The formula
Angle (°) = arctan(rise ÷ run). That is the whole job. Roof pitch is a ratio: rise over horizontal run. Use degree mode for arctan. Take the arctan of that ratio and you have the angle in degrees.
Want it as a grade instead? Same triangle: Grade (%) = (rise ÷ run) × 100.
1 rise. 2 run. 3 rafter (slope distance). 4 right angle where the run meets the rise. 5 pitch angle: the value both formulas above solve for.
Work it out by hand
Say you measure up in the roof space. Over a 3.6 m run, the rafter rises 1.8 m.
- Divide rise by run. 1.8 ÷ 3.6 = 0.5.
- Take the arctan for degrees. arctan(0.5) = 26.57°.
- Or ×100 for grade. 0.5 × 100 = 50% grade.
That 0.5 ratio is also a 6/12 pitch. That is the x-in-12 style roofing suppliers and truss quotes use. It means 6 inches of rise for every 12 of run. Any unit works, as long as rise and run use the same one.
Common pitches, converted
| Pitch (rise/run) | Angle | Grade |
|---|---|---|
| 3/12 | 14.04° | 25% |
| 4/12 | 18.43° | 33.3% |
| 6/12 | 26.57° | 50% |
| 9/12 | 36.87° | 75% |
| 12/12 | 45.00° | 100% |
Do it in 5 seconds
Related
- Full guide: How to Work Out Pitch of Roof in Degrees. How to measure rise and run from the attic or the roof, the tools to use, and the minimum pitch each roofing material needs.
- Next step: Rafter Length Calculation. Once you have the angle, work out how long to cut the rafters.
- AU code minimum: Minimum Roof Pitch (NCC 2025).
Calculation basis
The conversions use tan(angle) = rise ÷ horizontal run. The table values are rounded to two decimal places for angles. This page chooses no roof pitch or member size; those come from the approved design.