Slope Grade & Angle Calculator

How it works

Grade % = (rise ÷ run) × 100 · Angle = arctan(rise ÷ run) · Ratio = 1 : (run ÷ rise) · Pitch = 12 × rise ÷ run (in 12) · Slope length = √(rise² + run²) · From an angle and the slope length: run = length × cos(angle), rise = length × sin(angle) · From a grade and the rise: run = rise ÷ (grade ÷ 100)

Grade expresses steepness as a percentage — the rise divided by the horizontal run — so a 100% grade is a 45° angle, where you climb one metre for every metre forward. Because grade uses the tangent of the angle, it grows without bound as a slope approaches vertical, which is why very steep terrain is quoted in degrees instead. The same steepness can also be written as a ratio (1 : 12 for a ramp), a roof pitch (6 in 12) or per mille for railways, and the calculator shows all of them. You can start from whatever you know: rise and run, or a grade, angle, ratio or pitch plus one length — for example the rise of a ramp and the maximum grade, to get the run you need. Each length has its own unit, so mixing feet of rise and miles of road works. The slope length is the actual distance travelled along the incline, always a little longer than the horizontal run, and the comparison table puts your slope beside common limits for drainage, ramps, roads, rail, roofs, mowers and stairs.

Worked example

A ramp rising 3 m over a 12 m horizontal run has a grade of 3 ÷ 12 × 100 = 25%. Its angle is arctan(3/12) = arctan(0.25) ≈ 14.04°, its ratio 1 : 4, its pitch 3 in 12, and the sloped surface itself measures √(3² + 12²) = √153 ≈ 12.37 m — three times steeper than the 1:12 limit for wheelchair ramps. Going the other way, a 0.75 m rise at 8.33% needs 0.75 ÷ 0.0833 = 9.0 m of run.

Sources: Grade (slope) — Wikipedia · U.S. Access Board — ADA Standards, ramps (405)

Frequently asked questions