Slope Distance Calculator
Slope distance is the true straight-line length along an incline, the hypotenuse of the right triangle whose legs are the horizontal run and the vertical rise. It is always longer than the flat map distance because it includes the climb. This calculator takes the horizontal run and the vertical rise in the same units and returns the slope distance from the Pythagorean theorem, along with the grade percentage and the slope angle. Use it for trails, conveyors, pipe and cable runs, and survey reductions.
Slope distance formula
Slope distance = sqrt(run^2 + rise^2)
Grade (%) = (rise / run) * 100
Slope angle = atan(rise / run) in degrees
The slope distance is the hypotenuse of the right triangle formed by the horizontal run and the vertical rise. It is always at least as long as the run.
Slope distance context
- Slope distance is the hypotenuse; horizontal run is the map distance.
- At a 45 degree slope (100 percent grade) the slope distance is about 1.414 times the run.
- Total stations measure slope distance and reduce it to horizontal distance.
- Use consistent units for run and rise; the output is in the same unit.
- For trail or pipe runs, slope distance gives the true material or walking length.
Slope distance: frequently asked questions
What is slope distance?
Slope distance is the straight-line distance measured along an incline between two points, as opposed to the horizontal run (the map distance) or the vertical rise. It is the hypotenuse of the right triangle formed by the run and the rise.
How is slope distance calculated?
By the Pythagorean theorem: slope distance equals the square root of (run squared plus rise squared). For a 100-unit run and a 30-unit rise, the slope distance is the square root of (10,000 plus 900), about 104.4 units.
Why is slope distance longer than the horizontal run?
Because it accounts for the climb. A path up a hill is always longer than its shadow on flat ground. The steeper the grade, the larger the difference. At a 100 percent grade (45 degrees) the slope distance is about 1.414 times the run.
What is the difference between slope distance and grade?
Grade is the ratio of rise to horizontal run, expressed as a percentage. Slope distance is an absolute length along the incline. This calculator also reports the grade and slope angle so you can relate the two.
Where is slope distance used?
Surveying, construction, trail planning, conveyor and pipe runs, and cable length estimates all need slope distance. Total stations measure slope distance directly and then reduce it to horizontal distance using the vertical angle.
Official sources
- NOAA National Geodetic Survey: National Geodetic Survey.
- NIST DLMF: Digital Library of Mathematical Functions.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.