The formula
Rafter length = √(run² + rise²). That is plain Pythagoras. The horizontal run, the vertical rise and the sloping line form a right triangle. You can also use run ÷ cos(pitch angle). Both give the same answer.
Use whichever pair you have on hand. That means run and rise, or run and the angle from pitch to degrees.
1 rise · 2 run · 3 rafter length · 4 pitch angle · 5 birdsmouth seat cut on the wall plate.
Work it out by hand
Take a roof with a 3.6 m run and a 1.8 m rise. That is a 6/12 pitch, 26.57°.
1. No overhang yet.
√(3.6² + 1.8²) = √(12.96 + 3.24) = √16.2 ≈ 4.02 m.
That is the length from the ridge centre line to the outside edge of the wall plate.
2. Add the eave overhang. Say you want 450 mm of overhang, measured level, not up the slope. The overhang runs at the same pitch as the rafter. So add it to the run before you calculate. Do not just tack 450 mm onto the answer.
- New run: 3.6 + 0.45 = 4.05 m.
- New rise (same pitch, 0.5 ratio): 4.05 × 0.5 = 2.025 m.
- Rafter length: √(4.05² + 2.025²) = √20.5 ≈ 4.53 m.
That 450 mm of level overhang added about 510 mm to the actual rafter length. It runs at the roof’s angle, not straight out.
3. Round up to stock length. 4.53 m needs a 4.8 m length of timber. That leaves room for the plumb cut at the ridge and the birdsmouth notch at the plate in this example. Confirm stock availability, actual cut geometry and the required trimming allowance before ordering.
4. The birdsmouth. Mark a level seat cut and a plumb heel cut where the rafter crosses the wall plate. Cut them into the underside. Then the rafter beds down flat instead of rocking on one corner. The notch sits in timber you have already allowed for. It does not change the length sum above. Use the approved notch and bearing detail. Permissible cuts depend on the member, load, support and applicable code or manufacturer. The length calculation does not establish structural capacity.
Do it in 5 seconds
Related
- Get the angle first: Roof Pitch to Angle turns your rise and run into degrees.
- Full guide: How to Work Out Pitch of Roof in Degrees shows the roof pitch multiplier method side by side with Pythagoras.
- AU code minimum: Minimum Roof Pitch (NCC 2025).
Calculation basis
Pythagoras gives the sloping length from a horizontal run and vertical rise. The examples keep full precision before rounding. They do not check spans, bearing or notch limits. Get cut details from the approved design and the applicable standard or product instructions.