Grade to Angle Calculator
Convert percent grade into slope angle
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Grade to Angle Formula
angle = arctan(grade / 100)
Percent grade measures rise per 100 units of horizontal run. Dividing by 100 gives slope, and arctangent converts that slope into an angle.
⚠ Grade percent can be positive or negative. Positive values slope upward; negative values slope downward.
How Grade to Angle Conversion Works
A grade is a slope written as a percent. Because slope equals tangent of the angle, inverse tangent gives the angle in degrees.
Grade Percent
100×rise/run.
Angle
arctan converts slope to degrees.
Common Case
100% grade equals 45°.
💡 Example: A 10% grade gives angle=arctan(0.1)=5.710593°.
Applications of Grade to Angle
Road Grades Ramps Roofs Construction
Frequently Asked Questions
What is a grade to angle calculator?▼
It converts slope percent grade into an angle measured in degrees.
What is the grade to angle formula?▼
angle = arctan(grade/100).
How do I use this calculator?▼
Enter the grade percent and click Calculate.
What does 100 percent grade mean?▼
A 100% grade means rise equals run, which is a 45° angle.
Where is grade to angle used?▼
It is used for roads, ramps, roofs, trails, surveying, and construction.
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