Calculate true slope distance from run and rise or angle, or reverse-solve horizontal distance, with signed grade, slope ratio, and metric or imperial conversions.
Slope Distance Formula
The following formula is used to calculate the Slope Distance.
- Where SD is the Slope Distance (in)
- Ri is the rise of the slope (in)
- Ru is the run of the slope (in)
How to Calculate Slope Distance?
The following example problems outline how to calculate Slope Distance.
Example Problem #1:
- First, determine the rise of the slope (in).
- The rise of the slope (in) is given as 5.
- Next, determine the run of the slope (in).
- The run of the slope (in) is provided as 7.
- Finally, calculate the Slope Distance using the equation above:
SD = SQRT (Ri^2+Ru^2)
The values given above are inserted into the equation below and the solution is calculated:
SD = SQRT (5^2+7^2) = 8.6023 (in)
FAQ
What is the importance of calculating slope distance?
Slope distance is the straight diagonal distance between two points in a planar model. It can support geometric estimates for engineering and construction, but it does not by itself establish structural safety, terrain-path length or survey accuracy.
Can the slope distance formula be used for any type of slope?
The rise-and-run formula applies to a straight segment in a planar model, with a positive horizontal run and signed rise. It does not trace an uneven terrain profile. Angle modes require an angle strictly between -90 and 90 degrees; a vertical segment is outside these modes.
How does the slope distance differ from horizontal or vertical distance?
Slope distance is the direct diagonal distance between two points on a slope, taking into account both the vertical (rise) and horizontal (run) components. In contrast, horizontal distance measures the straight-line distance between two points ignoring any elevation change, while vertical distance measures the elevation difference disregarding horizontal separation. The calculated slope distance is the straight segment between the two points; distance traveled along an uneven surface can be longer.
