Roof Pitch Calculator
Convert a measured rise and run (both in inches, or any matching unit) into standard roof pitch. You get the pitch in x/12 form, the angle in degrees, the slope as a percent, and the multiplier that turns horizontal run into rafter length.
Example: with Rise (inches) 6 · Run (inches) 12 → Roof pitch: 6/12 pitch.
- Angle26.57°
- Slope50.0% grade
- Rafter multiplier×1.1180 per foot of run
Computed by the calculator below using its default values. Change any input to see your own numbers.
Pitch is rise per 12 inches of horizontal run: a 6/12 roof climbs 6 inches per foot, which is 26.57°, not 30°.
How roof pitch is measured
American roof pitch is written as rise over a 12-inch run: a 6/12 roof climbs 6 inches vertically for every 12 inches it travels horizontally. To measure an existing roof, hold a level horizontally against the slope (from inside the attic against a rafter is easiest), mark 12 inches along the level, and measure straight down from that mark to the roof surface. That vertical distance in inches is your pitch. This calculator accepts any rise and run pair and normalizes it to x/12, so measuring 8 inches of rise over a 24-inch run still reads out correctly as 4/12.
Pitch, angle, and percent slope are three ways of saying the same thing. The angle is arctan(rise ÷ run), and the percent grade is rise ÷ run × 100 — the same convention road signs use. A 12/12 roof is 45°, and a 6/12 roof is 26.57°, noticeably less than the 30° people tend to guess.
What the rafter multiplier does
The multiplier (sometimes called the slope or hip-valley factor) converts flat, horizontal dimensions into true along-the-slope dimensions. At 6/12 the multiplier is 1.1180, so a roof plane over 20 feet of horizontal run needs rafters about 22.36 feet long, and 1,000 square feet of footprint carries about 1,118 square feet of actual roof surface. Estimators use it constantly: multiply the building footprint by the factor to get shingle area, or multiply run by the factor to get rafter length.
How it’s calculated
Pitch per 12 = rise ÷ run × 12. Angle = arctan(rise ÷ run) in degrees. Slope percent = rise ÷ run × 100. Rafter multiplier = √(rise² + run²) ÷ run. Rise and run must be in the same unit; the ratio is unitless, so inches, feet, or centimeters all work.
Assumes a straight, uniform roof plane — on older roofs that have sagged, measure pitch at several spots and near the ridge rather than mid-span.
Common pitches: angle and rafter multiplier
| Pitch | Angle | Multiplier | Character |
|---|---|---|---|
| 3/12 | 14.04° | 1.031 | Minimum for many asphalt shingle installs |
| 4/12 | 18.43° | 1.054 | Low slope, walkable |
| 6/12 | 26.57° | 1.118 | Most common suburban pitch |
| 8/12 | 33.69° | 1.202 | Steep, roof jacks recommended |
| 12/12 | 45.00° | 1.414 | Very steep, staging required |
Computed from angle = arctan(pitch/12) and multiplier = √(12² + pitch²) ÷ 12; character notes are trade convention.
Common mistakes
- Measuring the run along the slope instead of truly horizontal — always use a level for the 12-inch reference.
- Confusing pitch with angle: 6/12 is 26.6°, not 30°, and guessing degrees by eye routinely overshoots.
- Using the building span instead of the run — on a symmetric gable the run is half the span.
- Reading pitch off a sagging rafter mid-span on an old roof, which understates the original pitch.
Frequently asked questions
What is the roof pitch formula?
Pitch = rise ÷ run × 12, expressed as x/12. Measure how many inches the roof rises over 12 inches of horizontal run: 6 inches of rise over 12 inches of run is a 6/12 pitch.
What angle is a 6/12 roof?
26.57 degrees. The conversion is arctan(6 ÷ 12). People often assume 6/12 means 30°, but pitch does not scale linearly with angle — 12/12 is 45°, not 60°.
What is the minimum pitch for shingles?
Asphalt shingles are generally allowed down to 2/12 with special double-underlayment detailing, and 4/12 or steeper is the standard territory where normal installation rules apply. Below 2/12 you need a membrane roof, not shingles.
How do I use the rafter multiplier?
Multiply any horizontal distance by it to get the true sloped distance. At 6/12 the multiplier is 1.118, so 20 feet of run needs a 22.4-foot rafter, and a 1,000 sq ft footprint carries about 1,118 sq ft of roof surface.