How to Convert Angle Degrees to Slope

By Chance E. Gartneer; Updated April 24, 2017

An angle can represent a slope, and a slope can be measured as an angle. A slope is the measured steepness of growth or decline over a specific amount of distance. In geometry, calculation of a slope develops from a ratio of a change of y-coordinates, also known as the rise, over a change in x-coordinates, known as the run. When given the degrees of an angle representing the slope, you can calculate the slope as both a gradient with the ratio in decimal form and a percentage by employing the trigonometric tangent function.

Obtain an angle in degrees. For this example, let the angle by 40 degrees.

Calculate the tangent function of the angle with your calculator. For this example, the tangent of 40 degrees equals approximately 0.83901. This is the slope as a gradient.

Multiply the gradient by a hundred on your calculator to obtain the percentage of the slope. For this example, multiplying 0.83901 by 100 equals 83.901 percent.

About the Author

Chance E. Gartneer began writing professionally in 2008 working in conjunction with FEMA. He has the unofficial record for the most undergraduate hours at the University of Texas at Austin. When not working on his children's book masterpiece, he writes educational pieces focusing on early mathematics and ESL topics.