Tobler’s Hiking Function Calculator (Walking Speed & Time on a Slope)
Estimate walking speed and hiking time on any slope with Tobler’s hiking function — horizontal distance, elevation change and terrain (trail, off-trail or horseback), in km and m or miles and feet.
How it works
W = 6 × e^(−3.5 × |S + 0.05|) km/h · S = elevation change ÷ horizontal distance (as a decimal) · time = horizontal distance ÷ W · off-trail W × 0.6, horseback W × 1.25.
Waldo Tobler published his hiking function in 1993 from Eduard Imhof’s field data on Swiss hikers. Walking speed peaks at 6 km/h on a gentle −5% downhill, is about 5 km/h on the flat, and falls off exponentially as the trail gets steeper either up or down. Unlike Naismith’s rule, which only adds time for ascent, Tobler also slows you on steep descents. Geographers use it in GIS route models; for a long route with ups and downs, split it into sections of similar slope and add the times.
Worked example
A 10 km trail section climbs 500 m on a path. Slope S = 500 ÷ 10,000 = 0.05 (5%). W = 6 × e^(−3.5 × 0.10) = 6 × 0.7047 = 4.23 km/h, so the hike takes 10 ÷ 4.23 = 2.37 h ≈ 2 h 22 min — versus about 1 h 59 min on flat ground.
Sources: Tobler, W. (1993) Three Presentations on Geographical Analysis and Modeling — NCGIA Technical Report 93-1 · Tobler’s hiking function
Frequently asked questions
What is Tobler’s hiking function?
An exponential formula that gives walking speed from the slope: W = 6 × e^(−3.5 × |S + 0.05|) km/h. It peaks at 6 km/h on a slight downhill and is about 5 km/h on level ground.
Is Tobler or Naismith more accurate?
They agree on moderate climbs. Tobler is better on steep descents, where Naismith gives no extra time, and on gentle downhills where Tobler is a bit faster. Neither includes breaks, heavy packs or rough ground, so add a margin.
Should I use horizontal or trail distance?
Tobler’s formula uses horizontal (map) distance. On steep ground the walked distance is slightly longer, but the formula already accounts for that through the slope.
How do I use it for a route with several climbs and descents?
Split the route into legs of similar slope, run each leg separately and add the times. Using one average slope for a route that goes up and then down will underestimate the time.
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This calculator is for educational purposes. Double-check important results before acting on them.