Outdoor Calculators
Tobler's hiking function.
Break your route into stretches, each with a distance and a grade, and get the walking speed and time for every stretch plus the total. Uses Waldo Tobler's 1993 hiking function. Runs in your browser; nothing is sent or stored.
Route segments
Result
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Worked example
A route of 4 km at +8% grade then 3 km at -6%. Tobler's speed at +8% is 6 x e^(-3.5 x |0.08 + 0.05|) = 3.81 km/h, so the climb takes 1 h 03 min. At -6% the speed is 6 x e^(-3.5 x 0.01) = 5.79 km/h, so the descent takes 31 min. Total: 1 h 34 min of walking, before rests.
How it works
W = 6 x e^(-3.5 x |S + 0.05|) km/h, where S is the slope as rise over run (a 10% grade is S = 0.10). Speed peaks at 6 km/h on a gentle downhill of about 5% and falls off on steeper ground in both directions. Time for a segment is distance divided by speed. Off the trail, Tobler multiplies speed by 0.6.
Tobler's function describes an unloaded walker. It does not know your fitness, pack weight, snow, scrambling or river crossings, so treat the result as a baseline and add time for those. Compare with Naismith's rule, which adds a fixed time per metre climbed instead of a smooth curve.
Sources and basis: Waldo Tobler, Three presentations on geographical analysis and modeling, NCGIA Technical Report 93-1, 1993 (hiking function). Checked 2026-10-05.
FAQ
What is Tobler's hiking function?
A formula by geographer Waldo Tobler that gives walking speed from the slope of the ground: W = 6 x e^(-3.5 x |S + 0.05|) km/h. It is widely used in GIS travel-time and cost-distance models.
Why is the fastest speed on a slight downhill?
The curve peaks where S = -0.05, a 5% downhill, where gravity helps without forcing you to brake. On flat ground the speed is 5.0 km/h and uphill it drops quickly.
How is it different from Naismith's rule?
Naismith's rule adds a fixed hour per 600 m climbed to a flat pace. Tobler's function is a continuous curve of speed against grade, so it handles descents and gentle grades without separate corrections.
What does off-trail mean here?
Tobler's off-path version multiplies the speed by 0.6, which is about 40% slower, for rough ground with no path.
How do I find the grade of a stretch?
Divide the elevation change by the horizontal distance and multiply by 100. A 150 m climb over 2 km is 7.5%. A topographic map or a GPS track's profile gives both numbers.