Two classic rules for how long a hill walk takes, worked out side by side: Naismith's rule with Langmuir's corrections, and Tobler's hiking function. Type the distance and climb, or drop in a GPX file.
Naismith + Langmuir
3 h 17 min
5 km/h plus 1 h per 600 m up
Tobler
3 h 16 min
average 3.7 km/h
The two rules agree to within 2 min on this route.
| Part | Naismith | Tobler |
|---|---|---|
| Distance on the map | 144 min | 115 min uphill and level |
| Climbing | +80 min | |
| Descending | −27 min | 81 min |
| Moving time | 3 h 17 min | 3 h 16 min |
Typed totals: we assume the climbing and descending are spread evenly at an average grade of 13%. Load a GPX file for a slope-by-slope estimate. Moving time only: add your stops.
Point at the profile to read the distance and height.
Point at the chart to compare speeds. Lines mark this route's average climb and descent.
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Naismith's rule comes from an 1892 trip report by the Scottish climber William Naismith: allow an hour for every three miles on the map, plus an hour for every 2,000 feet of ascent. The metric version is 5 km/h plus an hour per 600 m. Eric Langmuir later added corrections for descent: take off 10 minutes per 300 m on gentle slopes (5° to 12°) and add 10 minutes per 300 m on steeper ones.
Tobler's hiking function (1993) turns slope into speed: W = 6 e−3.5 |S + 0.05| km/h, where S is the rise over the run. That gives about 5 km/h on the level and a top speed of 6 km/h on a slight descent of 5%. Off paths, Tobler multiplies the speed by 3/5.
Naismith charges a fixed hour for every 600 m of climb, however steep. Tobler's speed falls away smoothly with steepness, so it is brisker than Naismith on moderate climbs and much slower on very steep ground. Downhill, Tobler slows on steep slopes, while Langmuir's gentle-descent credit can imply very fast walking near 12°. Where the two differ a lot, plan on the longer time. Both give moving time for a fit walker in good conditions.
With typed totals we assume one even climb and one even descent at the route's average grade. A GPX file is better: we smooth its heights over about 100 m, so GPS jitter does not inflate the ascent, and judge every short step on its own slope. Your level-ground speed scales both rules.
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Look up a shop with WebTraceCheckNeither exactly. Compare them with your own past walks. On unfamiliar or steep ground, plan on the longer one and add time for stops, weather and the slowest walker.
Apps smooth elevation in different ways, and raw GPS heights jitter up and down. Counting every small wiggle as climbing inflates the total, so two apps can report quite different figures for the same track.
Time yourself on a level walk you know and enter that speed. If your GPX file has timestamps, we also show the recorded time so you can compare it with both rules.