Roof Pitch Calculator

Background.

Ask a roofer how steep a roof is and the answer will be something like "six in twelve": the roof climbs 6 inches for every 12 inches it travels horizontally. Ask a solar installer or an engineer and you may hear 26.6 degrees. Both describe the same roof. Measure a rise over any horizontal run you like, in inches, and the pitch comes back in every form people use: the plain ratio of rise to run, the angle above horizontal, the rise per 12 inches of run, and the slope multiplier.

The x-in-12 form is the working language of the trade because it is what a carpenter's framing square reads directly, and because code and manufacturer rules are written in it. The 2021 International Residential Code, for example, allows asphalt shingles only on roofs of 2-in-12 or steeper and requires a double layer of underlayment between 2-in-12 and 4-in-12. Degrees are easier to picture, and they are what an angle-finder app or a solar mounting bracket gives you.

The multiplier is the least familiar of the four results and the one that goes furthest. It is the length of the sloping rafter line for each unit of horizontal run, 1.118 on a 6-in-12 roof, so it turns a run measured on a plan into a rafter length and a plan area into roof surface. Nothing in the geometry assumes a particular roof size, which is why one measurement, taken anywhere along a straight rafter, describes the whole plane.

What is roof pitch calculator?

Roof pitch is the steepness of a roof plane, set by a right triangle whose legs are the vertical rise and the horizontal run and whose long side follows the roof surface. The ratio rise ÷ run is the slope; multiplied by 100 it becomes a percentage, so a 6-in-12 roof has a 50% slope. The pitch angle is the angle between the roof and the horizontal. The x-in-12 figure restates the same slope as the rise over a 12-inch run. Older carpentry books use pitch differently, as rise divided by the whole span of the building, which is why a 6-in-12 roof is sometimes called a quarter pitch.

How to use this calculator.

1. 01Measure a rise and the run it occurs over. The simplest way is a level held horizontally against the roof or the underside of a rafter, marked at 12 inches, with the vertical distance measured from that mark to the roof line.
2. 02Enter both in inches, up to 240 each. Any run works: 9 inches of rise over a 24-inch run is converted to its 12-inch equivalent for you.
3. 03If you are working from a plan, use the horizontal distance from the outside wall to the ridge as the run; on a symmetrical gable that is half the building's width.
4. 04Read the x-in-12 pitch to compare with code or shingle-wrapper minimums, the angle for solar or angle-finder work, and the multiplier for rafter lengths or roof area.

The formula.

Four results come from the same two measurements. The ratio is rise ÷ run. The angle is θ = arctan(rise ÷ run), converted from radians to degrees by multiplying by 180/π. The slope multiplier is √(rise² + run²) ÷ run, which is Pythagoras: the square root gives the length of the sloping side, and dividing by the run expresses it per unit of horizontal distance; it can also be written √(1 + ratio²) or 1 ÷ cos θ. The x-in-12 pitch is rise × 12 ÷ run. Because every result depends only on the proportion between rise and run, the unit cancels: feet over feet give the same angle and multiplier as inches over inches. A rise of 0 is a level surface, with a ratio and angle of 0 and a multiplier of 1; a run of 0 would be a vertical wall, so the run must be positive. Steepness and angle are not proportional. Each extra inch of rise adds fewer degrees as the roof steepens: 3-in-12 is 14.04°, 6-in-12 is 26.57°, 8-in-12 is 33.69° and 12-in-12 is exactly 45°.

A worked example.

Frequently asked questions.

References& sources.

1. [1]National Roofing Contractors Association (2025). "The NRCA Roofing Manual: Steep-slope Roof Systems." NRCA.
2. [2]International Code Council (2021). "2021 International Residential Code, Chapter 9: Roof Assemblies." ICC.
3. [3]National Institute of Standards and Technology. "NIST Digital Library of Mathematical Functions, §4 — Elementary Functions (Trigonometric)."