How to Calculate Horizontal Distance

By Dan Richter
Calculating horizontal distance is a lesson typically learned in precalculus.

This reference is for calculating the horizontal distance between two geographic points at difference elevations and is based on the mathematical relationship between the sides of a right triangle. The mathematical horizontal distance formula is often used on maps because it does not factor in things like peaks, hills and valleys between the two points. To successfully calculate the horizontal distance, which is also known as the run, between two points, you need to know the vertical distance, or rise, between the two elevations and the percentage of slope at the beginning of the horizontal elevation to the top of the vertical elevation.

Look over the equation for calculating horizontal distance, which is slope = rise/run x 100. Plug your slope percentage and rise into the equation. For example, if you have a slope percentage of 6 and a rise of 25 feet, the equation would look like 6 = (25/run) x 100.

Multiply each side of the equation by the 'run' variable. Continuing with the example of a slope percentage of 6 and a rise of 25, the equation will look like this: run x 6 = [(25/run) x 100)] x run. The 'run' terms cancel on the right side of the equation and the results can be simplified in the following equation: 6 x run = 2,500.

Divide each side of the equation by the slope percent. Continuing with the example of a slope percentage of 6 and a rise of 25, the equation should look like this: (run x 6) / 6 = 2,500 / 6. After completing the division, the equation becomes run = 416.6. The horizontal distance between the two points is then 416.6 feet.

About the Author

Dan Richter began freelance writing in 2006. His work has appeared in a variety of publications, including the "Wausau Daily Herald," "Stevens Point Journal," "Central Wisconsin Business Magazine" and the "Iowa City Press-Citizen." Richter graduated from the University of Wisconsin-Stevens Point in 2009 with a Bachelor of Arts in communication and media studies.