How do you calculate roof pitch in degrees?
Short answer. To convert pitch to degrees, divide the rise by 12 and take the inverse tangent: a 7/12 pitch is arctan(7 divided by 12), or about 30.3 degrees. To go the other way, multiply 12 by the tangent of the angle: 35 degrees gives 12 times tan(35), about 8.4, so roughly an 8.4/12 pitch.
The two formulas
- Pitch to degrees: angle = arctan(rise divided by 12).
- Degrees to pitch: rise per 12 = 12 times tan(angle).
Any scientific calculator works, including the one on most phones when turned sideways. Make sure it is set to degrees, not radians; the label usually reads DEG.
Worked examples
- 5/12 to degrees: 5 divided by 12 = 0.4167. Inverse tangent (tan to the minus 1) of 0.4167 = about 22.6 degrees.
- 9/12 to degrees: 9 divided by 12 = 0.75. Inverse tangent = about 36.9 degrees.
- 25 degrees to pitch: tan(25) = 0.4663. Times 12 = about 5.6, so between a 5/12 and a 6/12, likely 5.5/12 or a measurement close to 6/12.
- 40 degrees to pitch: tan(40) = 0.8391. Times 12 = about 10.1, so a 10/12 roof.
Percent slope too
Percent slope = rise divided by run, times 100. A 6/12 roof is a 50 percent slope; a 12/12 roof is 100 percent. Percent is mostly used for drainage and low-slope work.
Tips for accurate inputs
- Measure angles on a rafter or a straight board laid across the shingles, not on bumpy shingle edges.
- Round results to the nearest whole or half pitch; framing is rarely odd values.
- Calculate each roof section separately.
For a full conversion chart and how pitch affects area and labor, see how roofers measure a roof.