How to Calculate Radians From a Slope

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The radians of a slope refer to its angle measurement. Radians are angle measurement units that stem from pi, a mathematical constant that is commonly known as 3.14, but is in fact an infinite and patternless number. A slope, also known as a gradient, is the ratio between the growth or decrease in vertical and horizontal distances between two defined points. You can easily calculate a slope's angle measurement in radians through the simple inverse trigonometric arctangent or arctan function, which works in reverse to find the angle of a tangent value.

    Define the growths in vertical and horizontal distances. For this example, the vertical distance growth is 1, and the horizontal growth change is 5.

    Divide growth in the vertical distance by the growth in horizontal distance to find the degree of the gradient. For this example, 1 divided by 5 results in 0.2.

    Calculate the arctan of the degree of the gradient to calculate the measure of its angle in radians on your scientific calculator. Enter the gradient, and then press the "arctan" or "tan^-1" key. For this example, the arctan of 0.2 is 0.197 radians.

    Check your answer with an online arctan calculator such as the one at RapidTable. Enter the degree of the gradient to the right of the "Arctan" label, select the "Rad" option from the pull-down menu to the left of the "Reset" button to select radian measurement, and then click the equal sign button. The answer will appear to the right of the equal sign.


    • Set your calculator to display the answer in radians and not degrees in its display options.

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