What is the Slope Percent to Degrees Calculator?
Slope can be expressed in two common ways: as a percentage (grade) or as an angle in degrees. A slope percentage describes the vertical rise divided by the horizontal run, multiplied by 100. For example, a 100% grade means the elevation rises 1 unit for every 1 unit of horizontal distance — which equals a 45° angle. This calculator converts any slope percentage into the equivalent angle in degrees (and radians).
How to use it
Enter the slope percentage (grade) into the input field and submit. The calculator returns the slope angle in degrees as the main result, plus the percentage and the angle in radians for reference. Negative percentages represent downhill slopes and will return a negative angle.
The formula explained
The slope percentage is the tangent of the angle multiplied by 100, so to reverse it we take the inverse tangent (arctangent) of the percentage divided by 100. Since most calculators and people work in degrees rather than radians, the result is multiplied by 180/π to convert from radians to degrees:
$$\theta = \arctan\!\left(\frac{\text{Slope (\%)}}{100}\right) \times \frac{180}{\pi}$$
Worked example
Suppose a road 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 (≈57.2958) to get approximately 14.04°. So a 25% grade corresponds to roughly a 14-degree incline.
$$\theta = \arctan\!\left(\frac{25}{100}\right) \times \frac{180}{\pi} = \arctan(0.25) \times 57.2958 \approx 0.2450 \times 57.2958 \approx 14.04°$$
FAQ
Is a 100% grade the same as vertical? No. A 100% grade is a 45° angle, because rise equals run. A truly vertical wall would be an infinite percentage.
Can the slope percentage exceed 100%? Yes. Any grade steeper than 45° produces a percentage greater than 100% — for instance a 200% grade equals about 63.43°.
How do I convert degrees back to percent? Use \(\text{percent} = \tan(\text{angle in degrees}) \times 100\).
