Naismith's rule, Langmuir and Tobler: how hiking time is estimated
The quickest way to estimate a hike is Naismith's rule: one hour for every 5 kilometres, plus one hour for every 600 metres of ascent. A 10 km walk with 600 m of climbing is therefore 2 + 1 = 3 hours of walking, before rests. Langmuir's correction refines the figure for descents, and Tobler's hiking function replaces the rule of thumb with a formula for speed on any slope. This guide explains all three, shows when they disagree, and explains how to calibrate them to your own pace using the hike time calculator.
Naismith's rule
William W. Naismith, a Scottish mountaineer, proposed the rule in 1892 for planning club outings. It assumes a fit walker in good conditions on a decent path carrying a light pack. Expressed in metric units: time in hours = distance in km ÷ 5 + ascent in metres ÷ 600. In imperial units it is one hour per 3 miles plus one hour per 2,000 feet of ascent, which is close enough that the two versions give nearly the same answer.
Take a 12 km loop with 800 m of ascent. The distance part is 12 ÷ 5 = 2.4 hours and the climbing part is 800 ÷ 600 = 1.33 hours, giving 3.73 hours, or 3 hours 44 minutes of moving time. The rule says nothing about rests, so the calculator adds them separately: at 10 minutes per hour walked plus a 30 minute lunch, the same day becomes about 4 hours 51 minutes door to door.
The rule works because walking is an effort budget. On the flat, a steady walker covers about 5 km/h. Each 600 m of height gained costs roughly as much time as another 5 km of flat walking. The rule is deliberately simple, so it is easy to apply on a map with a pencil, and that is the main reason it is still taught.
Langmuir's correction for descents
Naismith did not say what to do about downhill walking. Eric Langmuir, a Scottish mountaineering instructor, added a refinement that is now usually combined with the original rule: subtract 10 minutes for every 300 m of descent on gentle slopes (about 5 to 12 degrees), and add 10 minutes for every 300 m of descent on steep slopes (over 12 degrees). Gentle descents let you walk faster than on the flat. Steep descents slow you down because you brake with every step and need to place your feet carefully.
For the same 12 km loop with 800 m of descent on gentle slopes, the correction is 800 ÷ 300 × 10 = about 27 minutes, so the moving time falls from 3 h 44 to 3 h 17. If the descent were steep and rocky, the same 27 minutes would be added instead, giving 4 h 11. That 54 minute swing, on a single walk, is the reason the calculator asks what kind of descent to expect. Be honest when you choose: steep, loose or wet descents are where many people lose time and where most slips happen.
Tobler's hiking function
Waldo Tobler, a geographer, published a formula in 1993 that gives walking speed for any slope: v = 6 × e-3.5 × |s + 0.05| km/h, where s is the slope as a rise divided by run (a 10 percent climb is s = 0.10). The function peaks at 6 km/h on a gentle downhill of about 5 percent, falls to about 5 km/h on the flat, to 3.5 km/h on a 10 percent climb, and to 1.8 km/h on a 30 percent climb. It also slows you down on very steep descents: a 20 percent descent is as slow as a 10 percent climb.
Tobler's function was designed for computers working on terrain models, where every few metres has its own slope. Our calculator only has three totals, so it makes an explicit assumption: your climbing happens on slopes of the typical gradient you set (10 percent by default), your descending does the same, and the rest of the route is flat. For the 8 km route with 700 m of climbing and no descent, that gives 7 km of climbing at 10 percent and 1 km on the flat, which Tobler turns into 2 h 10 min compared with Naismith's 2 h 46 min. Tobler is optimistic on moderate slopes because it assumes smooth ground, so the faster result is less a prediction than a lower bound for a fit walker.
Where the methods disagree
| Situation | What usually happens |
|---|---|
| Long, gentle routes with little climbing | All three agree within about 10 percent. |
| Short, very steep climbs | Naismith is slower than Tobler. Check which is closer to your own experience on steep ground. |
| Big descents | Naismith ignores them, Langmuir adjusts them, Tobler penalises very steep ones. Expect the widest spread here. |
| Rough, pathless or snowy ground | All three assume a decent path, so apply the terrain multiplier. |
When the methods disagree by more than 20 minutes, treat the slower figure as your plan and the faster as your best case. If you are planning a turnaround time, the slower figure is the safe one: a late turnaround is the mistake that costs the most.
What none of the rules include
All of these methods estimate moving time under fair conditions. They leave out rests, photographs, navigation stops, queues at stiles and scrambles, deep mud, wind, heat and fatigue in the second half of the day. They also assume a certain fitness. A relaxed group or a group with children can easily take 25 percent longer than the rules say, and an overnight pack adds about 10 percent. These are the reasons the calculator has pace, pack and terrain multipliers and separate rest settings.
Calibrating the rule to your own pace
The best correction is your own data. After each walk, note the total moving time from a watch or phone app (not including long stops), the distance, and the ascent and compare it with the calculator's moving time for the same route. If you were 15 percent slower on three walks in a row, move the pace setting to Relaxed, or add that percentage to every estimate you make. If you are consistently faster, set the pace to Fast. After half a dozen walks your personal factor will be more reliable than any published formula.
A few other habits make estimates better. Read the ascent from a contour map or a GPX file, not from a guidebook figure that may leave out small ups and downs. A route that undulates gains much more height than its start-to-summit difference. Allow extra time for the last third of a long day, because pace usually drops. And add time when the plan includes scrambling, river crossings or snow, since none of the rules apply there.
From estimate to plan
A time estimate is only useful once it is attached to a clock. Choose a start time, add the estimate, and compare the result with sunset. If you will finish after dark, the answer is to start earlier, shorten the route or carry a headlamp: not to walk faster. For out-and-back walks you also need a turnaround time, which the calculator derives from the return leg. That topic, and how to leave a sensible call-for-help time with someone who is expecting you, is covered in how to set a hiking turnaround time and a call-for-help time.