Roof pitch multiplier
The roof pitch multiplier is the number you multiply a horizontal run by to get the length along the rafter. At 6/12 it is 1.118034, so ten feet of run is 11.18 feet of rafter. Roofers also call it the slope factor or the rafter factor. They are the same number.
Change the pitch
26.5651°≈
Multiply your run by 1.118034 for the rafter length. The cuts and the birdsmouth are in the app.
Multiplier by pitch
The last column is worked for a ten foot run, which is a twenty foot building span on a symmetrical gable.
| Pitch | Multiplier | Grade | Rafter over 10 ft run |
|---|---|---|---|
| 2/12 | 1.013794 | 16.67% | 10' 1-5/8" |
| 3/12 | 1.030776 | 25.00% | 10' 3-11/16" |
| 4/12 | 1.054093 | 33.33% | 10' 6-1/2" |
| 5/12 | 1.083333 | 41.67% | 10' 10" |
| 6/12 | 1.118034 | 50.00% | 11' 2-3/16" |
| 8/12 | 1.201850 | 66.67% | 12' 0-1/4" |
| 10/12 | 1.301708 | 83.33% | 13' 0-3/16" |
| 12/12 | 1.414214 | 100.00% | 14' 1-11/16" |
Every pitch from 1/12 to 24/12 is on the full chart.
Where the number comes from
It is the hypotenuse of the pitch triangle divided by its base. For a rise of r over twelve, that is √(12² + r²) ÷ 12. Nothing about it depends on the size of the roof, which is why one number works for any run.
It is also why the multiplier is never less than 1. A flat roof would be exactly 1, and every pitch above that adds length.
Two things it does not include: the birdsmouth and the ridge deduction, and the tail. Multiply for the theoretical length, then take those off at the bench.