Enter the rise and horizontal distance (run) in any length unit. The calculator automatically displays the slope in % (or ‰), the angle in degrees, radians, or gradians, and a visual ramp diagram.
Slope Percentage Calculator
Calculation 1 — Slope from rise and run
Calculation 2 — Rise from slope % and run
Calculation 3 — Run from slope % and rise
How to use the slope percentage calculator
- Calculation 1: Enter the rise (height difference) and run (horizontal distance) in any unit. Select the angle unit (degrees, radians, gradians, or π rad) and the result unit (% or ‰). The diagram updates automatically.
- Calculation 2: Given the slope percentage and run in meters, calculate the required rise.
- Calculation 3: Given the slope percentage and rise in meters, calculate the horizontal run.
Formulas
| Calculation | Formula |
|---|---|
| Slope (%) | (rise ÷ run) × 100 |
| Slope (‰) | (rise ÷ run) × 1000 |
| Angle (degrees) | arctan(rise ÷ run) × (180 ÷ π) |
| Angle (radians) | arctan(rise ÷ run) |
| Angle (gradians) | arctan(rise ÷ run) × (200 ÷ π) |
| Rise | run × (slope% ÷ 100) |
| Run | rise ÷ (slope% ÷ 100) |
Frequently asked questions
How do you calculate the slope percentage of a ramp?
Use: % = (rise ÷ run) × 100
Example: a rise of 23 m and a run of 34 m: (23 ÷ 34) × 100 = 67.65%
A 100% slope means that the rise equals the horizontal run (a 45° angle).
How do you convert slope percentage to degrees?
Use: angle (°) = arctan(% ÷ 100) × (180 ÷ π)
Example: a slope of 67.65%: arctan(0.6765) = 0.5946 rad → 0.5946 × 57.296 = 34.08°
What is the difference between slope in % and ‰?
Slope in % (percent) = (rise ÷ run) × 100. In ‰ (per mille) = (rise ÷ run) × 1000. The value in ‰ is exactly 10 times the value in %. Roads and railways generally express slope in ‰; accessible ramps and roofs in %.
What is the maximum permitted slope for accessible ramps?
Under Brazil's NBR 9050 standard, the maximum slope for accessible ramps is 8.33% (1:12), with intermediate landings for long ramps. For residential use, up to 10% is accepted in limited spaces.
Practical slope examples
| Location | Typical slope | Approx. angle |
|---|---|---|
| Accessible ramp (max.) | 8.33% | 4.76° |
| Steep mountain road | 10–12% | 5.7–6.8° |
| Gable roof | 30–100% | 16.7–45° |
| Legendary Tour de France climb | ≈ 12% | ≈ 6.8° |
| Mountain trail | 20–60% | 11–31° |
See also…
