Hiking Time Calculator: Naismith's Rule and Tobler's Hiking Function

How long will this hike take? Hill walkers have answered with Naismith's rule since 1892: an hour for every three miles on the map, plus an hour for every 2,000 feet of climbing. This hike time calculator runs that rule for your route and your pace, puts Tobler's hiking function from 1993 beside it, and shows what Langmuir's corrections for descents change. It also works as a walking time calculator: set the climb to zero for a flat walk.

Most hiking time calculators print one number from one rule. This one puts two methods side by side with a correction for descents, says where every constant comes from, and gives the error researchers measured when they checked the rules against thousands of GPS-tracked hikes.

How the hiking time calculator works

The calculator takes five inputs: the distance you will walk, the total climb, the total descent (the same as the climb unless you enter one), your walking speed on flat ground and any breaks you plan. It returns three walking times.

Naismith: hours = miles ÷ 3 + feet of climb ÷ 2,000
(metric: hours = km ÷ 4.83 + meters of climb ÷ 610)

Tobler: speed in km/h = 6 × exp(−3.5 × |S + 0.05|)

• Naismith's rule. An hour for every 3 miles of map distance and an hour for every 2,000 feet of total climb, which is 20 minutes a mile and 3 minutes for every 100 feet of climbing. Descents get no time of their own.
• Langmuir's corrections. On descents averaging 5 to 12 degrees, take off 10 minutes for every 300 m (about 1,000 feet) of descent. On descents steeper than 12 degrees, add 10 minutes per 300 m.
• Tobler's hiking function. Walking speed in km/h from the slope S, the rise or fall divided by the horizontal distance. It peaks at 6 km/h (3.7 mph) on a 5 percent downhill and gives 5.0 km/h (3.1 mph) on the flat.
• The route model. A distance and an elevation gain do not say where the hills are, so the calculator splits the distance into a climbing leg and a descending leg in proportion to the climb and the descent, both at the route's average grade, (climb + descent) ÷ distance. A 6-mile loop with 2,000 feet up and down has a 12.6 percent average grade: 3 miles climbing and 3 miles descending.
• Your pace. Naismith's 3 mph is the baseline. Enter a slower or faster flat speed and every figure scales by 3 ÷ your speed, climb included, for the reason explained in the next section.
• Breaks. The rules estimate walking time only. The minutes you enter are added to each figure.

For the default loop, Naismith gives 6 ÷ 3 = 2 hours for the distance and 2,000 ÷ 2,000 = 1 hour for the climb, 3 hours in all. Tobler's function walks the climbing half at 3.24 km/h (2.0 mph) and the descending half at 4.59 km/h (2.9 mph), 2 hours 33 minutes in all. The descents average 7.2 degrees, inside Langmuir's 5 to 12 degree band, so his correction takes off 2 seconds for each of the 610 meters of descent, about 20 minutes, for 2 hours 40 minutes.

Both rules use map distance, the horizontal length of the route. Even on a 12 percent grade the distance measured along the slope is less than 1 percent longer, so the distance your map or trail app shows works fine.

Naismith's rule: 3 mph plus an hour for every 2,000 feet

The Scottish mountaineer William Naismith published his rule in the Scottish Mountaineering Club Journal in 1892, in a note titled "Cruach Ardran, Stobinian, and Ben More." As Wood and colleagues (2023) quote it, the rule allows "an hour for every three miles on the map, with an additional hour for every 2,000 feet of ascent." We could not find the 1892 journal online, so the wording here is as they quote it.

In modern terms that is 20 minutes a mile plus 30 minutes for every 1,000 feet of climbing, or 3 mph on the flat. Metric versions round it to 5 km/h plus an hour per 600 m, which is about 3.5 percent quicker on the flat and 1.6 percent slower on the climb than Naismith's own figures. This calculator uses the 1892 figures in both unit systems, so switching units never changes the answer.

The rule also sets a trade between climbing and distance. An hour buys 3 miles of flat walking or 2,000 feet of climb, so 1 foot of climb counts as 7.92 feet of flat walking. Scarf (2007) tested that ratio against fell-running race records and found they supported it: he recommends a ratio of 1:8 for male runners and walkers and 1:10 for women. Since fell runners, who are far faster than walkers, showed nearly the same ratio as Naismith's walkers, this calculator scales the climb along with the flat when you change your pace. A hiker who walks the flat at 2.5 mph gets 20 percent more time for both.

Naismith's rule says nothing about descents, rough ground, a heavy pack, the weather or how fit you are. It came from experience rather than measurement, and the accuracy section below shows where that matters.

Langmuir's corrections for descents

Langmuir's handbook Mountaincraft and Leadership (1984) added a descent term, as Campbell and colleagues (2019) and Pharoah (2017) both set it out. On descents of 5 to 12 degrees, roughly 9 to 21 percent grades, take off 10 minutes for every 300 m of descent. On descents steeper than 12 degrees, add 10 minutes per 300 m. Below 5 degrees, nothing changes. We could not read the 1984 book online, so these figures are as those two papers give them.

