The rule this page uses, named plainly
This is Naismith's rule, published by the Scottish mountaineer William W. Naismith in 1892 in the Scottish Mountaineering Club Journal. In its original metric-adjacent form it allows one hour for every three miles on the map plus one hour for every 2,000 feet of ascent. The metric restatement in common use is 5 km/h on the flat plus one hour per 600 m of climb, and the two are the same rule: 600 m is 1,969 ft and 5 km/h is 3.11 mph.
The insight worth keeping is the exchange rate. Naismith says 2,000 feet of climbing costs the same time as three miles of flat walking. That ratio is what turns a "it's only four miles" trail description into an honest six-hour day, and it is why elevation profile matters more than mileage when you are reading a guidebook.
This calculator scales both terms down, because 3 mph plus 2,000 ft per hour is a fit Victorian mountaineer on Scottish hills with a light load, and it is optimistic for most people carrying a day pack. The three fitness settings run 1.9 mph with 1,000 ft/hr, 2.5 mph with 1,300 ft/hr, and 3.1 mph with 1,800 ft/hr. The middle one is the most commonly realistic for someone who hikes regularly but not weekly. The line labelled "Naismith as published" shows the unscaled original so you can see how far the adjustment moved things.
Naismith is not Tobler, and neither is a physics model
Tobler's hiking function is frequently cited in the same breath and is a genuinely different model. Waldo Tobler proposed it in 1993 for GIS work: walking speed equals 6 times the exponential of negative 3.5 times the absolute value of slope plus 0.05, giving speed directly as a smooth function of grade, with a peak of about 6 km/h at a slight downhill of roughly negative 3 percent. It was fitted to Eduard Imhof's Swiss survey data, it is continuous rather than additive, and it explicitly models descent as sometimes faster than flat.
The two disagree, and neither is the truth. Naismith is additive and gives descent nothing at all in its original form, which is why corrections exist — Langmuir's amendment subtracts ten minutes per 300 m for gentle descent and adds ten minutes per 300 m for steep descent; Tranter's corrections table adjusts the whole result for fitness and fatigue; Scarf proposed an equivalence distance formulation. This page uses Naismith with a Tranter-style descent penalty because the additive form is easier to reason about and the failure modes are transparent.
What no version models: pack weight, which measurably slows ascent once it exceeds roughly a tenth of body weight; terrain quality, where boulder fields, scree, blowdown and mud can double the horizontal term while the map distance stays identical; snow, where postholing can reduce a 2.5 mph hiker to under 1 mph; altitude, where anything above about 8,000 feet begins to cost aerobic capacity; heat and humidity; group size, which sets the pace to the slowest member and adds a stop every time anyone needs one; and darkness. A 30 percent error either way is normal and 100 percent is possible on genuinely bad ground.
Descent is not free, and this is the part people get hurt on
The intuition that coming down is quick is only true on moderate grades on good trail. Steep descent is slow because you are braking — eccentric muscle contraction, which produces more muscle damage than the equivalent uphill work and generates joint loads at the knee substantially higher than level walking. On sustained steep ground, descent speed falls toward ascent speed, and for a tired hiker on loose rock it can be slower.
It is also where the accidents are. Accident statistics from mountain rescue organisations consistently show descent overrepresented in injury reports: fatigue is highest, light is lowest, the hard part feels finished, and slips are downhill. The calculator's descent figure adds thirty minutes per thousand metres of drop on top of a faster flat rate for exactly this reason, and if your knees are a known issue you should treat that as a floor.
Cumulative gain, not summit minus trailhead
The elevation field wants total ascent over the whole route, which on rolling ground is substantially more than the difference between the trailhead and the high point. A ridge trail that drops into three saddles on the way to a summit can carry 30 to 50 percent more cumulative gain than the endpoints imply, and Naismith charges you for every foot of it. Get the figure from the trail description, from a GPX file, or from a mapping tool's elevation profile rather than subtracting two numbers off a topo.
Be aware that GPS-recorded cumulative gain is noisy and usually runs high, because barometric and satellite altitude both wander and the recording sums every wobble. Published route figures from a guidebook are generally more trustworthy than a watch total for planning purposes, even though the watch total is what you will see afterwards.
Turnaround time is the number that keeps you alive
The output that matters most on this page is not the round-trip estimate; it is the latest start. Reverse it into a turnaround time: pick the clock time at which you head back regardless of how close the summit looks, set it before you leave, and hold it. Overdue-hiker callouts overwhelmingly involve people who were an hour short of the top with two hours of daylight left and did the arithmetic optimistically.
Build the margin explicitly. The table assumes you are down one hour before sunset; under forest canopy, in a north-facing valley, or in winter, useful light ends well before that. Carry a headlamp on every hike including the short ones, tell someone your route and your expected return, and treat this calculator's number as the best case for the conditions you are imagining rather than the conditions you will find.
Questions people ask
Which rule does this use, exactly?
Naismith’s rule from 1892: three miles per hour on the flat, plus one hour for every 2,000 feet of ascent. The metric original was 5 km/h plus one hour per 600 m, which is the same thing. The flat rate and the climbing rate are both scaled down here by fitness setting because the published figures assume a fit hiker with a light load. A Tranter-style descent penalty of thirty minutes per 1,000 m of drop is added on top of a faster flat rate for the way back, and a rest multiplier is applied to the whole thing.
Why does it differ from Tobler’s hiking function?
Because they are different models built for different purposes. Naismith is additive — a flat time plus a climbing time — and was written for route planning by hand. Tobler’s function is an exponential curve giving speed as a continuous function of slope, fitted to Swiss survey data for use in GIS least-cost path analysis, and it peaks at a slight downhill grade rather than on the flat. On a steady moderate climb they land in the same neighbourhood; on rolling terrain and on descent they diverge noticeably. Neither is validated as a personal predictor, and both ignore pack, surface and weather entirely.
How much does pack weight change this?
Enough to matter and not enough to be predictable. The load-carriage literature broadly finds that energy cost rises roughly in proportion to total carried mass, with penalties growing faster once the load exceeds about a fifth of body weight, and that the effect is worse uphill than on the flat. In practical terms, a heavy overnight pack can push a hiker a full fitness setting down on this page. If you are carrying more than about a fifth of your body weight, select the lowest setting regardless of your actual fitness.
Why is my mapping app’s estimate different?
Different apps use different models and most do not tell you which. Some use a flat average speed with weak or no elevation weighting, which produces wildly optimistic times on steep ground. Some use Tobler, some use Naismith with corrections, and some use crowd-sourced actual times from other users’ recorded tracks — that last kind is often the most accurate for popular trails and the least accurate for obscure ones. The most useful calibration is your own: after two or three hikes, compare your real moving time to this page’s estimate and note the ratio. That personal multiplier will beat any published model.