How to use
- Enter the distance and whether it is miles or kilometers.
- Enter the grade as a percent. Zero is flat. Ten means ten feet of rise for every hundred feet of run. A descent is a negative percent.
- Press Calculate. The hero is minutes.
- The speed lines are the function's output in kilometers per hour and miles per hour.
How it's calculated
Slope S = grade ÷ 100. Speed in km/h = 6 × exp(−3.5 × |S + 0.05|). The small 0.05 shift is part of Tobler's function: the fastest walking is on a slight downhill, not on perfectly flat ground.
Miles are converted at 1.609344 kilometers per mile before dividing by that speed. Naismith's rule, on its own page, is a different estimate that uses distance and ascent rather than this exponential.
Worked example
Ten kilometers on flat ground: the function returns about 5.04 km/h, so the walk is about 119 minutes. The same ten kilometers at a 10 percent grade is about 3.55 km/h and about 169 minutes. A negative grade is allowed and uses the absolute value inside the formula.
Assumptions
A steady grade for the whole distance, and a walker who matches Tobler's curve. It is not a personal fitness test. Heat, pack weight, and trail surface are not inputs.
FAQ
Where does the formula come from?
Waldo Tobler, 1993, the hiking function that relates speed to slope. The page prints the expression in the result note.
Why is a slight downhill faster than flat?
The function adds 0.05 to the slope before taking the absolute value, so the peak speed sits on a gentle descent.
How is this different from Naismith?
Naismith adds time for climbing on top of a base pace. Tobler sets the speed from the grade alone. Use the page that matches the rule you want.
Can the grade be negative?
Yes. A descent is a negative percent. The absolute value in the formula treats a steep drop as slow, which matches careful footing.