Slope Percentage Calculator (Grade & Degrees)
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Slope Percentage Calculator
Slope (or grade) as a percentage tells you how steep a road, ramp, roof, or path is. This calculator finds the slope percentage from rise and run, and converts between percent slope and degrees in both directions.
The slope percentage formula
Slope % = (Rise ÷ Run) × 100
Rise is the vertical change, run is the horizontal distance. A rise of 3 metres over a run of 20 metres is (3 ÷ 20) × 100 = 15%. A "1 in 20" gradient is the same thing written as a ratio: 5%.
Slope percentage and degrees
Percent slope and angle are not the same number. To convert, use degrees = arctan(slope ÷ 100) and slope % = tan(angle) × 100. A 100% slope is a 45° angle — the point where rise equals run.
| Slope % | Degrees | Ratio |
|---|---|---|
| 5% | 2.86° | 1 in 20 |
| 10% | 5.71° | 1 in 10 |
| 15% | 8.53° | ≈1 in 6.7 |
| 25% | 14.04° | 1 in 4 |
| 50% | 26.57° | 1 in 2 |
| 100% | 45° | 1 in 1 |
Where slope percentage is used
Roads and cycle paths (a road sign showing 12% is a 12% grade), wheelchair ramps (often capped near 8%), roof pitch, and drainage. For plain "what percent of a number" math, use the percentage calculator.
FAQs
Divide the rise (vertical change) by the run (horizontal distance) and multiply by 100. A rise of 3 over a run of 20 is (3 ÷ 20) × 100 = 15% slope.
Take the inverse tangent (arctan) of the slope divided by 100. A 15% slope is arctan(0.15) ≈ 8.53°. A 100% slope equals exactly 45°.
Take the tangent of the angle and multiply by 100. A 10° angle is tan(10°) × 100 ≈ 17.63% slope.
A 1 in 20 gradient means 1 unit of rise for every 20 of run: (1 ÷ 20) × 100 = 5%.
No. Slope percentage is rise ÷ run × 100; the angle is measured in degrees. They only match at 0. A 100% slope is a 45° angle, not 100°.