Roof pitch calculator
Roof pitch is a right-triangle problem. Rise over run gives the angle, and the hypotenuse gives the rafter.
Pitch angle
26.565degrees
- Rise per 12 of run
- 6.000
- Pitch as a percentage
- 50.00 %
- Rafter length including overhang
- 4.972
- Roof pitch multiplier
- 1.118 03
- Roof surface area
- 99.44
- Plan area covered
- 80.00
Show the working
- Horizontal run = 4
- Vertical rise = 2
- Building length = 10
- Eaves overhang = 0.5
- Pitch angle = deg(atan(2 / 4)) = 26.5651
- Pitch as a percentage = 2 / 4 * 100 = 50
- Rise per 12 of run = 2 / 4 * 12 = 6
- Rafter length including overhang = hypot(2, 4) + 0.5 = 4.972 14
- Roof pitch multiplier = 4 > 0 ? hypot(2, 4) / 4 : 0 = 1.118 03
- Roof surface area = 2 * 4.972 14 * 10 = 99.4427
- Plan area covered = 2 * 4 * 10 = 80
- ridge_height = 2 = 2
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- angle = arctan(rise / run)
- rafter = sqrt(rise^2 + run^2)
- roof area = plan area x pitch multiplier
A 6-in-12 pitch is 26.57 degrees and has a multiplier of 1.118, so the roof surface is 12% larger than the plan.
Most concrete tiles need at least 17.5 degrees; slates and shingles have their own minimums.