By Dan Richter
Updated Aug 30, 2022
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This guide explains how to determine the horizontal distance—or run—between two geographic points at different elevations. It relies on basic trigonometry, using the relationship between the sides of a right triangle. The method is commonly applied in cartography because it provides a straightforward calculation that excludes terrain features such as peaks, hills, or valleys.
Begin with the standard slope formula: slope = (rise ÷ run) × 100. Insert the known slope percentage and vertical rise. For example, if the slope is 6 % and the rise is 25 feet, the equation becomes:
6 = (25 ÷ run) × 100
Multiply both sides by the unknown run to eliminate the denominator:
run × 6 = [(25 ÷ run) × 100] × run. The run terms cancel on the right, simplifying to:
6 × run = 2,500
Divide each side by the slope percentage to solve for run:
(run × 6) ÷ 6 = 2,500 ÷ 6. This yields:
run = 416.6 feet
Thus, the horizontal distance between the two points is 416.6 feet.
