What Is the Slope to Degrees Calculator?
This tool converts a numeric slope value m — defined as rise divided by run — into the angle of inclination measured in degrees. Slope is a dimensionless ratio commonly used in math, road and roof design, and engineering, while degrees are often more intuitive for describing how steep something feels. The calculator also returns the angle in radians and the equivalent percent grade.
How to Use It
Enter your slope value m. A slope of 1 means the line rises 1 unit for every 1 unit it runs horizontally. A slope of 0 is perfectly flat, and larger values are steeper. Negative slopes (descending lines) produce negative angles. Click calculate to see the angle in degrees, radians, and the percent grade.
The Formula Explained
The angle is the arctangent (inverse tangent) of the slope, converted from radians to degrees:
$$\theta = \arctan\!\left(\text{Slope }(m)\right) \times \frac{180}{\pi}$$
Because tangent of an angle equals the opposite side over the adjacent side (rise over run), taking the arctangent of the slope recovers the angle. Multiplying by \(\frac{180}{\pi}\) converts the result from radians to degrees.
Worked Example
Suppose your slope is \(m = 1\). The arctangent of 1 is \(\frac{\pi}{4}\) radians, which is \(0.7854\) radians. Multiplying by \(\frac{180}{\pi}\) gives exactly 45 degrees. The percent grade is \(1 \times 100 = 100\%\). So a 1:1 slope rises at a 45° angle.
FAQ
What is the angle for a slope of 0? A slope of 0 gives an angle of 0 degrees — a flat, horizontal line.
Can the slope be negative? Yes. A negative slope describes a descending line and produces a negative angle of the same magnitude.
What is percent grade? Percent grade is simply the slope multiplied by 100. A 5% grade equals a slope of \(0.05\), which is about \(2.86\) degrees.
