How do you convert roof pitch into degrees?
Short answer. Divide the rise by 12, then take the inverse tangent (tan⁻¹ or atan) of that number with your calculator in degree mode. For a 7/12 roof, 7 ÷ 12 = 0.583, and the inverse tangent of 0.583 is about 30.3 degrees.
On a phone calculator
- Turn the phone sideways to get the scientific calculator.
- Make sure it shows Deg, not Rad.
- Type the rise, divide by 12, press equals.
- Press the 2nd key, then tan⁻¹. The result is the angle in degrees.
In a spreadsheet
Type =DEGREES(ATAN(7/12)) and replace 7 with your rise. To go the other way, =12*TAN(RADIANS(30)) turns 30 degrees into a rise of about 6.93, which is essentially a 7/12 roof.
Quick reference for checking your work
- 3/12 = 14.0 degrees
- 5/12 = 22.6 degrees
- 7/12 = 30.3 degrees
- 9/12 = 36.9 degrees
- 12/12 = 45.0 degrees
Mistakes that give strange answers
- Radian mode: a 7/12 roof will come out as 0.53. If your answer is under 2 for a normal roof, switch to degrees.
- Using the rafter length: dividing rise by rafter length gives the sine, not the tangent. Always divide rise by horizontal run.
- Mixed units: feet over inches turns a 6/12 into nonsense. Convert both to inches first.
- Fractional rises: a 6 1/2 inch rise is 6.5, not 6.12.
Degrees are useful for phone apps and some product literature, but roofers, shingle instructions and insurance estimates use x/12. Once you have the angle, see how roofers measure a roof for how it turns into squares of material.