How roof pitch is calculated
Roof pitch in the US is written as rise over a run of 12: a 6:12 roof climbs 6 inches for every 12 inches of horizontal distance. The calculator accepts the pitch directly, an angle in degrees, or any rise and run you have measured, and converts between all three.
The formulas are simple trigonometry. With rise r and run R: pitch = 12 × r ÷ R, angle = arctan(r ÷ R), and slope percent = 100 × r ÷ R. The rafter multiplier is √(1 + (pitch ÷ 12)²), which is the length of rafter per foot of horizontal run; multiply it by the run from the wall plate to the ridge centreline to get the rafter length before overhangs and cuts.
Common pitches
A 3:12 (14°) is a low-slope roof that usually needs a membrane or special shingle underlayment. 4:12 to 6:12 (18° to 27°) covers most production housing and is the comfortable range to walk and shingle. 8:12 to 12:12 (34° to 45°) is typical of older homes, Cape Cods and anywhere with heavy snow. Anything over 12:12 is steeper than 45° and is treated as a wall for safety and flashing purposes.
Assumptions and limits
Rafter length is the hypotenuse of the rise and run only. It does not include the overhang, the ridge board, the birdsmouth seat cut or any waste, and it assumes a simple gable. Hip and valley rafters run at a different angle and need a hip-valley multiplier (for a regular hip, √(2 + (pitch ÷ 12)²) per foot of common run). Use the result to order lumber and set a saw, then confirm with a dry fit.