Rise Over Run to Degrees Converter
Convert slope rise/run ratio to angle in degrees, radians, and percent grade.
Instant conversion with formulas for ramps, roofs, and roads.
Rise Over Run — Slope to Angle Conversion
Rise over run expresses a slope as the vertical rise divided by the horizontal run. Converting this ratio to degrees or percent grade is essential in construction, road design, and accessibility planning.
Conversion Formulas
| Output | Formula |
|---|---|
| Angle (degrees) | θ = arctan(rise / run) × (180 / π) |
| Angle (radians) | θ = arctan(rise / run) |
| Percent Grade | grade = (rise / run) × 100 |
Common Reference Points
| Angle | Grade | Description |
|---|---|---|
| 0° | 0% | Flat surface |
| 5.7° | 10% | Steep driveway |
| 8.5° | 15% | Maximum highway grade |
| 26.6° | 50% | Very steep hill |
| 45° | 100% | Equal rise and run |
Roof Pitch
Roofers express pitch as rise per 12 inches of run (e.g., 4/12). A 4/12 pitch equals about 18.4°. A 12/12 pitch is exactly 45°.
ADA Ramp Standard
Wheelchair ramps must not exceed 1:12 (one inch of rise per foot of run), which equals 4.76° or 8.33% grade. Steeper ramps require handrails and landings.
Road Grades
Most highway grades stay under 6–8%. Steep mountain roads may reach 10–12%. Percent grade is the civil engineering standard for road design.
Why Degrees vs. Percent?
Degrees are intuitive for geometry and trigonometry work. Percent grade is the standard in civil engineering and cycling. Both describe the same physical slope — enter rise and run to get both instantly.