Walking time calculator: from distance and ascent to hours

4 h, 5 h 15 min or 5 h 40 min: for the same 14 km loop with 650 m of ascent, the tool above gives three times, and none of them is wrong. Each applies a different rule, with its own assumptions. Let’s do the sums.

What each of the three results calculates

The simple calculation adds two times: the distance at 4 km/h, and the ascent at 300 m per hour. These are the French Hiking Federation’s (FFRandonnée) benchmarks for a walker who is ‘neither a beginner nor a speedster’, breaks not included [1]. It leaves out the descent, even though the federation also gives 400 to 500 m of descent per hour [1].

The German standard DIN 33466 counts all three: 4 km/h on the flat, 300 m per hour uphill and 500 m per hour downhill. These are the values of the Austrian Alpine Club and of the German Alpine Club’s calculation table, whose signposts rest on them [2, 3]. The standard, titled ‘Wegweiser für Wanderwege’ (signposts for walking routes), dates from May 2004 [4]. It does not simply add them up: you work out the horizontal time on one side and the vertical time on the other, keep the longer and add half of the shorter [2].

Naismith’s rule dates from 1892: an hour for every three miles on the map, plus an hour for every 2,000 feet of ascent [5]. In metric terms, that is about 5 km/h and 10 extra minutes per 100 m of ascent. Its known weakness: the planned speed does not change on the descent, whatever the slope [6].

Four outings, three results

Take the tool’s default values: 14 km, 650 m of ascent and the same of descent. The simple calculation gives 3 h 30 min on the flat plus 2 h 10 min of ascent, or 5 h 40 min. The DIN standard keeps the 3 h 30 min on the flat (the vertical time, 2 h 10 min of ascent plus 1 h 18 min of descent, comes to 3 h 28 min) and adds half of 3 h 28 min: 5 h 15 min. Naismith counts 8.7 miles ÷ 3 plus 2,133 feet ÷ 2,000: 4 h.

The gap between the longest and the shortest of the three results runs from 25 minutes on the stroll to nearly 3 hours on the long day. The longer and higher the outing, the more the choice of method matters: on a stroll, the gap stays at half an hour.

Why the three results part company

First, because the starting speeds differ: 4 km/h on the flat for the first two, 5 km/h for Naismith. Second, because the descent is treated three ways: ignored, ignored, or counted at 500 m per hour. A curve shows it better than a table. Tobler’s, from an American geographer who proposed a slope-based speed formula in 1993 [7], is not in the tool, but it makes a useful yardstick: 5 km/h on the flat, a maximum of 6 km/h on a gentle descent [6].

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The choice depends on the terrain. On a good path with a light rucksack, Naismith is a lower bound: it was aimed at ‘men in fair condition’ on easy expeditions [5]. For a long, steep descent, prefer the DIN standard, the only one that counts it. The simple calculation is a rule of thumb: handy, but blind to the descent, and longer than Naismith in all four examples above.

On signposts, the time is not always yours

Yellow signposts follow their own rules, and they vary from country to country. In Switzerland, the signposts assume 4.2 km/h on the flat, plus an hour for every 400 m of ascent or 800 m of descent; until 1981, the benchmark was 4.5 km/h [8]. The current official formula is a 15th-degree polynomial of the gradient: hard to redo by hand [8]. These are times for walking without breaks, and not every signpost carries them: a signpost with times costs more, and a diversion can make them misleading [9].

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A time on a signpost is therefore a signposting benchmark, not a promise. The tool does not try to reproduce it: it calculates the time for a route you have drawn yourself, using rules you can read.

What the tool does not know

A research team tested several walking speed models on public GPS tracks covering nearly 88,000 km of British paths. Its model, which takes account of the type of terrain, the slope of the hillside and obstacles, is wrong by 23.7% on average over a 50 m stretch; Naismith’s by 26.4% and Tobler’s by 26.2% [6]. In other words, even a model fitted on tens of thousands of kilometres is still out by about a quarter over a short stretch. The message is clear: a calculator’s result is an order of magnitude.

• Breaks are counted in none of the three methods: photos, map checks, picnic, waiting for a companion.
• Terrain matters: the type of ground and off-path obstacles affect speed, whatever the slope [6].
• Your form on the day, your rucksack, the weather appear in no formula: correcting for them is up to you.
• A group moves at the pace of its slowest walker: work the sums out for them.

From walking time to a day out

The tool’s result is a walking time, not a time to be home. To get to a full day, add about ten minutes of stops per hour of walking, then lunch: generous, and deliberately so. On the default loop, the 5 h 40 min of the simple calculation becomes about 7 h 20 min out. Leave at 9am and you will be back around 4.20pm.

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Finding your own correction factor

The most reliable method is still your own. The German Alpine Club offers a table where you replace its values with yours: metres of ascent per hour, metres of descent per hour and kilometres on the flat per hour [3]. The French Hiking Federation advises comparing your actual walking time with the guidebook times [1]. Do it on two or three walks you know, taking off the breaks.

If a walk estimated at 4 h took you 4 h 40 min of walking, your factor is 1.17 (280 minutes ÷ 240). Applied to the 5 h 15 min of the DIN standard for the default loop, it gives about 6 h 10 min: the time to allow for yourself, before breaks.

For the logic of the calculation and the corrections to make, see the walking time guide; for effort on the trail, the kilometre-effort; for how hard a route is, the grading of mountain walks; to forget nothing, planning your walk.

The rule fits in one sentence: pick one method and apply it in full, add your breaks, then correct with your own factor.

Worth watching

Walks through Naismith’s rule, from its 1892 wording to the modern version of 5 km/h plus 10 minutes per 100 m of ascent, and explains why it is only a rough guide.

The video is hosted by YouTube (Google): nothing loads until you play it, and Google may then set cookies.

Julien de Jurquet

Campervans, motorhomes, cycling and calculators

Julien de Jurquet writes for Outfarer about campervans, motorhomes, cycling and calculators. He reads instruction manuals to the very end and never lets a figure through without its unit, so that your choices rest on sums rather than promises.

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