A rafter is the hypotenuse of run and rise
The rafter, run and rise form a right triangle. Fix the run (half the building width) and the pitch, and the rest follows.
Pitch is written x:12 — x inches of rise for every 12 inches of run. At 6:12 with a 20 ft run, rise = 20 × 6⁄12 = 10 ft, so the rafter is √(400 + 100) = 22.36 ft. That length runs ridge to wall and does not yet include the overhang.
Run is half the span — the number people get wrong
A rafter reaches from the ridge in the center to the wall, so it spans the run, not the full building width. Use the whole width and your rafter comes out twice as long as it should.
On a 40 ft building each rafter covers the 20 ft run, from the center ridge out to one wall — never the full span.
Rafter multiplier by pitch
Skip the square root: rafter length per foot of run is a fixed factor for each pitch. Multiply the run by it, then add the tail.
| Pitch | Angle | Multiplier (per ft of run) |
|---|---|---|
| 3:12 | 14.0° | 1.031 |
| 4:12 | 18.4° | 1.054 |
| 6:12 | 26.6° | 1.118 |
| 8:12 | 33.7° | 1.202 |
| 10:12 | 39.8° | 1.302 |
| 12:12 | 45.0° | 1.414 |
A 20 ft run at 6:12 is 20 × 1.118 = 22.36 ft — the same answer. Hip and valley rafters run diagonally, so multiply the common rafter by about 1.06.
Common questions
How do I calculate rafter length?
It is the hypotenuse of the run and the rise. Take the square root of run squared plus rise squared, where rise equals run times pitch over 12. For a 20-foot run at 6:12 pitch, rise is 10 feet and the rafter is the square root of 400 plus 100, about 22.36 feet.
Is run the same as the width of the roof?
No, and this is the most common mistake. Run is half the building width, measured from the outside wall to the center ridge. A 40-foot-wide building has a 20-foot run per side.
Does the overhang add to rafter length?
Yes. The tail past the wall is its own small hypotenuse: the square root of the overhang squared plus (overhang times pitch over 12) squared. A 2-foot overhang at 6:12 adds about 2.24 feet.