The calculator applies the band that matches your route's average descent angle. Two cautions come with it. Applied slope by slope, the rule makes a hiker fastest on a 12-degree descent and much slower just past it: Campbell and colleagues work it out at 3.39 m/s at 12 degrees and 0.87 m/s at 12.1 degrees, a pattern they call highly improbable. And in GPS data, hikers came down more slowly than the rule assumes (see the accuracy section), so the time it takes off for gentle descents is usually optimistic.

Tobler's hiking function: speed from the slope

In 1993 the geographer Waldo Tobler published a formula for walking speed on footpaths in hilly terrain, in a technical report for the National Center for Geographic Information and Analysis:

W = 6 exp(−3.5 × |S + 0.05|)

W is walking speed in km/h and S is the slope, the change in height divided by the horizontal distance. On flat ground it gives 5.0 km/h (3.1 mph), close to Naismith's 3 mph, and its fastest pace, 6 km/h (3.7 mph), comes on a 5 percent downhill, about 3 degrees. Tobler fitted it to walking-time data published by the Swiss cartographer Eduard Imhof in 1950. Campbell and colleagues point out that Imhof presented those data only as a chart of travel-time lines, and that Tobler reported no measure of how well the formula fits. For travel off paths, Tobler multiplied the speed by 3/5.

Unlike Naismith, Tobler gives descents their own speed: faster than the flat on descents up to about a 10 percent grade, and slower beyond that. On climbs he expects you to keep moving faster than Naismith does, as the table in the next section shows.

This calculator runs Tobler's function at one average grade for the climbing leg and the same grade for the descending leg, because a distance and an elevation gain cannot tell it more. Real trails mix steep pitches with gentle stretches, and the steep pitches cost more time than the gentle ones save, so the single-grade figure runs fast on uneven trails. The studies in the accuracy section ran Tobler's function slope by slope along real GPS tracks.

Hiking pace by grade: what each rule expects

Your hiking pace depends mostly on the grade. Here is the pace each rule expects on a steady grade, uphill (+) and downhill (−), at Naismith's standard flat speed. Naismith's rule gives descents no time of their own, so the downhill rows use its flat pace.

On the flat the two rules agree within a minute a mile. On a 10 percent climb, Naismith allows about 36 minutes a mile and Tobler about 27; on a 20 percent climb, about 52 and 39. Tobler's quickest pace is a 16-minute mile on a gentle 5 percent descent, and by a 20 percent descent he is as slow as on a 10 percent climb.

For a sense of real speeds, healthy adults walk about 1.31 m/s (2.9 mph) at their usual pace on flat outdoor paths, from a meta-analysis of 35 studies and 14,015 people by Murtagh and colleagues (2021), close to both rules' flat speeds. On a hilly trail the average drops: the 100 GPS-tracked hikes of Utah's Lake Blanche Trail that Campbell and colleagues analyzed covered 11.7 km in about 3.7 hours on average, about 3.2 km/h (2 mph) with the climb included.

Worked examples: hiking times for eight hikes

Eight hikes run through the calculator at Naismith's 3 mph, with no breaks. The last row is the trail Campbell and colleagues used to check the rules against 100 real hikes; we used the 818 m difference between its high and low points as the climb.

Three patterns stand out. On gentle routes Tobler's function is the quickest, because it walks gentle descents faster than the flat: on the long valley hike it comes in 46 minutes under Naismith. On the short, steep summit it is the slowest of the three, because it slows hard on steep descents that Naismith treats as flat, and Langmuir adds 25 minutes for the same reason. On Lake Blanche, where 100 real hikes averaged about 3.7 hours, Naismith's 3 hours 46 minutes landed closest, and the single-grade Tobler and Langmuir figures came in well under the average.

Training for a bigger hike? Step-ups, lunges and single-leg work build the strength that long climbs and steep descents ask for, and a personalized training program shaped around your goal and schedule makes those sessions easier to keep doing.

How accurate is this hiking time calculator?

The calculator runs the three rules exactly, so the real question is how close the rules come to the time real hikers take. Researchers have checked them against GPS tracks, and three findings repeat. For a whole route, the rules usually land within about 15 percent of the real time. They allow too long for climbs and too little for descents, and those errors partly cancel. And the spread from one hiker to the next is far wider than the error of any rule.

Read together, the studies say two things about Naismith's rule. For a typical hiker on a typical route it lands close: on Lake Blanche, our Naismith figure of 3 hours 46 minutes sits within a few minutes of the 3.7-hour average. For keen hikers who record and upload their walks, it runs long, by 9 to 13 percent in Pharoah's tracks once Langmuir's corrections are added, mostly because it allows too much time for climbing. Tobler's function, run slope by slope, came within 3 percent of the total in Pharoah's tracks, and Wood's team found it no more accurate than Naismith's rule overall.

