9/12 roof pitch: 36.87 degrees
A 9/12 roof pitch is 36.8699° to four places. Its multiplier, or rafter factor, is 1.250000, its grade is 75.00% and its slope ratio is 1 : 1.3333.
Change the pitch
36.8699°≈
Multiply your run by 1.250000 for the rafter length. Hips and valleys at this pitch are in the app.
Rafter length at 9/12, 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 | 12' 6" | 12.500 ft |
| 24 ft | 12 ft | 15' 0" | 15.000 ft |
| 28 ft | 14 ft | 17' 6" | 17.500 ft |
| 32 ft | 16 ft | 20' 0" | 20.000 ft |
| 36 ft | 18 ft | 22' 6" | 22.500 ft |
Every row is the run multiplied by 1.250000, the rafter factor for 9/12. The multiplier for every pitch is on the roof pitch multiplier table.
What 9/12 means on the roof
Nine in twelve is the one pitch whose rafter factor comes out exact. 9, 12 and 15 are a Pythagorean triple, so the factor is 15/12 — 1.25 precisely, with no rounding and no ≈. It is the mirror of 12/12: that one has the exact angle and an irrational factor, this one has the exact factor and an irrational angle.
The working is the arctangent of the rise over the run: atan(9 ÷ 12) = 36.8699°. The rafter factor is the hypotenuse of the same triangle over its base, √(12² + 9²) ÷ 12, which is why multiplying any run by 1.250000 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 9/12 runs at 45° across the plan, so it is longer than the common rafter beside it: 1.6008 ft of hip for every foot of common run, which is 16' 1/16" over a 10 ft common run against 12' 6" 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 · 10/12 · 11/12 · 12/12. Every pitch from 1/12 to 24/12 is on the roof pitch to degrees chart.
