Roof pitch to angle, multiplier and rafters
Enter the pitch as rise per 12, degrees or percent. Get the pitch multiplier for roof area, the hip and valley factor, and rafter lengths from the run.
Rafter lengths are line lengths along the top edge before the ridge-board deduction and the plumb and seat cuts. Hip and valley figures assume both roof planes have the same pitch.
| Pitch | Angle | Multiplier | Hip/valley |
|---|
Roof pitch is the rise in inches per 12 inches of run. The angle is arctan(rise ÷ 12): a 6/12 roof is 26.57°, a 50% slope. The pitch multiplier, √(rise² + 144) ÷ 12, turns plan area into roof area (1.118 for 6/12), and the hip or valley factor is √(rise² + 288) ÷ 12, which is 1.5 for 6/12.
How to use the roof pitch calculator
Enter the pitch
As rise per 12 inches, degrees or slope percent; the other two fill in.
Add the run
Optional: the run from wall to ridge centerline and the overhang, in feet.
Read the factors
Multiplier, hip and valley factor, total rise, and common and hip rafter lengths.
What the roof pitch calculator does
Three ways in
Rise per 12, degrees or percent slope, converted both ways.
Pitch multiplier
√(rise² + 144) ÷ 12, the factor that turns footprint area into roof area.
Hip and valley factor
√(rise² + 288) ÷ 12 for hips and valleys between planes of equal pitch.
Rafter lengths
Common and hip rafter line lengths in feet and in feet and inches to the nearest 1/8 in.
Pitch table
1/12 to 12/12 with angle, multiplier and hip factor, and code notes for low slopes.
- Angle
- arctan(rise ÷ 12)
- Slope %
- rise ÷ 12 × 100
- Pitch multiplier
- √(rise² + 144) ÷ 12 (6/12 = 1.118)
- Hip/valley factor
- √(rise² + 288) ÷ 12 (6/12 = 1.5), equal pitches
- Shingle slope limits
- IRC R905.2.2: 2/12 minimum; double underlayment from 2/12 to 4/12
Roof Pitch Calculator FAQ
How do I calculate roof pitch?
Measure how many inches the roof rises over 12 inches of level run. Hold a level 12 inches long against the rafter or roof surface and measure straight down or up to the roof. A 6-inch rise is a 6/12 pitch.
How do I convert roof pitch to degrees?
Take the arctangent of the rise divided by 12. 4/12 is 18.43°, 6/12 is 26.57°, 8/12 is 33.69° and 12/12 is 45°.
What is a pitch multiplier?
The ratio of the sloped roof surface to its level footprint: √(rise² + 144) ÷ 12. Multiply the plan area, including overhangs, by it to get roof area. A 6/12 roof's multiplier is 1.118, not 1.24 as some older tables print.
What is the minimum pitch for asphalt shingles?
The International Residential Code allows asphalt shingles on slopes of 2/12 and steeper, and requires double underlayment from 2/12 up to 4/12. Below 2/12 you need a low-slope roofing system. Check the shingle manufacturer's instructions too.
How long is a hip rafter?
For a hip between two planes of the same pitch, multiply the common run by √(rise² + 288) ÷ 12. On a 6/12 roof with a 14 ft run that's 14 × 1.5 = 21 ft, before the ridge deduction and the cuts.
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