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Roof pitch calculator: pitch, slope and rafter length

Roof maths is one triangle used three times: pitch, rafter length and roof area. Here are the formulas, a table for common pitches and a 6/12 example.

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What is roof pitch and how do you calculate it?

Pitch is the rise in inches for every 12 inches of horizontal run, written 6/12 or "6 in 12". To find it, measure a rise over a 12 in run with a level, or use the angle: pitch = 12 × tan(angle). The slope factor, which turns a horizontal distance into a distance along the roof, is √(1 + (pitch ÷ 12)²).

How do you calculate common rafter length?

Rafter length along the slope = the horizontal run × the slope factor. The run is half the building width for a simple gable roof. Add the overhang and subtract half the thickness of the ridge board separately.

Example. A 24 ft wide building has a 12 ft run. At 6/12 the rafter is 12 × 1.118 = 13.416 ft, which is 13 ft 5 in to the nearest inch, before overhang.

Roof square footage calculator

For a simple roof with no overhang, roof area = the building's footprint area × the slope factor.

Example. A 30 ft by 40 ft footprint at 6/12: 1,200 sq ft × 1.118 = 1,341.6 sq ft, or 13.4 roofing squares.

Shingle calculator: how many bundles?

One roofing square covers 100 sq ft. Most architectural shingles come three bundles to the square, but some products use four, so read the package. Add waste, usually 10 percent, for cuts, hips and valleys.

Example. 13.4 squares plus 10 percent = 14.8, rounded up to 15 squares. At three bundles a square that is 45 bundles.

Hip, valley and jack rafters

A hip or valley rafter runs along the diagonal, so its horizontal run is longer than a common rafter's run and its cuts differ. Jack rafters are the shortened common rafters that meet a hip or valley.

Roof tools in Clad

Clad works out common, hip, valley and jack rafters, roof squares and shingle bundles, a gable roof with the ridge height, tail and birdsmouth, and a pitch gauge that reads the slope from the phone's motion sensor. Every result states how it was rounded.

See what Clad does. Clad is coming soon to the iPhone.

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How this page was made

Written with the help of an AI assistant (Claude, by Anthropic). Every worked example was computed again by a program and checked against its formula. Building codes differ by place: check yours before you build.