Roof Slope Calculator
Turn a roof rise and run into pitch, slope angle, the rafter length per foot of run and the area multiplier.
How it works
pitch = rise ÷ run × 12 · angle = atan(rise ÷ run) · area multiplier = √(1 + (rise ÷ run)²)
Roof pitch is written as rise-over-run with the run fixed at 12 inches, so a roof that climbs 6 inches for every 12 inches of horizontal travel is a 6/12 pitch. The slope angle is the arctangent of rise over run, and the area multiplier — the hypotenuse of that right triangle for a run of 1 — is what you multiply a flat footprint by to get the real surface a roofer has to cover. That same multiplier scales the rafter length: a foot of run needs more than a foot of rafter once the roof tilts.
Worked example
A 6 in rise over a 12 in run: pitch = 6 ÷ 12 × 12 = 6/12. The angle is atan(6/12) = 26.6°, and the multiplier is √(1 + 0.5²) = 1.118 — so 1,000 sq ft of footprint is 1,118 sq ft of roof, and each foot of run needs 13.4 in of rafter.
Sources: Roof pitch — Wikipedia
Frequently asked questions
What is the difference between pitch, slope and angle?
They describe the same steepness three ways. Pitch is rise per 12 of run (6/12), grade is rise over run as a percent (50%), and angle is the actual degrees off horizontal (26.6°). Roofers use pitch; this tool gives all three.
Why does roof area need a multiplier?
The footprint you measure on the ground is the horizontal projection of a tilted surface. The steeper the roof, the more material it takes to cover the same footprint, and the multiplier — √(1 + slope²) — captures exactly that.
What pitch counts as "low slope"?
Anything below about 3/12 is treated as low slope and usually needs membrane or rolled roofing rather than standard shingles, because shingles rely on gravity to shed water and can leak on shallow roofs.
Related calculators
Estimates only — add for waste and confirm against local building codes and supplier specs.