Calculate run length from slope and rise height 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 calculation of run length (H) from slope and rise height (V). The slope (in degrees) is the tangent of the angle of slope. The formula to calculate run length is V / Tan(θ).
- Tan(θ) = V/H (tangent of the angle in degrees equals vertical rise divided by the horizontal run)
- H = V / Tan(θ) (horizontal run length)
Examples:
θ = 10°, V = 5m => H = V / Tan(10) = app. 28.35m
θ = 45°, V = 10m => H = V / Tan(45) = 10m
θ = 60°, V = 6m => H = V / Tan(60) = app. 9.23m
To calculate rise height, use this converter. To convert other slope units use these converters.