Roof Pitch Calculator
Measure the rise over a run (12 inches is standard), or type the angle. Add the building run and footprint if you want rafter length and roof squares.
Estimate only. Rafter length here is the line length along the slope. Ridge board, birdsmouth, and plumb cuts change the real cut. Check the plans and the roofing product's install sheet for its lowest allowed pitch.
Result
Fill in your numbers and hit Calculate.
How the math works
Pitch = rise / run x 12 (shown as X/12)
From an angle: pitch = tan(angle) x 12
Angle = atan(pitch / 12) Slope % = pitch / 12 x 100
Slope factor = square root of (12 x 12 + pitch x pitch) / 12
Rafter line length = rafter run x slope factor (overhang the same way)
Roof area = footprint x slope factor Squares = area x (1 + waste%) / 100The footprint is the flat area the roof covers, overhangs included, as if you looked down from above. The slope factor turns that into real roof area. Hips, valleys, and dormers add waste, so bump the waste % on cut-up roofs.
Most shingles come 3 bundles to a square, but check the wrapper. Need to add up feet and inches first? Use the Tape Measure Calculator.
Worked examples
Real numbers, run through the same math the calculator uses. Tap a link to load it into the calculator.
What is the angle of a 6/12 roof pitch?
About 26.57 degrees. A 6/12 roof rises 6 inches for every 12 inches of run, which is a 50% slope, and the slope factor is 1.1180.
Angle = atan(6 / 12) = atan(0.5) = 26.57 degrees
Slope = 6 / 12 x 100 = 50%
Slope factor = square root of (144 + 36) / 12 = 13.416 / 12 = 1.1180How long is a rafter for a 24 ft wide building with a 6/12 pitch?
The common rafter line length is 13' 5". With a 12 inch overhang it is 14' 6 7/16". That is before the ridge board and birdsmouth cuts.
Rafter run = half of 24 ft = 12 ft = 144 in
144 in x 1.1180 slope factor = 161.0 in = 13' 5"
Overhang: 12 in x 1.1180 = 13.42 in
161.0 + 13.42 = 174.4 in = 14' 6 7/16"How many squares of shingles for a 1,500 sq ft roof footprint at 6/12?
About 18.45 squares with 10% waste, or 56 bundles at 3 bundles per square. The real roof area is about 1,677 sq ft.
Roof area = 1,500 sq ft x 1.1180 = 1,677 sq ft
With waste = 1,677 x 1.10 = 1,845 sq ft
Squares = 1,845 / 100 = 18.45
Bundles = 18.45 x 3 = 55.3, round up to 56What pitch is a 30 degree roof?
About 6.93/12, so close to a 7/12 pitch. It rises about 6 15/16" per foot of run.
Pitch = tan(30 degrees) x 12
tan(30) = 0.5774
0.5774 x 12 = 6.93, so 6.93/12Free weekly email
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