Envelope · Roof
Roof pitch calculator
Pitch in degrees = atan(rise ÷ run); in per cent = 100 × rise ÷ run; in the US, rise in inches per 12 inches of run. A 6 in 12 roof rises 6 for every 12: 50 %, 26.57°. Its pitch factor √(1 + 0.5²) = 1.118 turns a 4000 mm run into a 4472 mm rafter and 80 m² of plan into 89.44 m² of roof. Type the pitch in whichever form you have.
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Degrees
— °
Per cent
— %
X in 12
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Pitch factor
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Rafter length
— mm
Roof area
— m²
Insulating the roof? The U-value calculator works out the build-up, and the condensation check tells you whether it stays dry.
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How this is calculated
slope = rise / run
degrees = atan(slope)
per cent = 100 × slope
X in 12 = 12 × slope
pitch factor = √(1 + slope²) = 1 / cos(degrees)
rafter = run of the rafter × pitch factor
roof area = plan area × pitch factor
The rafter is measured along the pitch line from wall plate to ridge, before the overhang, the birdsmouth and the ridge board are allowed for. The roof area is for one uniform pitch; a hipped or valleyed roof is the sum of its planes.
What this page does not do
- No minimum pitch check. The lowest pitch allowed depends on the tile, slate or sheet: use the manufacturer's figure.
- No loads. Snow and wind on the roof and the rafter size are structural design.
Questions people ask
- How do you convert roof pitch to degrees?
- Degrees = atan(rise ÷ run). A 6 in 12 pitch: atan(6 ÷ 12) = atan(0.5) = 26.57°. A 4 in 12 pitch is 18.43°, 8 in 12 is 33.69°, 12 in 12 is 45°.
- What is a 30 degree roof pitch in per cent?
- tan(30°) × 100 = 57.7 %, or 6.93 in 12.
- How do you work out the length of a rafter from the pitch?
- Multiply the horizontal run by the pitch factor √(1 + slope²): at 6 in 12 the factor is 1.118, so a 4000 mm run needs a 4472 mm rafter before the overhang.