you can take a photo of the gable end and use measure angle from photo.