What is the Percent Grade to Degrees Calculator?
This tool converts a slope expressed as a percent grade into the equivalent angle in degrees. Percent grade is widely used on road signs, railways, ramps, and trail maps, where it describes how many units of vertical rise occur for every 100 units of horizontal run. Engineers, surveyors, hikers, and cyclists often need that same slope expressed as an angle, which this calculator provides instantly.
How to use it
Enter the grade as a percentage. For example, a road sign reading "8%" means you type 8. The calculator returns the slope angle in degrees and also shows the angle in radians for convenience. A 100% grade equals a 45-degree angle, because the rise equals the run.
The formula explained
The relationship comes from basic trigonometry. The tangent of the slope angle equals rise over run, and percent grade is exactly rise over run multiplied by 100. So the angle is the arctangent of the grade divided by 100. The result is in radians, so we multiply by 180/π to convert to degrees:
$$\theta = \arctan\left(\frac{\text{Grade (\%)}}{100}\right) \times \frac{180}{\pi}$$
Worked example
Suppose a trail has a 25% grade. Divide 25 by 100 to get 0.25. The arctangent of 0.25 is about 0.2450 radians. Multiply by 180/π (about 57.2958) to get approximately 14.04 degrees. So a 25% grade corresponds to a slope of roughly 14 degrees.
$$\theta = \arctan\left(\frac{25}{100}\right) \times \frac{180}{\pi} \approx 0.2450 \times 57.2958 \approx 14.04^\circ$$
FAQ
Is 100% grade the same as vertical? No. A 100% grade is a 45-degree angle. A vertical cliff would be an infinite grade.
Why does a small percent give a similar number of degrees? For small slopes, grade and degrees are nearly equal because the tangent of a small angle is close to the angle itself, but they diverge as the slope steepens.
Can I enter a negative grade? Yes. A downhill slope of -10% returns about -5.71 degrees.
