How this calculator works
Roof pitch describes how steep a roof is, using the US roofing convention of inches of vertical rise for every 12 inches of horizontal run — a 6/12 roof, a 9/12 roof, and so on. Enter the rise (or, in angle mode, the angle from horizontal) along with the horizontal run from wall to ridge and any eave overhang, and this calculator returns the pitch, the equivalent angle in degrees, the slope as a percentage, and the rafter length.
Rafter length is found with the Pythagorean theorem: the horizontal run (including overhang) forms one leg of a right triangle, the vertical rise forms the other, and the rafter itself is the hypotenuse. This calculator computes it directly as run ÷ cos(angle), which is mathematically the same result, so you get the actual board length needed before any birdsmouth notch or ridge cut is taken into account.
The formula
Pitch = rise ÷ 12 (expressed as rise/12); angle = atan(rise ÷ 12)From an angle: rise = 12 × tan(angle); slope % = tan(angle) × 100Rafter length = (run + overhang) ÷ cos(angle)Rise-per-12 is the standard US residential convention; many other countries express roof steepness directly as an angle or a slope percentage instead, both of which this calculator also provides.
Worked example: a 6/12 pitch, 12 ft run, 12 in overhang
- Angle: atan(6 ÷ 12) ≈ 26.57°.
- Slope: (6 ÷ 12) × 100 = 50%.
- Total horizontal run including overhang: 12 + (12 ÷ 12) = 13 ft.
- Rafter length: 13 ÷ cos(26.57°) ≈ 14.53 ft.
Frequently asked questions
What are common roof pitches?
3/12 (about 14.0°) is a common low-slope minimum for shingles; 4/12 (18.4°) and 6/12 (26.6°) are widespread on standard homes; 9/12 (36.9°) and 12/12 (45°) are considered steep pitches, often chosen for heavy snow regions or a particular architectural style.
Does a steeper pitch need more roofing material?
Yes — a steeper roof has a longer rafter and larger actual surface area than its footprint suggests, so shingles, underlayment and other materials are calculated from the rafter length and slope, not the flat horizontal square footage of the house below.
How is 'run' measured for this calculator?
Run is the horizontal distance from the outside of the wall (or ridge centerline, for a full-width calculation) to the point where the rafter starts, not including the overhang — enter the overhang separately and it's added to the total run for the rafter length calculation.
Why does the angle field cap out below 90°?
A 90° roof would be perfectly vertical, with an undefined (infinite) pitch and rafter length — no real roof approaches this. The calculator guards against angles at or above 90° for that reason.
Is slope percentage the same as pitch?
They describe the same steepness with different math: pitch is rise per 12 units of run, while slope percentage is rise ÷ run × 100, without the fixed 12-unit reference. A 12/12 pitch and a 100% slope both describe a 45° roof.