Convert slopes from Degrees to Percent automatically. Read about degrees (°) and percent (%) units, and understand the conversion between degrees and percent.
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).
About percent. Slope percentage 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.
Conversion. Understanding the conversion between degrees and percent. 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. This is the equitation for slope 30°: tan(30) = app. 0.58 = 1:1.72. The formula to convert slope degrees to slope percentage is Tan(θ)*100.
- Tan(θ) = V/H (tangent of the angle in degrees equals vertical rise divided by the horizontal run)
- (V/H) * 100 (slope percentage)
- Tan(θ) * 100 (replaced V/H with Tan(θ) to get the slope percentage)
Examples:
10° = Tan(10) * 100 = app. 17.63%
45° = Tan(45) * 100 = 100%
60° = Tan(60) * 100 = app. 173.20%
To convert vice versa, from percent to degrees, use this converter. To convert other angle units use these converters.