How do you calculate roof pitch with rise and run?
Short answer. Pitch is rise over run, stated per 12 inches of run: measure how many inches the roof climbs over 12 inches of horizontal distance, and that number over 12 is the pitch. If you measure a different run, divide the rise by the run and multiply by 12, so a 9 inch rise over 18 inches of run is a 6/12 pitch.
The formula
Pitch (per 12) = rise divided by run, times 12. Rise is the vertical change. Run is the horizontal distance, measured level, not along the slope of the roof.
Worked examples
- Small measurement: 4 inches of rise over 12 inches of run is 4/12.
- Different run: 10 inches of rise over 24 inches of run is 10 divided by 24, times 12, which equals 5/12.
- Whole roof: a gable that rises 8 feet over a run of 12 feet, half of a 24 foot span, is 8 divided by 12, times 12, which equals 8/12.
- Odd numbers: 7 feet of rise over 13 feet of run works out to about 6.5/12. Roofs are usually framed to whole or half numbers, so this is likely a 6.5/12 or a measuring error near 6/12 or 7/12.
Converting to other formats
- Percent slope: rise divided by run, times 100. A 6/12 pitch is a 50 percent slope.
- Degrees: the inverse tangent of rise divided by run. A 6/12 pitch is about 26.6 degrees; 12/12 is 45 degrees.
Common mistakes
- Measuring run along the roof surface instead of level. That gives a number that is too large and a pitch that is too low.
- Using the full building width as the run on a gable roof. Run is half the span, from the wall to the point under the ridge.
- Measuring on the shingle surface where lumps throw off a short level.
For how pitch feeds into roof area and pricing, see how roofers measure a roof and roof anatomy explained.