Roof pitch is the inches of rise per 12" of level run, written X/12. This chart gives each pitch from 1/12 to 12/12 as an angle, as a slope factor (sloped length per foot of level run, √(1 + (X/12)²)), and as the common rafter length per foot of run that a framing square's rafter table shows.
The second table is for hips and valleys where both roof planes have the same pitch. They run at 45° in plan, so each foot of common run is 16.97" of hip run: the hip or valley length per foot of common run is √(288 + X²), and the hip/valley factor is that ÷ 12.
Pitch, angle and common rafter
Pitch, angle and common rafter| Pitch | Angle | Slope factor | Rafter per ft of run |
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| 1/12 | 4.76° | 1.003 | 12.04" |
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| 2/12 | 9.46° | 1.014 | 12.17" |
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| 3/12 | 14.04° | 1.031 | 12.37" |
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| 4/12 | 18.43° | 1.054 | 12.65" |
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| 5/12 | 22.62° | 1.083 | 13.00" |
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| 6/12 | 26.57° | 1.118 | 13.42" |
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| 7/12 | 30.26° | 1.158 | 13.89" |
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| 8/12 | 33.69° | 1.202 | 14.42" |
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| 9/12 | 36.87° | 1.250 | 15.00" |
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| 10/12 | 39.81° | 1.302 | 15.62" |
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| 11/12 | 42.51° | 1.357 | 16.28" |
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| 12/12 | 45.00° | 1.414 | 16.97" |
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Hip and valley rafters
Hip and valley rafters| Pitch | Hip / valley per ft of run | Hip / valley factor | Hip / valley angle |
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| 1/12 | 17.00" | 1.417 | 3.37° |
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| 2/12 | 17.09" | 1.424 | 6.72° |
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| 3/12 | 17.23" | 1.436 | 10.02° |
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| 4/12 | 17.44" | 1.453 | 13.26° |
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| 5/12 | 17.69" | 1.474 | 16.42° |
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| 6/12 | 18.00" | 1.500 | 19.47° |
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| 7/12 | 18.36" | 1.530 | 22.42° |
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| 8/12 | 18.76" | 1.563 | 25.24° |
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| 9/12 | 19.21" | 1.601 | 27.94° |
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| 10/12 | 19.70" | 1.641 | 30.51° |
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| 11/12 | 20.22" | 1.685 | 32.95° |
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| 12/12 | 20.78" | 1.732 | 35.26° |
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Rounding and how to use the chart
Multiply by the run in feet: a 6/12 roof with 12 ft of run has a common rafter of 12 × 13.42" = 161" (13' 5") from the ridge center to the outside of the wall, and a hip of 12 × 18" = 216" (18' 0"). Take off half the ridge thickness and add the overhang for the cut length; the rafter calculator does both and gives the cut angles.
The slope factor works for area too: plan area × slope factor = roof surface, which is how the roofing calculator counts squares. Angles are rounded to 0.01°, factors to three decimals and lengths to 0.01".
Estimates only. Check measurements, product labels and local building codes before you buy or build.