Degrees to Slope Percent Converter
Convert elevation angles to slope percentage and vice versa. Includes visual slope rendering and engineering reference data for gradients.
Visual representation of steepness
Quick Reference
About
Understanding the relationship between slope angle and percentage grade is vital for civil engineering, road safety, and outdoor logistics. A common misconception is that a 100% slope equates to a vertical wall. In reality, 100% represents a 45° angle, where rise equals run. This calculator provides accurate bidirectional conversion between degrees and percentage gradients. It assists cyclists in route planning, architects in ramp design, and surveyors in land grading. The tool includes visualization to provide immediate context to the steepness of the input value.
Formulas
Slope percentage is calculated using the tangent trigonometric function. It represents the ratio of vertical rise to horizontal run, multiplied by 100.
Degrees to Percent:
Slope% = tan(θ) × 100
Percent to Degrees:
Angle° = arctan(Slope100)
Ratio Conversion:
For a ratio 1:n, Slope% = 100n
This relationship is non-linear. Doubling the angle from 30° to 60° increases the slope percentage from 57.7% to 173.2%.
Reference Data
| Grade (%) | Angle (°) | Ratio (Rise:Run) | Context / Regulation |
|---|---|---|---|
| 0% | 0° | Flat | Level ground |
| 2% | 1.15° | 1:50 | Max standard railway grade |
| 5% | 2.86° | 1:20 | Typical max for highway drainage |
| 8.3% | 4.76° | 1:12 | Max ADA Wheelchair Ramp (USA) |
| 10% | 5.71° | 1:10 | Steep mountain road (Tour de France HC) |
| 15% | 8.53° | 1:6.7 | Extreme steep driveway |
| 40% | 21.8° | 1:2.5 | Advanced Ski Slope (Black Diamond) |
| 100% | 45° | 1:1 | Rise equals Run |
| ∞ | 90° | 1:0 | Vertical Wall |