4.5/12 roof pitch: 20.56 degrees
A 4.5/12 roof pitch is 20.5560° to four places. Its multiplier, or rafter factor, is 1.068000, its grade is 37.50% and its slope ratio is 1 : 2.6667.
Change the pitch
20.5560°≈
Multiply your run by 1.068000 for the rafter length. Hips and valleys at this pitch 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 multiplier for every pitch is on the roof pitch multiplier table.
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.
A hip or valley where both roofs are 4.5/12 runs at 45° across the plan, so it is longer than the common rafter beside it: 1.4631 ft of hip for every foot of common run, which is 14' 7-9/16" over a 10 ft common run against 10' 8-3/16" 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 · 5/12 · 6/12 · 6.5/12 · 7/12 · 8/12 · 9/12 · 10/12 · 11/12 · 12/12. Every pitch from 1/12 to 24/12 is on the roof pitch to degrees chart.
