Convert slopes from Degrees to Ratio automatically. Read about degrees (°) and ratio, and understand the conversion between degrees and ratio.
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 ratio. Ratio is the relation between vertical rise and horizontal run of the slope.
Conversion. Understanding the conversion between degrees and ratio. The slope (in degrees) is the tangent of the angle of slope. At first you need to convert slope degrees to slope percentage using the formula Tan(θ)*100. Then convert percentage to ratio by adding “:100” as percentage is related to 100. This is the equitation for slope 12°: Tan(12)*100 : 100 = app. 21.3 : 100. The formula to convert slope degrees to slope ratio is Tan(θ)*100 : 100.
- Tan(θ) = V/H (tangent of the angle in degrees equals vertical rise divided by the horizontal run)
- Tan(12)*100 (multiply by 100 to get slope percentage)
- Tan(θ)*100 : 100 is the slope ratio
Examples:
10° = Tan(10)*100 : 100 = 17.6:100
45° = Tan(45)*100 : 100 = 100:100
60° = Tan(60)*100 : 100 = 173.2:100
To convert vice versa, from ratio to degrees, use this converter. To convert other angle units use these converters.