4.5/12 roof pitch in degrees
A 4.5/12 roof pitch is 20.5560°. That is a 37.50% grade, a slope ratio of 1 : 2.6667, and a rafter factor of 1.068000, and the angle is irrational so it carries the ≈.
Change the pitch
20.5560°≈
Multiply your run by 1.068000 for the rafter length. The cuts and the birdsmouth are in the app.
Rafter length at 4.5/12, 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 | 10' 8-3/16" | 10.680 ft |
| 24 ft | 12 ft | 12' 9-13/16" | 12.816 ft |
| 28 ft | 14 ft | 14' 11-7/16" | 14.952 ft |
| 32 ft | 16 ft | 17' 1-1/16" | 17.088 ft |
| 36 ft | 18 ft | 19' 2-11/16" | 19.224 ft |
Every row is the run multiplied by 1.068000, the rafter factor for 4.5/12. The same figure for every pitch is on the full roof pitch chart.
What 4.5/12 means on the roof
Four and a half in twelve is rarely chosen and usually arrived at. It is the pitch you end up with when the ridge height is already fixed — by a planning limit, an existing wall, or a dormer that has to tuck under something — and the slope falls where the geometry puts it. It clears the low-slope band by half a twelfth, so the shingles still go down over a single underlayment.
The working is the arctangent of the rise over the run: atan(4.5 ÷ 12) = 20.5560°. The rafter factor is the hypotenuse of the same triangle over its base, √(12² + 4.5²) ÷ 12, which is why multiplying any run by 1.068000 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.
