How do you write roof pitch as a decimal?
Short answer. Divide the rise by 12. A 6/12 pitch is 0.5, a 4/12 is 0.333 and a 9/12 is 0.75. Multiply the decimal by 100 to get percent grade, or by 12 to turn a decimal back into a standard x/12 pitch.
Decimal chart
- 2/12 = 0.167
- 3/12 = 0.250
- 4/12 = 0.333
- 5/12 = 0.417
- 6/12 = 0.500
- 7/12 = 0.583
- 8/12 = 0.667
- 9/12 = 0.750
- 10/12 = 0.833
- 12/12 = 1.000
Why the decimal is handy
- Rafter length: rafter length = run × the square root of (1 + decimal squared). For a 14 foot run at 0.5, that is 14 × 1.118, or about 15.65 feet before the overhang.
- Ridge height: run × decimal. A 14 foot run at 0.5 rises 7 feet.
- Percent grade: decimal × 100. Building codes sometimes state minimum slopes this way, such as 2/12 being about a 17 percent slope.
- Spreadsheets: most calculators and spreadsheet functions want a decimal, not a fraction.
Going from measurements to a decimal
Measure rise and run in the same units. If the ridge sits 54 inches above the wall plate over a 144 inch run, 54 divided by 144 is 0.375. Multiply by 12 to get 4.5, so the roof is a 4.5/12, which most roofers would call a four and a half pitch.
Watch the units
The decimal is unitless only when rise and run share a unit. Mixing feet and inches is the most common mistake and produces pitches that make no sense, such as 0.04. If you need degrees instead, take the inverse tangent of the decimal. More context is in how roofers measure a roof and roof anatomy explained.