Convert slopes from Percent to Degrees automatically. Read about percent (%) and degrees (°) units, and understand the conversion between percent and degrees.
About percent. The percent slope is related to the vertical rise and horizontal run of the slope. As the angle approaches 90 degrees, the slope percentage approaches infinity. Do not confuse this percent measure with the percent we use to measure angles.
About degrees. Degrees (°) are used to express angles between sloped line and horizontal or level line. Calculating slopes in degrees is the most complex as it requires knowledge of tangent and inverse tangent. Slope degrees are related to the inverse tangent of the slope ratio. Unlike angles that can be in range 0-360°, slopes can be in range between 0-90°. Keyboard shortcut for a degrees symbol: Alt + 0176 (numeric pad).
Conversion. Understanding the conversion between percent and degrees. The slopes of straight lines are given by tangents. The slope (in degrees) is the tangent of the angle of slope. Tangent equals rise/run. So at the 90 degrees, the tangent does not exist because tan(90) = rise/run = x/0. The formula to convert slope percentage to slope degrees is ArcTan(x/100).
- x/100 (convert the percent slope to the decimal fraction)
- ArcTan(x/100) (inverse tangent of the percent slope expressed in the decimal fraction)
Examples:
8% = ArcTan(8/100) = app. 4.57°
25% = ArcTan(25/100) = app. 14.04°
45% = ArcTan(45/100) = app. 24.23°
To convert vice versa, from degrees to percent, use this converter. To convert other angle units use these converters.