Naismith Hiking Time Calculator
Naismith's rule hiking time calculator: his 1892 rule in miles and feet, the usual metric version in kilometres, and a separate Tobler estimate that counts descent.
Naismith's Rule Hiking Time Calculator
Each part is rounded to the minute, and the total is their sum.
How to use the hiking time calculator
Choose the units
Miles and feet apply Naismith's rule exactly as he wrote it in 1892. Kilometres and metres apply the usual metric version, which gives slightly different answers. Switching converts the figures you have entered.
Enter the map distance and the total ascent
Naismith counted distance "on the map". For climbing, add up every rise on the route, not just the difference between the start and the top; his own example used the day's "total climb".
Enter the total descent
Naismith's figure ignores it. The calculator uses it only for a second, separate estimate from Tobler's hiking function.
Choose a pace factor and compare
×1.0 is the rule as written; the other factors are our own convention and scale both estimates. If the trail is in a park that publishes its own walking time, compare the result with that figure.
Naismith's rule, from his 1892 note
What Naismith wrote
The rule comes from a short note by W. W. Naismith in the Scottish Mountaineering Club Journal (Vol. II, No. 3, September 1892, p. 136), describing a day on Cruach Ardran, Stobinian and Ben More. He gave the day as ten miles with a total climb of 6,300 feet, taking "six and a half hours (including short halts)", and wrote that this "tallies exactly with a simple formula" for what "men in fair condition should allow for easy expeditions": an hour for every three miles on the map, plus an hour for every 2,000 feet of ascent. Applied to his own day, the formula gives 6 h 29 min.
So the day Naismith offered as matching the rule included short halts, and nothing in the note presents it as moving time. The note does not say how long the halts were.
"An hour for every three miles on the map, with an additional hour for every 2,000 feet of ascent." — W. W. Naismith, Scottish Mountaineering Club Journal, Vol. II, No. 3 (1892), p. 136. Scan at the Internet Archive
The metric version gives a different answer
The usual metric version, which this calculator's kilometre mode applies, is an hour per 5 km plus an hour per 600 m. That is a conversion, not Naismith's wording, and it is rounded: three miles is 4.83 km and 2,000 feet is 609.6 m. On Naismith's own day the metric version gives 6 h 25 min against the 1892 wording's 6 h 29 min. On a flat 24-mile day the two give 7 h 43 min and 8 h 0 min. In miles-and-feet mode the calculator applies the 1892 figures exactly.
The two versions also price climbing differently. In the 1892 wording, a metre of climb costs as much time as 7.92 m of map distance; in the metric version, 8.33 m. Scarf's 2007 paper in the Journal of Sports Sciences works out that ratio for Naismith's rule (1:7.92) and, from fell-running records, recommends counting a metre of climb as 8 m of distance for men and 10 m for women (Scarf P. J Sports Sci 2007;25(6):719–726, doi:10.1080/02640410600874906).
Descent: a separate estimate from Tobler
Naismith's rule adds nothing for going downhill, and the calculator never changes the Naismith figure for descent. It shows a second estimate instead, from Waldo Tobler's hiking function (Tobler W. Three Presentations on Geographical Analysis and Modeling. NCGIA Technical Report 93-1, 1993): walking speed is 6 × e−3.5 × |S + 0.05| km/h, where S is the slope, rise over run, negative downhill. Tobler estimated it from empirical data in Imhof (1950), for walking on footpaths in hilly terrain. It gives 5.04 km/h on the flat and its top speed, 6 km/h, on a 5% descent.
The calculator knows only the route's totals, so it assumes every climb and descent runs at one steady gradient and splits the map distance between them in proportion to total ascent and total descent. Real routes are not like that. On the default 15 km route with 600 m up and 600 m down, Naismith gives 4 h 0 min and Tobler 3 h 22 min. Treat the gap as two models disagreeing, not as a correction.
