12/12 roof pitch: 45.00 degrees
A 12/12 roof pitch is 45.0000° exactly. Its multiplier, or rafter factor, is 1.414214, its grade is 100.00% and its slope ratio is 1 : 1.
Change the pitch
45.0000°
Multiply your run by 1.414214 for the rafter length. Hips and valleys at this pitch 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 multiplier for every pitch is on the roof pitch multiplier table.
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.
A hip or valley where both roofs are 12/12 runs at 45° across the plan, so it is longer than the common rafter beside it: 1.7321 ft of hip for every foot of common run, which is 17' 3-7/8" over a 10 ft common run against 14' 1-11/16" for the rafter.
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.
Other pitches: 1/12 · 2/12 · 3/12 · 4/12 · 4.5/12 · 5/12 · 6/12 · 6.5/12 · 7/12 · 8/12 · 9/12 · 10/12 · 11/12. Every pitch from 1/12 to 24/12 is on the roof pitch to degrees chart.
