How do you calculate roof pitch to angle and angle to pitch?
Short answer. To convert pitch to an angle, divide the rise by 12 and take the arctangent: angle = arctan(rise / 12). To go from an angle back to pitch, multiply 12 by the tangent of the angle: rise = 12 × tan(angle). For example, 7/12 is arctan(0.583), about 30.3 degrees.
Pitch to angle
- Divide the rise by 12. For 8/12: 8 ÷ 12 = 0.667.
- Take the inverse tangent (tan⁻¹ or atan) in degree mode: atan(0.667) = 33.7 degrees.
Angle to pitch
- Take the tangent of the angle in degree mode. For 35 degrees: tan(35) = 0.700.
- Multiply by 12: 0.700 × 12 = 8.4. That is about 8.4/12, which a roofer would call an 8 pitch, or between 8 and 9.
Doing it on a phone
Turn the phone's calculator sideways to get the scientific keys. Make sure it shows Deg, not Rad. Use the 2nd or inv key to reach tan⁻¹.
Worked examples
- 4/12: atan(0.333) = 18.4 degrees
- 6/12: atan(0.5) = 26.6 degrees
- 9/12: atan(0.75) = 36.9 degrees
- 30 degrees: 12 × tan(30) = 6.93, about 7/12
- 40 degrees: 12 × tan(40) = 10.07, about 10/12
- 45 degrees: 12 × tan(45) = 12, exactly 12/12
Accuracy tip
Angle readings from apps can drift a degree or two. On low pitches that is small, but between 8/12 and 10/12 one degree is about a third of an inch of rise. If the number matters for materials or an estimate, measure rise and run directly. See how roofers measure a roof.