Inputs
Provide any two of the following fields to solve the rest. For percent and angle only, lengths remain indeterminate until a length is given.
All length inputs/outputs use this unit.
Results
Percent grade
— %
Angle
— deg
1 : —
Per‑mille: — ‰
Rise
— m
Run
— m
Slope length
— m
Example Data Table
Use Add to table to append your calculation. You can also load sample rows.
| # | Rise | Run | Slope | Unit | Percent (%) | Angle (deg) | Ratio (1:N) | Per‑mille (‰) |
|---|
Formula used
- percent = (rise / run) × 100
- angle (deg) = atan(rise / run) × 180/π
- slope length = √(rise² + run²)
- ratio 1:N where N = run / rise (for rise > 0)
- per‑mille = percent × 10
Given any two of {rise, run, slope length, percent, angle}, the right‑triangle relations determine the remaining values.
How to use this calculator
- Select your preferred unit for all lengths.
- Enter any two known values (e.g., percent and run; rise and slope length; angle and run).
- Click Calculate to compute the remaining fields instantly.
- Press Add to table to store the result row.
- Use Download CSV or Download PDF to export the table.
If only percent and angle are provided, lengths remain undefined until one length is entered.
How to calculate percent grade slope?
percent = (rise / run) × 100
1
Measure the rise (vertical change).
2
Measure the run (horizontal distance).
3
Compute the percent using the formula above.
Angle relation: angle = atan(percent / 100) (degrees).
Slope length: √(rise² + run²).
Ratio: 1 : (run / rise) (rise > 0).
At a glance
- Upgrade: percent positive; downgrade: percent negative.
- 1:12 ramp ≈ 8.33% (accessibility reference).
- 1:20 ramp = 5% for gentle approaches.
Worked examples
rise 0.15, run 1.80 → 8.33%, 4.76°, 1:12.00
rise 0.10, run 2.00 → 5.00%, 2.86°, 1:20.00
rise 0.10, run 2.00 → 5.00%, 2.86°, 1:20.00
Percent grade vs. angle of incline (quick conversions)
| Percent (%) | Angle (deg) | Ratio (1:N) |
|---|---|---|
| 2.00 | 1.15 | 1:50.00 |
| 5.00 | 2.86 | 1:20.00 |
| 8.33 | 4.76 | 1:12.00 |
| 10.00 | 5.71 | 1:10.00 |
| 12.50 | 7.13 | 1:8.00 |
| 15.00 | 8.53 | 1:6.67 |
Angles are rounded from atan(percent/100). Ratios are rounded to two decimals.
Slope ratio equivalents
- 1:20 → 5.00% → 2.86°
- 1:12 → 8.33% → 4.76°
- 1:10 → 10.00% → 5.71°
- 1:8 → 12.50% → 7.13°
- 1:6 → 16.67% → 9.46°
Convert ratio 1:N to percent with percent = 100 / N.
Convert back with N = 100 / percent (rise > 0).
Design notes & checks
- For ramps, 1:12 (~8.33%) is a common design reference; verify local standards.
- Sidewalks and gentle paths often target ≤ 5% where feasible.
- Driveways may reach 10–15%; ensure drainage and traction considerations.
- When run = 0, percent is undefined; use angle or slope length instead.
- Use consistent units; ratios and percent are unitless and unaffected by unit switches.
- For accuracy, measure over longer runs to reduce small-error amplification.
This tool is educational; confirm requirements against your project documents and local regulations.
Tips & Notes
- Negative percent indicates a downgrade (downhill). The angle sign follows the rise/run sign.
- Common ramp ratios include 1:12 (≈ 8.33%) and 1:20 (5%).
- Angles above ~45° imply percent greater than 100% (rise > run).
- Ensure consistent units across inputs; the unit selector controls all lengths.
Quality checks
- When three or more inputs are supplied, the calculator validates internal consistency.
- For tiny runs, percent may explode due to division sensitivity.
- Rounded outputs display up to four decimals; exports include full precision.