What this converter does
This converter turns a percent grade into a slope angle in degrees and back. Since the angle is the arctangent of the grade, it is not a fixed ratio — a 100% grade is 45°, not 100°. Type a grade and read the angle instantly, or swap to reverse it.
Grades are quoted for roads, drainage and ramps; converting to degrees helps with setting-out, roof pitch and machine control. A 20% grade is about 11.3°.
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 17.63% grade to a slope angle.
angle = arctan(% ÷ 100)arctan(0.1763) = 10.0°So a 17.63% grade is a 10-degree slope for setting-out.
The units in this example
Rise divided by run, times 100 — the standard way roads, drainage falls and ramps are specified.
- 1% ≈ 0.57°
- 8.33% = 1:12 ADA ramp
- 100% = 45°
- angle = arctan(% ÷ 100)
The angle above horizontal, in degrees — used for setting-out, roof pitch, batters and machine-control models.
- 1° ≈ 1.75%
- 11.31° = 20%
- 26.57° = 50%
- 45° = 100%