🏠 Construction
Roof Pitch to Angle
Convert roof pitch between rise-over-12, degrees, slope percentage and the rafter multiplier. Choose what you know, enter it, then press Convert.
About the Roof Pitch to Angle
Roof pitch is usually written as rise over a 12-inch run: a 6/12 roof rises 6 inches for every 12 inches of horizontal run. That is an angle of 26.57° and a slope of 50%. The rafter multiplier — 1.118 for a 6/12 — is the number you multiply the run by to get the rafter length, including the diagonal.
The three descriptions are different views of the same triangle. Builders use rise/12 because it maps directly to a framing square; engineers use degrees; drainage and accessibility guidance often uses percent. This converter keeps all three in sync, plus the multiplier for rafter layout.
How the calculation works
- Angle = arctan(rise ÷ run).
- Pitch (x/12) = tan(angle) × 12.
- Slope % = tan(angle) × 100.
- Rafter multiplier = √(1 + (rise ÷ run)²).
Reference values
| Pitch | Angle | Slope | Multiplier |
|---|---|---|---|
| 1/12 | 4.76° | 8.33% | 1.003 |
| 3/12 | 14.04° | 25% | 1.031 |
| 4/12 | 18.43° | 33.33% | 1.054 |
| 6/12 | 26.57° | 50% | 1.118 |
| 8/12 | 33.69° | 66.67% | 1.202 |
| 10/12 | 39.81° | 83.33% | 1.302 |
| 12/12 | 45° | 100% | 1.414 |
Worked example: a 10/12 roof
A 10/12 roof rises 10 inches for every 12 inches of horizontal run. The angle is arctan(10 ÷ 12) = 39.81°, the slope is 83.33%, and the rafter multiplier is 1.302. For a building 24 ft wide, the run to the ridge is 12 ft, so the rafter length is 12 × 1.302 = 15.62 ft before the overhang is added. A 12/12 roof is steeper: 45°, 100% slope and a multiplier of 1.414, which makes the rafter 41% longer than the run.
The multiplier is the quickest check on a framing square. Measure the horizontal run, multiply, and you have the diagonal. Add the overhang to the run first if the rafter is to extend past the wall; multiplying only the indoor span understates the board length.
Pitch, drainage and roofing material
Pitch is not only a structural choice; it sets what will keep water out. Asphalt shingles generally need at least 2/12, and many manufacturers require 4/12 or a double underlayment below that. Clay and concrete tiles typically need 4/12 or steeper, slate wants more, and standing-seam metal will follow a low pitch only with a sealed seam. Flat roofs rely on a membrane and a fall of about 1/4 inch per foot rather than on slope alone.
Snow load, wind uplift and the local code all interact with pitch. A steeper roof sheds snow and rain faster but catches more wind and uses more material per square metre of floor area. Confirm the minimum for your chosen covering before the framing is cut, because changing pitch later means rebuilding the roof.