Slope percentage (also called grade or gradient) expresses how steep a slope is by comparing the vertical rise to the horizontal run. A slope of 5% rises 5 units for every 100 units of horizontal distance. Road signs, ramp specifications, and topographic maps all use this system. This calculator converts in both directions — from rise and run to grade, or from angle in degrees to grade.
How to Use This Calculator
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Choose your input mode. Select "Rise and run" if you measured vertical and horizontal distances. Select "Angle in degrees" if you have the slope angle.
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For rise and run mode — enter the rise (vertical distance, negative for downhill) and the run (horizontal distance, always positive). Both must be in the same unit.
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For angle mode — enter the angle in degrees between −90° and 90°.
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Read the slope percentage, equivalent angle, and rise-to-run ratio from the results.
Slope Percentage Formulas
Two equivalent ways to calculate slope percentage, depending on what you know.
slope % = (rise / run) × 100
slope % = tan(angle) × 100
angle = atan(slope % / 100)
Worked Example: Ramp with Rise 1 m, Run 20 m
Rise = 1 m, Run = 20 m.
Step 1 — divide: 1 / 20 = 0.05
Step 2 — percentage: 0.05 × 100 = 5%
Step 3 — angle: atan(0.05) × (180/π) ≈ 2.862°
A 5% ramp grade is the maximum allowed for wheelchair-accessible ramps in many building codes. It feels gentle underfoot but is steep enough to require effort when pushing a wheelchair uphill.
Worked Example: Converting a 45-Degree Angle
Angle = 45°.
Step 1 — take the tangent: tan(45°) = 1.0000
Step 2 — percentage: 1.0000 × 100 = 100%
A 45° slope is a 100% grade — for every 1 unit of horizontal run, the terrain rises exactly 1 unit. This is the steepest slope most off-road vehicles can manage.
Slope Percentage vs. Angle — Common Values
| Angle | Slope percentage | Description |
|---|---|---|
| 1° | 1.75% | Barely perceptible — gentle drainage slope |
| 2° | 3.49% | Slight incline — comfortable walking |
| 2.86° | 5% | Maximum accessible ramp grade |
| 5° | 8.75% | Moderate hill — noticeable on a bicycle |
| 5.71° | 10% | Steep for a road, common on mountain passes |
| 8.53° | 15% | Very steep road — trucks need low gear |
| 11.31° | 20% | Extreme road grade — rare on public roads |
| 26.57° | 50% | Very steep trail or ski slope |
| 45° | 100% | Equal rise and run — maximum off-road vehicle grade |
| 60° | 173.2% | Cliff-like — not a driveable surface |
Slope Percentage in Practice
Road engineering — highway grades are specified as percentages. A 6% grade means the road rises 6 m per 100 m of horizontal run. Most highway design standards cap grades at 6–8% for main roads and up to 15% for secondary mountain roads.
Accessibility — building codes (such as ADA in the United States) limit wheelchair ramp grades to 8.33% (1:12 ratio). A 5% grade (1:20) is preferred for longer ramps.
Roofing — roof pitch is often expressed as rise over run (e.g., 4:12), which equals a slope of 4/12 × 100 ≈ 33.3% and corresponds to about 18.4°.
Cycling — professional road cycling considers anything above 8% steep. The steepest Tour de France climbs average 8–12% over long distances, with short pitches above 20%.
The slope percentage calculator converts between rise, run, angle, and slope percentage (grade). Enter the rise and run to get the grade, or enter an angle in degrees to get the equivalent slope percentage.