What this converter does
This converter turns a slope angle in degrees into percent grade and back. Because grade is the tangent of the angle, the relationship is not a straight factor — 45° is 100%, not 45%. Type an angle and read the grade instantly, or swap to go the other way.
Percent grade is used for roads, ramps, drainage falls and site batters. A 5° slope is about 8.7% — steeper than it sounds when written as a percentage.
The units it covers
Slope is expressed three ways — an angle, a percentage grade, or a ratio. They relate through the tangent, not a fixed factor.
View all units & their values
| Unit | Symbol | Value | Mainly used |
|---|---|---|---|
| Angle | ° | θ | Degrees from horizontal |
| Percent grade | % | tan θ × 100 | Roads, drainage, ramps |
| Ratio | 1:X | 1 ÷ tan θ | Earthworks & batters |
The formula
Percent grade is the tangent of the slope angle, times 100:
% = tan(angle) × 100 (and angle = arctan(% ÷ 100))Where:
- angle = the slope angle in degrees from horizontal
- % = the grade — rise ÷ run × 100
- tan = the tangent function
Worked example
Convert a 10° slope to percent grade.
% = tan(angle) × 100tan(10°) × 100 = 17.63 %So a 10-degree slope is a 17.6% grade — a steep road or ramp.
The units in this example
The angle of the slope above horizontal, in degrees. Surveyors and designers often set batters and roof pitches this way.
- 1° ≈ 1.75%
- 5° ≈ 8.75%
- 26.57° = 50%
- 45° = 100%
Rise divided by run, times 100. The standard for road gradients, drainage falls and accessible ramps.
- 1% ≈ 0.57°
- 8.33% = 1:12 ADA ramp
- 100% = 45°
- % = tan(angle) × 100