Building
Roof Pitch Calculator
Roof pitch is written as inches of rise per 12 inches of horizontal run, such as 6:12. Enter the pitch and the building span to get the angle, slope factor and common rafter length.
Formula
Angle = arctan(rise ÷ 12). Percent = rise ÷ 12 × 100. Pitch multiplier = √(12² + rise²) ÷ 12, the ratio of sloped length to horizontal run. Rafter length = (span ÷ 2 + overhang) × multiplier, measured along the slope, ignoring ridge board thickness.
Worked example
A 6:12 roof over a 28 ft span with 1 ft overhangs: angle = arctan(0.5) = 26.57 degrees, slope = 50%, multiplier = √180 ÷ 12 = 1.118. Rafter = (14 + 1) × 1.118 = 16.77 ft.
Assumptions and limits
- Symmetrical gable roof.
- Subtract half the ridge board thickness from the run for cut length; add stock for the birdsmouth and tail cuts.
Frequently asked questions
What is the minimum roof pitch for asphalt shingles?
IRC Section R905.2.2 allows asphalt shingles on slopes of 2:12 or greater, with double underlayment required between 2:12 and 4:12.
How do I find the roof area from the footprint?
Multiply the footprint area, including overhangs, by the pitch multiplier. A 6:12 roof has 11.8% more area than its footprint.
What angle is a 12:12 roof?
45 degrees, since the rise equals the run.