12/12 roof pitch in degrees
A 12/12 roof pitch is 45.0000°. That is a 100.00% grade, a slope ratio of 1 : 1, and a rafter factor of 1.414214, exactly.
Change the pitch
45.0000°
Multiply your run by 1.414214 for the rafter length. The cuts and the birdsmouth are in the app.
Rafter length at 12/12, by span
Run is half the span on a symmetrical gable. Length is along the rafter, before any birdsmouth, ridge or tail is taken off.
| Building span | Run | Rafter length | Decimal feet |
|---|---|---|---|
| 20 ft | 10 ft | 14' 1-11/16" | 14.142 ft |
| 24 ft | 12 ft | 16' 11-5/8" | 16.971 ft |
| 28 ft | 14 ft | 19' 9-9/16" | 19.799 ft |
| 32 ft | 16 ft | 22' 7-1/2" | 22.627 ft |
| 36 ft | 18 ft | 25' 5-1/2" | 25.456 ft |
Every row is the run multiplied by 1.414214, the rafter factor for 12/12. The same figure for every pitch is on the full roof pitch chart.
What 12/12 means on the roof
Twelve in twelve is exactly 45°, and it is the only pitch on the whole chart whose angle comes out as a round number. The rise equals the run, so the arctangent lands on 45 exactly. Every other pitch is irrational and carries the ≈.
The working is the arctangent of the rise over the run: atan(12 ÷ 12) = 45.0000°. The rafter factor is the hypotenuse of the same triangle over its base, √(12² + 12²) ÷ 12, which is why multiplying any run by 1.414214 gives the rafter. That figure is the roof pitch multiplier, and it is the same number whatever the size of the roof.
Shingle slope limits quoted here are from the IRC, the United States model code. Your state, province or county may amend them, and several do.