Slope angle in degrees is the inverse tangent of rise over run, converted from radians by multiplying by 180/π. The math is one line; the calculator above handles every input format and shows the result instantly.
This guide walks through the formula, three worked examples, and a reference table for the angles you will see most often.
The formula
Angle in degrees = arctan(rise ÷ run) × (180 ÷ π). Most calculators have a built-in arctan or "tan⁻¹" function. The factor 180/π ≈ 57.296 converts radians to degrees.
In one line: angle (°) = atan(rise/run) × 57.296.
Worked examples
From a 4/12 roof pitch: arctan(4/12) × 57.296 = arctan(0.333) × 57.296 ≈ 18.43°.
From a 6% road grade: arctan(0.06) × 57.296 ≈ 3.43°.
From a measured rise of 9 inches over 36 inches of run: arctan(9/36) × 57.296 = arctan(0.25) × 57.296 ≈ 14.04° — which is also a 3/12 pitch.
| Roof pitch | Slope (rise/run) | Slope % | Angle (degrees) |
|---|---|---|---|
| 1/12 | 0.083 | 8.3% | 4.76° |
| 2/12 | 0.167 | 16.7% | 9.46° |
| 3/12 | 0.250 | 25.0% | 14.04° |
| 4/12 | 0.333 | 33.3% | 18.43° |
| 5/12 | 0.417 | 41.7% | 22.62° |
| 6/12 | 0.500 | 50.0% | 26.57° |
| 7/12 | 0.583 | 58.3% | 30.26° |
| 8/12 | 0.667 | 66.7% | 33.69° |
| 9/12 | 0.750 | 75.0% | 36.87° |
| 10/12 | 0.833 | 83.3% | 39.81° |
| 11/12 | 0.917 | 91.7% | 42.51° |
| 12/12 | 1.000 | 100% | 45.00° |
| 16/12 | 1.333 | 133.3% | 53.13° |
| 18/12 | 1.500 | 150% | 56.31° |
| 24/12 | 2.000 | 200% | 63.43° |
Need to run the numbers?Use the free roof pitch calculator on the home page to convert pitch to angle, calculate rafter length, or estimate roof area in any unit.