Park trails publish their own times
Where a park authority publishes a time for a trail, it can differ widely from the rule. At Bukit Timah Nature Reserve, NParks's 2012 trail guide, still linked from its current hiking page, says the 1.2 km main route to the summit of Singapore's highest hill, 163 m, takes "approximately 45 minutes to an hour to reach the summit, at a leisurely pace". The current page lists that route as Route 1 and gives no time. Naismith's rule gives 30 min even if the whole 163 m were climbed, and the climb from the start is less than that. For a park trail, the authority's own times and guidance come first.
Langmuir and Tranter
Langmuir's descent adjustment and Tranter's corrections are commonly cited refinements of Naismith's rule. We could not check either against its original publication, so the calculator uses neither and this page gives no figures for them.
Six and a half hours with short halts: what Naismith's 1892 note says
Published by W. W. Naismith in the Scottish Mountaineering Club Journal, September 1892, p. 136.
His wording: an hour for every three miles on the map.
Plus an hour for every 2,000 feet of ascent.
His test day took six and a half hours, "including short halts".
Written for "men in fair condition" on "easy expeditions".
He used the day's total climb, not the net height gain.
5 km and 600 m is a metric conversion, not his wording.
A metre of climb counts as 7.92 m of distance in the 1892 wording.
Scarf (2007): count a metre of climb as 8 m of distance for men, 10 m for women.
The rule has no descent term; Tobler's 1993 function has one.
Frequently asked questions
A way of estimating walking time in hills from two numbers off the map. W. W. Naismith wrote it in 1892 as an hour for every three miles on the map, plus an hour for every 2,000 feet of ascent. In metric it is usually given as an hour per 5 km plus an hour per 600 m, which is a rounded conversion rather than his wording.
Short ones, by Naismith's own account. The day he said "tallies exactly" with the rule was ten miles with 6,300 feet of climbing and took "six and a half hours (including short halts)"; the formula gives 6 h 29 min for it. The note does not say how long the halts were or mention longer stops.
Because 5 km and 600 m are roundings of three miles (4.83 km) and 2,000 feet (609.6 m). Miles-and-feet mode applies Naismith's figures exactly; kilometre mode applies the metric version. On a flat 24-mile day the 1892 wording gives 8 h 0 min and the metric version 7 h 43 min.
Total ascent, the sum of every rise on the route. Naismith's own example gave the day's "total climb" of 6,300 feet. A route that crosses several tops has more total ascent than the height of its highest point suggests.
Naismith's rule has no descent term, and the calculator leaves his figure as he defined it. The descent you enter feeds a separate estimate from Tobler's hiking function (1993), which is fastest on a gentle 5% descent and slower on steeper ground either way. It is a different model, shown beside the rule rather than mixed into it.
×1.0 is the rule as Naismith wrote it. The other factors (×0.8, ×1.25, ×1.5) are our own convention, not taken from Naismith or from a study, and they scale both estimates. They are a way to see how the time moves, not a measure of fitness. For a park trail, compare with the time the park authority publishes.
We do not give an accuracy figure. Naismith checked the rule against one day of his own, and it matched that day within a minute. Published park times can sit far from it: for Bukit Timah's 1.2 km main route, NParks's 2012 trail guide allows 45 minutes to an hour at a leisurely pace, while the rule gives 30 min even counting the hill's full 163 m as climb.
Scarf's 2007 paper is about how much distance a metre of climb is worth: 7.92 m in Naismith's rule, and from fell-running records he recommends counting a metre of climb as 8 m of distance for men and 10 m for women. Langmuir's descent adjustment and Tranter's corrections are commonly cited refinements, but we could not check either against its original publication, so the calculator uses neither and we give no figures for them.
No. Neither Naismith's rule nor Tobler's function has an input for them. For a trail in a park, the authority's published times and guidance cover its own conditions.
No. The values you enter are processed entirely in your browser. Nothing is sent to a server, stored, or shared, and no account is required. The calculation runs on your device only.
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