By Chance E. Gartneer | Updated Aug 30, 2022
The angle of a slope—often called its gradient—is measured in radians when expressed in terms of the trigonometric unit rad. Radians are derived from π (≈ 3.14159) and provide a natural, unit‑less way to express angles in mathematics and engineering.
Determine the rise (vertical change) and run (horizontal change) between two points on the line. In our example, the rise is 1 unit and the run is 5 units.
Divide the rise by the run to obtain the gradient: 1 ÷ 5 = 0.20.
Use the inverse tangent function (arctan or tan−1) on a scientific calculator. Enter 0.20 and press the arctan key. The result, expressed in radians, is approximately 0.197 rad.
To double‑check your calculation, visit the RapidTable arctan calculator. Input 0.20 in the “Arctan” field, choose the “Rad” option from the drop‑down menu, and click “=”. The displayed value should match the one obtained from your scientific calculator.
Set your calculator to radian mode, input the slope’s gradient, and press arctan. The answer is the slope’s angle in radians.
