Rise Over Run to Angle Calculator: slope angle, grade, pitch and ratio
Turn a rise and a run into the slope angle in degrees (and degrees-minutes-seconds), percent grade, 1:n ratio, roof pitch in 12 and sloped length, or work back from an angle, grade or sloped length. Includes ADA ramp and stair checks.
How it works
Slope m = rise ÷ run · Angle = arctan(m) · Grade (%) = m × 100 · Pitch = 12 × m “in 12” · Ratio = 1 : (run ÷ rise) · Sloped length = √(rise² + run²) · Reverse: rise = run × tan(angle) = run × grade ÷ 100
Slope is rise over run: how far something climbs vertically for a given horizontal distance. The angle it makes with the ground is the arctangent of that ratio, and the same ratio times 100 is the percent grade used for roads, ramps and drainage. Builders quote roof pitch as the rise for every 12 units of run (a 6 in 12 roof climbs 6 inches per foot), while accessibility rules use a 1:n ratio (1:12 means one unit up for every 12 across). Grade and angle are not proportional: a 100% grade is 45°, not 90°, and a vertical wall has an infinite grade. Choose another option to work from a sloped length (a ramp, ladder or rafter you can measure along its face) or to find the rise from an angle or a grade. Rise and run must be in the same unit; the angle, grade and ratio do not depend on which unit you use. The checks compare the result with the ADA 1:12 ramp limit, the usual stair range and the 4-to-1 ladder rule.
Worked example
A rise of 3 over a run of 12: slope = 3 ÷ 12 = 0.25, angle = arctan(0.25) = 14.04° (14° 2′ 10″, 0.244979 rad), grade = 25%, ratio 1 : 4, pitch 3 in 12, and the sloped length is √(9 + 144) = 12.3693. The angle from vertical is 75.96°. At 25% it is far steeper than the 1:12 (8.33%) ADA ramp limit, but a common low-slope roof.
Sources: ADA Guide, Chapter 4: Ramps and Curb Ramps — U.S. Access Board · Slope calculator formulas — Inch Calculator · Rise over run — Omni Calculator · 29 CFR 1926.1053 Ladders — OSHA
Frequently asked questions
How do I turn rise and run into an angle?
Divide the rise by the run and take the arctangent (tan⁻¹ on a calculator). For 3 over 12: arctan(0.25) ≈ 14.04°. In a spreadsheet use =DEGREES(ATAN(rise/run)).
What is the difference between grade and angle?
Grade is rise ÷ run written as a percent; the angle is that ratio passed through arctangent. A 10% grade is 5.71°, a 50% grade is 26.57° and a 100% grade is 45°, not 90°.
What angle is a 6 in 12 roof pitch?
Rise 6, run 12 gives arctan(0.5) ≈ 26.57°, a 50% grade. A 4 in 12 roof is 18.43° and a 12 in 12 roof is 45°.
What is the maximum slope for a wheelchair ramp?
The ADA Standards limit a ramp’s running slope to 1:12 (8.33%, about 4.76°), with no more than 30 inches of rise per run between landings, and cross slopes to 1:48.
How do I find the rise from an angle?
Multiply the run by the tangent of the angle: a 10 ft run at 5° rises 10 × tan 5° = 0.875 ft (10.5 in). Choose “Angle and run” to do this.
Can the rise be negative?
Yes. A negative rise describes a downhill slope; the angle and grade come out negative with the same size as the uphill case.
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This calculator is for educational purposes. Double-check important results before acting on them.