How do you calculate roof pitch from measurements?
The basic formula
Pitch = (rise divided by run) times 12. If you measured over exactly 12 inches of run, the rise is the pitch directly: 6 inches of rise over 12 inches of run is a 6/12 roof.
When you did not measure over 12 inches
- Rise 5 inches over 9 inches of run: 5 divided by 9 is 0.556, times 12 is about 6.7, so about 7/12.
- Rise 10 inches over 24 inches: 0.417 times 12 is 5, so 5/12.
- Ridge 8 feet above the wall top with a 16 foot half span: 0.5 times 12 is 6, so 6/12.
Converting to degrees
Angle = arctangent of rise over run. Common values: 4/12 is 18.4 degrees, 5/12 is 22.6, 6/12 is 26.6, 7/12 is 30.3, 8/12 is 33.7, 9/12 is 36.9, 10/12 is 39.8, and 12/12 is 45.
Converting to percent
Rise over run times 100. A 6/12 roof is a 50 percent slope; a 3/12 roof is 25 percent.
Pitch multiplier for roof area
Multiplier = square root of (1 plus (pitch divided by 12) squared). A 6/12 roof gives 1.118, so a 1,600 square foot footprint becomes about 1,789 square feet of roof surface before overhangs and waste.
Why the number matters
Pitch decides which materials are allowed, how much material is needed and how the work is priced. See how roofers measure a roof and roof anatomy explained.