How to calculate slope in percent — step by step
Slope (grade) in percent tells you how many metres of rise occur per 100 metres of horizontal run. The formula is rise ÷ run · 100. Worked example: a 3 m rise over a 20 m run gives 15%. Suitable for the percentage maths covered in Grade 7 / Year 8.
Quick answer
Slope in percent is the rise divided by the horizontal run, times 100: rise ÷ run · 100. Example: a 3 m rise over a 20 m run gives 3 ÷ 20 · 100 = 15%. The matching slope angle is arctan(3 ÷ 20) ≈ 8.53°.
At a glance
| Example | 3 m ÷ 20 m · 100 |
|---|---|
| Method | rise ÷ run · 100 |
| Steps | 3 |
| Result | 15% |
| Angle | ≈ 8.53° |
| Grade level | Grade 7 (ages 12–13) |
Worked example: 3 m over 20 m
We divide the rise (3 m) by the run (20 m) and multiply by 100.
How to calculate slope in percent — the steps
These steps work for any combination of rise and horizontal run.
Step 1 · Start
3 ÷ 20 · 100Rise divided by run, times 100.Step 2 · ÷
0.15 · 1003 ÷ 20 gives the ratio 0.15.Step 3 · ·100
= 15%0.15 times 100 gives the percent grade.Step 4 · arctan
≈ 8.53°arctan(0.15) gives the slope angle in degrees.
Why the formula works
Slope in percent is simply a proportion: how much height do you gain compared with the horizontal distance you travel? Multiplying rise ÷ run by 100 expresses that ratio as a "per hundred" figure — which is exactly what percent means. The angle is another view of the same ratio: tan(α) = rise ÷ run, so α = arctan(rise ÷ run). That is why 100% equals 45° (rise = run), not 90°.