Slope calculator
Rise, run, length and grade
Enter any two values and the calculator works out the rest. Typing into a third field hands the oldest one back to the calculator.
Lengths can be in any unit, as long as all three use the same one.
Result
Your answer appears here as you type.
About this tool
Enter any two of rise, run, sloped length and angle to solve the rest. See the slope as degrees, percent grade, a 1:N ratio, a pitch and per mille.
How the slope calculator works
A slope is a right triangle: the rise is the vertical side, the run the horizontal side, the sloped length the hypotenuse, and the angle sits between the run and the slope. Any two of those four fix the triangle, which is why the calculator needs exactly two.
The formulas
- Angle = arctan(rise ÷ run), or arcsin(rise ÷ length) if you know the sloped length.
- Percent grade = rise ÷ run × 100. Per mille is the same ratio × 1000, used for drains and railways.
- Percent grade from an angle = tan(angle) × 100: 17.63% at 10°, 57.74% at 30° and 100% at 45°. The degree angle table gives the grade for every 5°.
- Ratio 1:N, where N = run ÷ rise.
- Pitch = rise ÷ run × 12, the roofing convention.
Worked example
A path rises 0.5 m over a horizontal run of 6 m. The angle is arctan(0.5 ÷ 6) = 4.76°, the grade is 8.33% or 83‰, and the ratio is 1:12: exactly the steepest slope the US accessibility standards allow for a ramp. For ramp lengths and landings, use the wheelchair ramp calculator.
A common mistake
Measuring along the slope and entering it as the run. On a gentle slope the two are almost the same, but they part quickly as it steepens: at 30°, a sloped length of 10 m has a run of only 8.66 m, 13% shorter. Enter a length measured along the surface in the sloped-length field, and the calculator finds the run.
Frequently asked questions
How is percent slope calculated?
Percent slope, also called grade, is the rise divided by the run, multiplied by 100. A path that climbs 5 m over 100 m of horizontal distance has a 5% slope, and a drain that falls 1 unit over a run of 50 has a 2% slope.
Percent is not the same as degrees: a 100% slope rises as far as it runs, which is 45°, not 90°. Enter any two of rise, run, length and angle above and the calculator shows the slope in degrees, percent, as a ratio and as a pitch.
How do you find the angle of a slope?
Divide the rise by the run and take the inverse tangent: angle = arctan(rise ÷ run). A slope that rises 1 m over a 4 m run is at arctan(1 ÷ 4), about 14°.
If you know the sloped length instead of the run, use the inverse sine: angle = arcsin(rise ÷ length). To measure the angle of a real slope, lay your phone on it and read the inclinometer.
Guides
About these measurements
Readings are estimates taken from rendered pixels and consumer device sensors. Do not rely on them for structural engineering, surveying, manufacturing inspection, navigation, or medical decisions. Check anything safety-critical with a calibrated instrument.
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