Convert slopes from Ratio to Degrees automatically. Read about ratio and degrees (°), and understand the conversion between ratio and degrees.
About ratio. Ratio is the relation between vertical rise and horizontal run of the slope.
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 ratio 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. The angle of slope equals inverse tangent (arctan) of the slope. The formula to convert slope ratio to slope degrees is ArcTan(V/H).
- V/H (convert the percent ratio to the decimal fraction)
- ArcTan(V/H) (inverse tangent of the percent ratio expressed in the decimal fraction)
Examples:
1:5 = ArcTan(1/5) = app. 11.31°
1:12 = ArcTan(1/12) = app. 4.76°
5:8 = ArcTan(5/8) = app. 32°
To convert vice versa, from degrees to ratio, use this converter. To convert other angle units use these converters.