Which way the rules miss

Wood and colleagues found that Naismith's rule underestimates walking speed on climbs and overestimates it on descents. In time, that means too long for the way up and too short for the way down, which is why the errors shrink over a loop that climbs and descends the same height. By the same logic, a one-way hike that mostly climbs will probably take less time than Naismith's rule says, and one that mostly descends will take more. Tobler's function was too fast on slight descents and on paths that cut across a slope, and its off-path factor of 0.6 slowed walkers more than real off-path data showed.

Your own pace matters more than the formula

On Lake Blanche the quickest of the 100 hikes took 1.9 hours and the slowest 5.6, a threefold spread on the same trail, against rule errors of about 15 percent. That is why the calculator asks for your flat walking speed. Time one familiar hike, compare it with the calculator at 3 mph, and set the speed that matches; the climb scales with it. Campbell and colleagues also note that fitness-app data can lean toward faster, more competitive users, so averages built from app data may be quicker than the average hiker.

Plan the whole day: breaks, daylight and the way down

Naismith's and Tobler's rules estimate walking time and make no allowance for stops, so the calculator adds exactly the minutes you enter: a 30-minute lunch on a 3-hour loop makes it 3 hours 30 minutes. Set a turnaround time before you start, leave daylight to spare, and give a steep, rocky or wet descent extra time of its own.

Heat, snow, a heavy pack and altitude can all slow you, and none of the rules allows for them. In Pharoah's preprint, for example, a model fitted to GPS tracks put a 20 percent climb about 14 percent slower at 3,000 m than at sea level. When conditions are against you, enter a slower flat speed rather than trusting the default.

When to ignore this calculator

The rules were built for healthy adults walking on footpaths in fair weather. In these cases, plan with more margin or ask a professional first.

• Heart, lung or circulation conditions. A long climb keeps your heart rate up for hours. Check with a doctor before big hiking days, and turn back if you feel chest pain, faintness or breathlessness out of proportion to the effort.
• Pregnancy. Balance and breathing change as pregnancy goes on. Ask your obstetric care team about long or steep hikes.
• Knee, hip or ankle problems. Long descents load the knees most. Our walking vs hiking guide covers what trekking poles do for the knees on the way down.
• Altitude, snow, scrambling or off-trail ground. The rules assume footpaths. Enter a slower flat speed and get local advice on conditions.
• Heat. Pace drops and fluid needs climb. The sweat rate calculator estimates how much fluid you lose per hour from a before-and-after weigh-in.
• Children. The rules and the studies that tested them come from adult walkers. Plan shorter days and more stops with children.

Related reading

References

1. Naismith WW. "Cruach Ardran, Stobinian, and Ben More." Scottish Mountaineering Club Journal. 1892;2. Not openly available online; the rule's wording is quoted in Wood et al. 2023 (reference 4).
2. Tobler W. "Three presentations on geographical analysis and modeling: non-isotropic geographic modeling, speculations on the geometry of geography, and global spatial analysis." Technical Report 93-1. Santa Barbara, CA: National Center for Geographic Information and Analysis; 1993. eScholarship (open access)
3. Langmuir E. Mountaincraft and Leadership. Edinburgh: Scottish Sports Council; 1984. Not openly available online; the corrections are as set out in Campbell et al. 2019 (reference 5) and in reference 7.
4. Wood A, Mackaness W, Simpson TI, Armstrong JD. "Improved prediction of hiking speeds using a data driven approach." PLoS One. 2023;18(12):e0295848. doi:10.1371/journal.pone.0295848, PMC10727444
5. Campbell MJ, Dennison PE, Butler BW, Page WG. "Using crowdsourced fitness tracker data to model the relationship between slope and travel rates." Appl Geogr. 2019;106:93-107. doi:10.1016/j.apgeog.2019.03.008, open accepted manuscript (NSF Public Access Repository)
6. Scarf P. "Route choice in mountain navigation, Naismith's rule, and the equivalence of distance and climb." J Sports Sci. 2007;25(6):719-726. doi:10.1080/02640410600874906, PubMed 17454539
7. Pharoah PDP. "Development and validation of a new walking pace function using crowd-sourced GPS data." bioRxiv preprint, 2017, not peer reviewed. doi:10.1101/188417
8. Murtagh EM, Mair JL, Aguiar E, Tudor-Locke C, Murphy MH. "Outdoor walking speeds of apparently healthy adults: a systematic review and meta-analysis." Sports Med. 2021;51(1):125-141. doi:10.1007/s40279-020-01351-3, PubMed 33030707

How this calculator differs from typical hiking time calculators

Most online hiking time calculators print a single number from one rule, usually a version of Naismith's, with no second method to compare it against and no word on how far the rule misses real hiking times. That leaves you guessing whether the number suits your route and your pace.

This calculator runs Naismith's rule with his original 1892 figures, puts Tobler's hiking function beside it at the route's average grade, and shows what Langmuir's descent corrections change and which band your descents fall in. It scales every figure to your own flat speed using the equivalence of climb and distance that the rule implies, keeps your breaks separate from walking time, and gives the error measured against GPS-tracked hikes, including which way each rule leans on climbs and descents. Every input is checked against realistic ranges, and no estimate appears for an average grade steeper than 50 percent, where hiking turns into scrambling.