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 that ratio to degrees or percent grade comes up constantly 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, so enter rise and run and you get both at once.
One thing worth keeping straight: grade and degrees only track each other on gentle slopes. Below about 10% the two numbers are within half a degree of each other, which is why people get away with treating them as interchangeable. They part company fast after that. 100% grade is 45°, not 90°, and no percent grade however large will ever reach vertical.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
SuperGlobalCalculator is independently built and maintained. See how we build and verify our calculators.