How to use
- Enter the horizontal distance from the map, in whatever unit you want back.
- Enter the grade as a percent. Ten means a 10 percent grade. A descent can be negative. The square removes the sign.
- Press Calculate. The hero uses the same unit you typed.
- The slope factor is shown so you can see how much the hill stretched the map.
How it's calculated
Grade as a decimal is the percent divided by 100. Slope factor = √(1 + decimal grade squared). Slope distance = horizontal distance × that factor.
A zero grade returns the horizontal distance unchanged, with a factor of 1. The page does not convert miles to feet.
Worked example
One thousand feet of map distance at a 10 percent grade is about 1,005 feet along the slope. The factor is about 1.005. A 50 percent grade stretches the same thousand feet to about 1,118 feet. Most hiking grades change the distance less than people expect. They change the effort more, which is what the grade and Tobler pages are for.
Assumptions
One steady grade for the whole horizontal distance. A trail that rolls up and down needs to be split, or the grade you type is only an average and the slope distance will be a little short of the sum of the pieces.
FAQ
Why is a 10 percent grade almost the same distance?
Because the extra length grows with the square of the grade. Ten percent is a small decimal, and its square is 0.01.
Is the horizontal distance the map distance?
Yes, if the map distance is the flat run and not a slope distance someone already corrected.
How do I get the grade?
From the trail-grade page, using the rise and the run, or from a source that already states the percent.
Does this change Tobler's time?
Only if you feed it a longer distance. Tobler wants a distance and a grade. This page does not apply his speed.