Roof Pitch Calculator
Enter the rise and run of your roof to get the pitch in the standard "X-in-12" notation, the slope angle in degrees, the percent grade, and the rafter length — all from one ratio.
Pitch (rise per 12 of run)
6
- Slope angle (degrees)
- 26.57
- Slope (percent grade)
- 50%
- Rafter length (same units as inputs)
- 13.42
Roof pitch is the slope of the roof expressed three equivalent ways. The X-in-12 form (12 × rise ÷ run) is the standard US framing notation — a "6 in 12" roof rises 6 units for every 12 units of horizontal run. The slope angle is arctan(rise ÷ run), and the slope percent is 100 × rise ÷ run. Rafter length is the hypotenuse √(rise² + run²) — the actual diagonal length of timber needed for the run.
How to use this calculator
Measure the vertical rise of your roof from the top of the wall plate up to the underside of the ridge. Measure the horizontal run — the distance from the wall plate inwards to the point directly under the ridge. Enter both numbers in the same unit (inches, feet, centimetres, or millimetres — the calculator is unit-agnostic, so the rafter length comes out in whatever unit you put in). The pitch is reported as "X-in-12" (the US framing standard), in degrees from horizontal, and as a percent grade. The rafter length is the diagonal — the actual timber length you need before allowing for overhang and birdsmouth cuts.
How the calculation works
A roof is a right triangle in cross-section. Rise is the vertical leg, run is the horizontal leg, and the rafter is the hypotenuse. The pitch ratio rise ÷ run drives every common pitch expression: multiply by 12 to get the US "X-in-12" form, take the arctangent to get the angle from horizontal in degrees, and multiply by 100 to get the percent grade used in road-slope notation. The rafter length follows directly from Pythagoras: √(rise² + run²). A 6-in-12 pitch — the most common residential roof — works out to 26.57°, a 50% grade, and a rafter length of √180 ≈ 13.42 per 12 units of run.
Worked example
A roof rises 8 feet over a 12 foot run. Ratio = 8 ÷ 12 = 0.6667. Pitch in X-in-12 form = 12 × 0.6667 = 8 (an "8 in 12" pitch). Slope angle = atan(0.6667) = 33.69°. Slope percent = 66.67%. Rafter length = √(8² + 12²) = √208 ≈ 14.42 ft. So each common rafter needs at least 14.42 ft of timber for the sloped portion before adding any overhang past the eave or cutting the birdsmouth seat at the wall plate.
Frequently asked questions
What does "6 in 12" roof pitch mean?
It means the roof rises 6 units vertically for every 12 units of horizontal run. The 12 is fixed by convention — it is the standard US framing reference — and the first number tells you how steep the roof is. A 6-in-12 pitch is roughly 26.57° from horizontal, or a 50% grade. Higher first numbers mean a steeper roof: 12-in-12 is exactly 45°, and anything above that is considered very steep. Lower numbers mean a shallow roof: 2-in-12 is the practical minimum for shingles to shed water reliably.
How do I convert roof pitch to degrees?
Divide the rise by the run, take the arctangent, and convert to degrees. For an "X in 12" pitch, the formula is angle = atan(X ÷ 12) × 180 ÷ π. So a 4-in-12 pitch is atan(4 ÷ 12) ≈ 18.43°, a 6-in-12 is 26.57°, an 8-in-12 is 33.69°, a 9-in-12 is 36.87°, a 10-in-12 is 39.81°, and a 12-in-12 is exactly 45°. The calculator does this conversion automatically once you enter rise and run.
What is the difference between pitch, slope and grade?
They describe the same thing in different notation. Pitch in carpentry is the "X-in-12" ratio. Slope in mathematics and engineering is the dimensionless ratio rise ÷ run, often expressed as a percent grade — used for roads and ramps. Angle (in degrees) is the most universal form and the one used in trigonometry. All three are equivalent: a 6-in-12 pitch is a 50% slope is a 26.57° angle. The calculator reports all of them so you can match whichever notation your plans, supplier or building code uses.
How do I measure rise and run without climbing on the roof?
From inside the attic, set a 12-inch level against the underside of a rafter. Hold one end of the level horizontal, then measure straight down from the 12-inch mark to the rafter — that distance is the rise per 12 inches of run, giving you the pitch directly. From outside, place a level horizontally on the roof and measure down to the surface 12 inches along; same principle. For a more accurate whole-roof reading, measure ridge height above wall-plate height and the horizontal half-span — those are your rise and run.
Why does rafter length need adding to before cutting?
The rafter length the calculator returns is the pure diagonal from the wall plate to the ridge — the structural span. In practice you need extra timber at both ends: the birdsmouth notch that sits on the wall plate (1.5 to 2 inches of seat cut), the overhang past the eave (anywhere from 6 inches to 2 feet depending on style), and the plumb cut at the ridge. Add at least 12–24 inches to the calculated length before buying timber, and always measure-and-cut one rafter as a template before cutting the rest.
What pitch is too shallow or too steep for shingles?
Asphalt shingle manufacturers and most building codes require at least a 2-in-12 pitch (≈ 9.5°), with double underlayment between 2-in-12 and 4-in-12. Below 2-in-12 is considered a low-slope roof and needs a membrane system (TPO, EPDM, modified bitumen) rather than shingles, because water can be driven uphill by wind. There is no upper limit for shingles structurally, but above 12-in-12 (45°) walkability becomes a serious issue and you usually need roof jacks or scaffolding to install them safely.