Roof Pitch Angle Calculator
Start from the angle and get everything else. Enter an angle in degrees or an X/12 pitch to convert between angle, pitch, slope percent, and the roof area multiplier — with a quick reference chart of common pitches below.
Pitch is always stated against a 12-inch run: 6/12 means 6 inches of rise per foot.
Planning estimates only — verify against local building codes and roofing-manufacturer requirements before you build.
How the roof pitch angle calculator works
Pitch and angle are two dialects of the same slope. Pitch counts inches of rise per 12-inch run; angle measures the tilt in degrees. Convert with the arctangent: a 6/12 pitch is atan(6/12) ≈ 26.6°, and going the other way, tan(30°) × 12 ≈ 6.9, so a 30° roof is roughly 7/12.
The area multiplier comes from the same triangle: 1 ÷ cos(angle). Multiply your roof’s flat footprint by it to order the right amount of shingles, metal, or membrane.
Common roof pitches reference
| Pitch | Angle | Slope | Area multiplier |
|---|---|---|---|
| 1/12 | 4.8° | 8.3% | 1.0035 |
| 2/12 | 9.5° | 16.7% | 1.0138 |
| 3/12 | 14.0° | 25.0% | 1.0308 |
| 4/12 | 18.4° | 33.3% | 1.0541 |
| 5/12 | 22.6° | 41.7% | 1.0833 |
| 6/12 | 26.6° | 50.0% | 1.1180 |
| 7/12 | 30.3° | 58.3% | 1.1577 |
| 8/12 | 33.7° | 66.7% | 1.2019 |
| 9/12 | 36.9° | 75.0% | 1.2500 |
| 10/12 | 39.8° | 83.3% | 1.3017 |
| 12/12 | 45.0° | 100.0% | 1.4142 |
angle = atan(pitch/12) · pitch = tan(angle)×12 · slope % = tan(angle)×100 · multiplier = 1/cos(angle)
Related tools
Keep exploring: Roof Pitch Calculator · Slope of Roof Calculator · Shed Roof Pitch Calculator · Lean-To Roof Pitch Calculator.
Roof pitch angle calculator FAQ
How do you convert roof pitch to angle?
Take the arctangent of pitch divided by 12: angle = atan(pitch/12). For 6/12, atan(6/12) = atan(0.5) ≈ 26.6°.
What angle is a 6/12 roof pitch?
26.6 degrees. Common benchmarks: 4/12 ≈ 18.4°, 6/12 ≈ 26.6°, 8/12 ≈ 33.7°, 12/12 = 45° exactly.
What pitch is a 30-degree roof?
Multiply the tangent by 12: tan(30°) × 12 ≈ 6.93, so about 7/12 pitch.
Why is roof pitch measured over 12 inches?
US framing standardized on the 12-inch run because rafters are laid out per foot — a framing square reads pitch directly as rise-per-foot, so 6/12 is instantly meaningful on the job.
What is the difference between angle and slope percent?
Angle is the tilt in degrees (0–90°); slope percent is rise ÷ run × 100, which can exceed 100% (a 12/12 roof is 100% slope at 45°). This calculator shows both.