How Do You Convert Percent Slope to Degrees?

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Percent slope can be converted to degrees by simply taking the arctan, or the inverse of the tangent function, of one-hundredth of the percent slope. Mathematically, the conversion formula is written as: degrees = arctan (percent slope/100).

  1. Find the corresponding vertical and horizontal distances

    For any side of a triangle whose percent slope is unknown, it can be calculated from the corresponding values of vertical rise and horizontal distance. Usually, vertical distance is denoted by Y, and the horizontal distance is denoted by X. Find out the values of these two distances.

  2. Calculate the percent slope

    The percent slope of a line can be calculated from the values of X and Y by using the formula: percent slope = 100 * (Y/X). For example, if both the values of X and Y are equal to two, then the percent slope is: percent slope = 100 * (2/2) = 100.

  3. Convert the percent slope to degrees

    Convert the percent slope of the line to degrees by using the formula: degrees = arctan (percent slope/100). For example, if the percent slope of a line is 100, then converting it to degrees yields the result: degrees = arctan (100/100) = arctan (1) = 45 degrees.