Roof Pitch Calculator
Pitch = rise ÷ run × 12, and angle = arctan(rise ÷ run). A roof that rises 6 in over 12 in of level run is a 6/12 pitch: 26.57°, a 50 % slope. Below 2/12, asphalt shingles are not allowed (IRC R905.2.2); from 2/12 up to 4/12 they need two layers of underlayment.
Roof pitch
6/12
26.57° · 50 % slope
Estimate only. Check dimensions, loads and local code requirements with a qualified professional before you build.
- Angle
- 26.57°
- Slope
- 50 %
- Slope factor (roof area ÷ footprint)
- × 1.118
Worked examples
With a level and a tape: 6 in of rise over 12 in
- Pitch = 6 ÷ 12 × 12 = 6/12
- Angle = arctan(0.5) = 26.57°; slope 6 ÷ 12 × 100 = 50 %
- Slope factor √(1 + 0.5²) = 1.118
Result: 6/12, 26.57°, a 50 % slope.
Checked by the automated test “roof pitch — 6 in of rise over 12 in of run → 6/12, 26.57°, 50 % slope, factor 1.118”.
From the plans: 24 ft span, ridge 6 ft above the walls
- Run = 24 ÷ 2 = 12 ft; pitch = 6 ÷ 12 × 12 = 6/12
- Rafter = √(12² + 6²) = 13.42 ft = 13 ft 5 in, wall plate to ridge centre
Result: 6/12, common rafter 13 ft 5 in before the overhang.
Checked by the automated test “roof pitch — 24 ft span with a 6 ft ridge → 6/12, common rafter 13 ft 5 in”.
How it works
Pitch (x/12) = rise ÷ run × 12 · from the span: run = span ÷ 2, rise = ridge height
Angle = arctan(rise ÷ run) · Slope % = rise ÷ run × 100
Slope factor = √(1 + (rise ÷ run)²)
Common rafter, no overhang = √(run² + rise²)
Assumptions
- The run is measured level, not along the roof. Any run works: the calculator scales it to 12.
- Span mode: the run is half the span between the outside of the walls and the rise is the ridge height above the wall top. The rafter is measured to the centre of the ridge, with no overhang.
- Shingle limits from IRC R905.2.2, the same rule as the roofing calculator. Just under a limit, figures are rounded down, so 1.999/12 never reads 2/12.
Reference table
| Pitch | Angle | Slope | Slope factor |
|---|---|---|---|
| 1/12 | 4.76° | 8.3 % | 1.003 |
| 2/12 | 9.46° | 16.7 % | 1.014 |
| 3/12 | 14.04° | 25 % | 1.031 |
| 4/12 | 18.43° | 33.3 % | 1.054 |
| 5/12 | 22.62° | 41.7 % | 1.083 |
| 6/12 | 26.57° | 50 % | 1.118 |
| 7/12 | 30.26° | 58.3 % | 1.158 |
| 8/12 | 33.69° | 66.7 % | 1.202 |
| 9/12 | 36.87° | 75 % | 1.25 |
| 10/12 | 39.81° | 83.3 % | 1.302 |
| 11/12 | 42.51° | 91.7 % | 1.357 |
| 12/12 | 45° | 100 % | 1.414 |
Angles match the City of Dallas roof pitch chart to 2 decimals. Roof area = footprint × slope factor.
Measuring a real roof
- From the attic. If the roof is out of reach, take the same measurement on a rafter in the attic: the rafter has the roof’s pitch.
- Then the roof area. Enter the pitch in the roofing calculator for the roof surface, the squares and the shingle bundles.
- Rafter length is a start. Add the overhang and take off half the ridge board before cutting, and check the length against your plans.
Common mistakes
- Measuring 12 in along the roof The 12 in run is level. Laid along a 6/12 roof, a 12 in rule rises only 5.37 in, and the pitch reads low.
- Mixing up percent and degrees A 6/12 roof is a 50 % slope but 26.57°; a 100 % slope is 45° (12/12), not a vertical wall.
- Shingles on a low slope Under 2/12, IRC R905.2.2 rules out asphalt shingles; from 2/12 up to 4/12 it asks for two layers of underlayment. ARMA puts standard shingle application at 4/12 to 21/12. The roofing calculator applies the same rule.
Frequently asked questions
How do I find the pitch of a roof?
Use a 12 in carpenter's level and a tape measure, the method of the Asphalt Roofing Manufacturers Association. Set one end of the level on the roof and hold it level. Measure straight down from its other end to the roof: 6 in means a 6/12 pitch. A phone slope app gives the angle instead; enter it in angle mode.
How do I calculate roof pitch in degrees?
Angle = arctan(rise ÷ 12). For 4/12, arctan(0.333) = 18.43°; for 6/12, 26.57°; for 12/12, 45°: the values of the City of Dallas pitch chart.
How do I figure out roof slope as a percentage?
Divide the rise by the run and multiply by 100: 4/12 is 33.3 %, 6/12 is 50 %. In metric, the percentage is also the centimetres of rise per metre of run.
Sources
Formula, examples and sources checked on by the Yardstick Math team. How we check our formulas.
- Roof Pitch Diagram Chart (0/12 to 21/12 in degrees) — City of Dallas, accessed
- Roofing Practices Manual – Conversion Tables and Charts (slope ratio, percent, degrees) — RCABC, accessed
- Seattle Residential Code, Chapter 9 (IRC R905.2.2: shingles on slopes of 2/12 or more) — Seattle SDCI, accessed
- Residential Asphalt Roofing Manual, 2014, ch. 5: Determining your roof's slope (12 in level and tape measure; shingles on 2/12 or more) — Asphalt Roofing Manufacturers Association (ARMA), accessed