How To Convert Angle Degrees To Slope

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.

Step 1

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

Step 2

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.

Step 3

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.