Slope angle and percent grade describe the same steepness in different formats. Tangent converts angle into slope, and multiplying by 100 converts slope to percent.
⚠Angle must be greater than -90° and less than 90°. Near 90°, grade becomes extremely large.
How Angle to Grade Conversion Works
The tangent of an angle equals rise over run. Percent grade is that same ratio multiplied by 100.
Angle
Measured from horizontal.
Tangent
tan(angle)=rise/run.
Percent Grade
100×slope.
Boundary
90° is undefined.
💡 Example: A 5° angle gives grade=tan(5°)×100=8.748866%.
Applications of Angle to Grade
Road DesignRampsRoofsSurveying
Frequently Asked Questions
What is an angle to grade calculator?▼
It converts a slope angle in degrees into percent grade.
What is the angle to grade formula?▼
grade percent = tan(angle) × 100.
How do I use this calculator?▼
Enter the angle in degrees and click Calculate.
What angle range is allowed?▼
The angle must be greater than -90° and less than 90° because tangent is undefined at 90°.
Where is angle to grade used?▼
It is used for roads, ramps, roofs, accessibility slopes, and surveying.
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