How to Find Rafter Length from the Roof Pitch

A roof’s pitch says how many inches it rises for every 12 inches of level run: an 8/12 roof climbs 8 inches per foot. From the pitch and the run you can find the rafter length with the Pythagorean theorem.

For learning and planning practice. Check your local building codes and the manufacturer’s numbers before you build: the code numbers here are typical values, not the law where you live.

Try it with your own problem ↓

The steps

Find the run: the level distance from the outside of the wall to the center of the ridge. On a simple gable roof it is half the span.
Rafter length per foot of run = √(12² + pitch²) inches. This is the number in a framing square’s rafter table.
Rafter length = run in feet × length per foot. Change the inches to feet and inches.
Rise = run × pitch ÷ 12, and the roof angle = tan⁻¹(pitch ÷ 12).
Add any overhang along the slope, and remember that this is the line length, before the cuts.

A worked example

A roof has an 8/12 pitch and a run of 12 ft. Find the rafter length (wall to ridge center), the rise and the roof angle.

Length per foot of run: √(12² + 8²) = √208 ≈ 14.42".
Rafter: 12 × 14.4222 ≈ 173.07". That is 14 ft (168") and 5.07", about 14' 5 1/16".
Rise: 12 ft = 144", and 144 × 8 ÷ 12 = 96" = 8' 0".
Angle: tan⁻¹(8 ÷ 12) ≈ 33.7°.
Check: √(144² + 96²) ≈ 173.07". ✓

The rafter is about 14' 5 1/16", the ridge sits 8' 0" above the wall, and the roof slopes about 33.7°.

Why it works

Under each foot of run, the rafter is the long side of a small right triangle with legs of 12 inches (the run) and 8 inches (the rise). Every foot of run adds another copy of that triangle, so the rafter grows by the same 14.42 inches each foot. It is the Pythagorean theorem done once for one foot, then multiplied.

Try it with your own problem

Open The Framing Square (free) with this example already filled in. It shows every step, and you can type over it with your own numbers.

Work it out: 8/12 pitch, 12 ft runOpens The Framing Square with this example

Or try these

More carpentry math, every step written out: open The Framing Square.

Common mistakes

Using the whole span as the run. On a gable roof each rafter covers half the span.
Treating the pitch as an angle. 8/12 is a ratio, not 8°. The angle is tan⁻¹(8/12) ≈ 33.7°.
Leaving out the overhang. Add it along the slope: level overhang × length per foot ÷ 12.
Cutting to the line length. At the top, take off half the ridge board’s thickness, measured level.

Questions people ask

What is the rafter length for a 6/12 pitch over a 12 ft run?

√(144 + 36) ≈ 13.42" per foot of run, and 12 × 13.42 ≈ 161", about 13' 5".

What angle is a 7/12 pitch?

tan⁻¹(7 ÷ 12) ≈ 30.3°.

How much rafter does an 18 inch overhang add on an 8/12 roof?

Along the slope it is 18 × 14.42 ÷ 12 ≈ 21.6" more rafter.

Keep learning

Show The Steps is free, with no accounts or ads, and everything is worked out in your own browser. Start at the home page.