How do I calculate rafter length?

Rafter length = √(run² + rise²) — 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, because 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 cut into the underside of the rafter where it lands on the wall's top plate — a level seat cut and a plumb heel cut, so the rafter sits flush on the plate instead of just the corner touching it. It doesn't change the calculated rafter length; it's cut into timber you've already allowed for. Keep the notch shallow — commonly no more than about a third of the rafter's depth — so you're not cutting away too much of its strength at the bearing point.

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. Always order a bit longer than the bare minimum; you lose some length to the plumb cut at the ridge and the birdsmouth at the plate.

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

A common rafter, its run and its rise form a right triangle — so rafter length is straight Pythagoras:

Rafter length = √(run² + rise²)

Which is the same thing as:

Rafter length = run ÷ cos(pitch angle)

Use whichever you have handy — the run and rise, or the run and the angle from pitch to degrees.

1 rise · 2 run · 3 rafter length (the hypotenuse) · 4 pitch angle · 5 birdsmouth seat cut, where the rafter lands on the wall plate.

Work it out by hand

Take a roof with a 3.6 m run and a 1.8 m rise — a 6/12 pitch, 26.57°.

1. No overhang yet.

√(3.6² + 1.8²) = √(12.96 + 3.24) = √16.2 ≈ 4.02 m

That’s the theoretical length from the ridge centreline to the outside edge of the wall plate.

2. Add the eave overhang. Say you want a 450 mm overhang, measured horizontally. Because the overhang sits at the same pitch, add it to the run before you calculate — don’t 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

The 450 mm of horizontal overhang added about 510 mm to the actual rafter length — because it’s travelling 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 without running short.

4. The birdsmouth. Mark a level seat cut and a plumb heel cut into the underside of the rafter where it crosses the wall plate, so it beds down flat instead of pivoting on one corner. It’s cut into timber you’ve already allowed for — it doesn’t change the length sum above. Keep the notch depth shallow, commonly no more than about a third of the rafter’s depth, so there’s still enough timber left at that point to carry the load.

Do it in 5 seconds

Get the angle first: Roof Pitch to Angle — convert your rise/run to degrees before working out rafter length.
Full guide: How to Work Out Pitch of Roof in Degrees — includes 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) — 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, because 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 cut into the underside of the rafter where it lands on the wall's top plate — a level seat cut and a plumb heel cut, so the rafter sits flush on the plate instead of just the corner touching it. It doesn't change the calculated rafter length; it's cut into timber you've already allowed for. Keep the notch shallow — commonly no more than about a third of the rafter's depth — so you're not cutting away too much of its strength at the bearing point.
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. Always order a bit longer than the bare minimum; you lose some length to the plumb cut at the ridge and the birdsmouth at the plate.
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.