How do I calculate rafter length?

Rafter length = √(run² + rise²). That is Pythagoras, using the horizontal run and vertical rise. It's the same as run ÷ cos(pitch angle). For a 3.6 m run and 1.8 m rise (a 6/12 pitch), that's √(3.6² + 1.8²) = √16.2 ≈ 4.02 m.

Does the eave overhang change the rafter length?

Yes. Add the overhang's horizontal distance to the run before you calculate. The overhang runs at the same pitch as the rest of the rafter. A 450 mm overhang on a 3.6 m run (6/12 pitch) makes the total rafter length about 4.53 m instead of 4.02 m.

What is a birdsmouth cut and does it add length?

It's the notch in the rafter's underside where it lands on the wall's top plate. A level seat cut and a plumb heel cut let it sit flat. It adds no length; it's cut into timber you've already allowed for. Keep it shallow: no more than about a third of the rafter's depth.

What length timber do I order for a rafter?

Calculate the true rafter length (run to run, plus overhang). Then round up to the next standard stock length, commonly 4.8 m or 6.0 m, so you're not joining timber mid-span. Order a bit longer than the bare minimum; you lose length to the ridge plumb cut and the birdsmouth.

Is rafter length the same as roof pitch multiplier × run?

Yes, same answer, different route. The roof pitch multiplier is 1 ÷ cos(pitch angle). For a 6/12 pitch that's about 1.118. Multiply your run by it and you get the same rafter length as the Pythagoras method: 3.6 m × 1.118 ≈ 4.02 m.

In this section

Rafter Length Calculation: Run, Rise & Overhang

Work out common rafter length with Pythagoras — run and rise to the exact length, plus how the eave overhang and birdsmouth seat cut change what you order and cut.

The formula

Rafter length = √(run² + rise²). That is plain Pythagoras. The run, the rise and the rafter 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. You will not run short.

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. Keep the notch shallow. As a rule, cut no more than about a third of the rafter’s depth. That leaves enough timber to carry the load at that point.

Do it in 5 seconds

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).

Sources

American Wood Council (AWC), Wood Frame Construction Manual — rafter geometry and span-table technical guidance, including birdsmouth seat-cut practice.
Engineering ToolBox, “Rafter Length” — reference calculator, cross-checked against the Pythagorean method above.

Frequently asked questions

How do I calculate rafter length?: Rafter length = √(run² + rise²). That is Pythagoras, using the horizontal run and vertical rise. It's the same as run ÷ cos(pitch angle). For a 3.6 m run and 1.8 m rise (a 6/12 pitch), that's √(3.6² + 1.8²) = √16.2 ≈ 4.02 m.
Does the eave overhang change the rafter length?: Yes. Add the overhang's horizontal distance to the run before you calculate. The overhang runs at the same pitch as the rest of the rafter. A 450 mm overhang on a 3.6 m run (6/12 pitch) makes the total rafter length about 4.53 m instead of 4.02 m.
What is a birdsmouth cut and does it add length?: It's the notch in the rafter's underside where it lands on the wall's top plate. A level seat cut and a plumb heel cut let it sit flat. It adds no length; it's cut into timber you've already allowed for. Keep it shallow: no more than about a third of the rafter's depth.
What length timber do I order for a rafter?: Calculate the true rafter length (run to run, plus overhang). Then round up to the next standard stock length, commonly 4.8 m or 6.0 m, so you're not joining timber mid-span. Order a bit longer than the bare minimum; you lose length to the ridge plumb cut and the birdsmouth.
Is rafter length the same as roof pitch multiplier × run?: Yes, same answer, different route. The roof pitch multiplier is 1 ÷ cos(pitch angle). For a 6/12 pitch that's about 1.118. Multiply your run by it and you get the same rafter length as the Pythagoras method: 3.6 m × 1.118 ≈ 4.02 m.