Roof pitch is just the rise over the run — how far the roof climbs for a given horizontal distance — but trades quote it in four different ways. Carpenters use the x:12 ratio (rise per 12 of run), engineers use the angle in degrees, surveyors use a percentage, and everyone eventually needs the rafter length, which is simply the diagonal across the rise and run. They are all the same slope wearing different clothes, and this calculator converts between them from one pair of numbers.
Reviewed: June 19, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: right-triangle roof geometry.
The roof-pitch equations
The rise-to-run fraction is the single quantity behind every form: feed it to arctangent for the angle, multiply by 12 for the carpenter's ratio, by 100 for the percent. The rafter is the hypotenuse, so it always exceeds the run by the "rafter factor" √(1 + (rise/run)²) — about 1.05 for a 4:12 roof and 1.41 for a 12:12. Multiply your horizontal run by that factor to get the sloping rafter line.
Worked example — a 4:12 roof
Scenario: A gable roof rises 4 ft for every 12 ft of run, with a 12 ft run from wall to ridge.
The 4:12 roof sits at a gentle 18.4°, sheds water well and is still safe to walk. Over the 12 ft run each rafter line is about 12.65 ft before you add the eave overhang and trim for the ridge board. Steepen it to 9:12 and the angle jumps to 36.9° with a 1.25 rafter factor — more dramatic, more material, and steep enough to want roof anchors when working on it.
Frequently Asked Questions
Pitch = rise/run. As x:12 it's the rise per 12 run (4 over 12 = 4:12); as an angle it's atan(rise/run) ≈ 18.4° for 4:12.
angle = atan(x/12). 6:12 = atan(0.5) ≈ 26.6°; 12:12 = 45°. Reverse: x = 12 × tan(angle).
rafter = √(rise² + run²). A 4 ft rise / 12 ft run ≈ 12.65 ft. Add overhang and ridge allowance.
Most homes are 4:12 to 9:12. 6:12 (~27°) is very common; below 2:12 is low-slope needing membrane roofing.
Same steepness: pitch as a ratio (6:12), slope as an angle or percent. This tool shows all three from rise and run.