Roof pitch multiplier table
The roof pitch multiplier is the number you multiply a level 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, the pitch 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. Hips and valleys at this pitch are in the app.
Rafter and hip multipliers by pitch
The hip and valley multiplier is for two roofs of the same pitch meeting at 45° in plan, per foot of common run. The last column is worked for a ten foot run, which is a twenty foot building span on a symmetrical gable.
| Pitch | Rafter multiplier | Hip and valley | Rafter over 10 ft run |
|---|---|---|---|
| 1/12 | 1.003466 | 1.416667 | 10' 7/16" |
| 2/12 | 1.013794 | 1.424001 | 10' 1-5/8" |
| 3/12 | 1.030776 | 1.436141 | 10' 3-11/16" |
| 4/12 | 1.054093 | 1.452966 | 10' 6-1/2" |
| 4.5/12 | 1.068000 | 1.463087 | 10' 8-3/16" |
| 5/12 | 1.083333 | 1.474317 | 10' 10" |
| 6/12 | 1.118034 | 1.500000 | 11' 2-3/16" |
| 6.5/12 | 1.137279 | 1.514398 | 11' 4-1/2" |
| 7/12 | 1.157704 | 1.529797 | 11' 6-15/16" |
| 8/12 | 1.201850 | 1.563472 | 12' 1/4" |
| 9/12 | 1.250000 | 1.600781 | 12' 6" |
| 10/12 | 1.301708 | 1.641476 | 13' 3/16" |
| 11/12 | 1.356568 | 1.685312 | 13' 6-13/16" |
| 12/12 | 1.414214 | 1.732051 | 14' 1-11/16" |
| 13/12 | 1.474317 | 1.781463 | 14' 8-15/16" |
| 14/12 | 1.536591 | 1.833333 | 15' 4-3/8" |
| 15/12 | 1.600781 | 1.887459 | 16' 1/16" |
| 16/12 | 1.666667 | 1.943651 | 16' 8" |
| 17/12 | 1.734054 | 2.001735 | 17' 4-1/16" |
| 18/12 | 1.802776 | 2.061553 | 18' 5/16" |
| 19/12 | 1.872684 | 2.122957 | 18' 8-3/4" |
| 20/12 | 1.943651 | 2.185813 | 19' 5-1/4" |
| 21/12 | 2.015564 | 2.250000 | 20' 1-7/8" |
| 22/12 | 2.088327 | 2.315407 | 20' 10-5/8" |
| 23/12 | 2.161854 | 2.381934 | 21' 7-7/16" |
| 24/12 | 2.236068 | 2.449490 | 22' 4-5/16" |
Angles in degrees for every pitch are on the roof pitch to degrees chart.
How to use a pitch multiplier
Multiply the level run by the multiplier for your pitch. A 6/12 roof over a 14 ft run has a 15' 7-13/16" common rafter, because 168 in × 1.118034 = 187.83 in. Add any overhang to the run first, measured level. For the hip or valley on the same roof, multiply the common run by the hip and valley multiplier instead: 14 ft × 1.500000 is 21' 0".
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.
