The model: the Naismith rule made honest

In 1892 the Scottish mountaineer William Naismith noted a rule that hut wardens still use: one hour per five kilometres on the flat, plus one hour per six hundred metres of climb. This calculator makes it parametric and honest: the flat speed is not fixed at five kilometres per hour — you choose it, from the quiet pace to the brisk march — and the climb penalty stays the classic one, ten minutes per hundred metres of ascent. The walking time is the sum of the two pieces; breaks are added as a percentage, because in reality nobody walks eight hours without stopping.

The result is four numbers: the total time with breaks (the one to compare with the daylight hours), the walking-only time, the equivalent kilometres — the distance the legs will "feel" — and the climb share of the time, the dimensionless number that says what kind of day awaits you.

The four knobs: distance, ascent, pace and breaks

The distance runs from 2 to 30 kilometres: from the lakeside stroll to the long trek. The total ascent runs from 0 to 2000 metres in steps of 100 — only the climb counts: the classic rule treats the descent as flat ground, and that is the model's first declared limit. The flat speed is set in tenths of a kilometre per hour, from 30 to 60 (that is, 3 to 6 km/h): 35-40 is the relaxed pace, 45 the standard hiking pace, 55-60 the trained march. The breaks run from 0 to 30 percent of the walking time: ten percent is the physiological stop, thirty is the contemplative day with a packed lunch.

The distance scale: from two hours to the full day

Eight hundred metres of climb, standard pace of 4.5 km/h, breaks at ten percent; only the distance changes:

The table tells two stories at once. The time grows row by row, as expected; but the climb share falls — from sixty percent of the straight climb to seventeen of the trek — because the same eight hundred metres always weigh eighty minutes, while the flat stretches out. And the last row deserves a note: 528 minutes are almost nine hours — the thirty-kilometre trek with real ascent is already beyond the full-day threshold, and is planned as such.

Naismith's equivalence: a hundred metres are worth a kilometre

With the penalty of ten minutes per hundred metres and the reference pace, the rule's algebra produces an elegant equivalence: every hundred metres of climb cost as much as one kilometre on the flat. That is the meaning of the equivalent kilometres: twelve kilometres with eight hundred metres of ascent "weigh" like twenty flat kilometres. It is the most useful number to give whoever stays in the valley, and the most honest to compare with your own experience: if your twenty flat kilometres are a demanding but feasible walk, this route will be just as much.

The climb share: the column that ignores the breaks

The fourth number is the day's character: how much of the walking time is written by the ascent. It has a property the calculator stages: it is identical with any percentage of breaks — the stops stretch the flat and the climb in the same ratio, and the share does not notice. You can go from the stop-free march to the contemplative day: the total time changes, the route's character does not. It is the proof that breaks and gradient are two independent decisions: one is negotiated with the clock, the other with the mountain.

The fast walker's paradox

The model's most counterintuitive property: the faster you walk, the higher the climb share. At 3 km/h the example's climb writes twenty-five percent of the time; at 6 km/h it writes forty. The reason is physical, not arithmetic: flat speed shortens the flat, but a hundred metres of ascent cost ten minutes to anyone — the climb is the great leveller. That is why trained walkers "feel" the mountain more than beginners in proportion to their time: their flat is fast, their climb is not.

The full day: the eight-hour threshold

The verdict flags when the total time goes beyond 480 minutes: eight hours, the full day. It is not an arbitrary threshold: it is the perimeter of the useful daylight hours in mid-season, minus the dawn and dusk margins. Beyond that line the walk changes category — you leave at dawn, the headlamp enters the pack not as a scruple but as a tool, and the backup plan (the turn-back point, the short variant) is written before leaving, not improvised on the trail.

From the valley floor to the scramble: the four readings

The calculator classifies the route by the climb share. Below fifteen percent it is the valley floor: the pace writes the time, the estimate is the most reliable. Between fifteen and thirty it is the climb that accompanies: felt, not commanding — the classic hike. Between thirty and fifty it is the real mountain: the route is planned on the ascent, not the distance. Beyond fifty it is the scramble: the horizontal kilometres are a detail and the prudence on the estimate doubles, because that is precisely where Naismith is most optimistic.

The model's limits: what Naismith does not see

The rule is a planning estimate, not a stopwatch. It does not see the terrain: boulder fields, cabled sections and snow slow you down more than any gradient. It does not see the steep descent, which below a certain gradient costs time instead of giving it. It does not see altitude: above 2500 metres the breath shortens the stride even for the fittest. And it does not see the pack, the heat, the group moving at the slowest member's pace. The honest way to use it: the estimate is the reasonable minimum in normal conditions — on technical ground you add margin, you do not remove it.

The ascent scale: from the lakeside to the scramble

Twelve kilometres, pace of 4.5 km/h, breaks at ten percent; only the ascent changes:

The scale crosses all four readings of the model: from the valley floor at zero ascent to the scramble beyond fifty percent. And it shows the most useful progression to memorise: every extra five hundred metres of ascent are worth about an extra hour on the total — fifty minutes of climb plus the breaks' tail. The distance has not changed by a metre, yet between the first and the last row run three hours and forty minutes: it is the ascent, not the mileage, the first question to ask about an unknown route.

The speed scale: the paradox in five rows

Same route — twelve kilometres, eight hundred metres, breaks at ten percent — and five different paces:

The time falls row by row — from the quiet pace to the march you save more than two hours — but the climb share walks the opposite way: from twenty-five to forty percent. It is the fast walker's paradox turned into a table: doubling the speed halves the flat, but the eighty minutes of climb stay eighty for everyone. The practical consequence for pace training: the real gain is made on flat outings; on serious climbs, the fast walker's advantage thins out almost to nothing.

The breaks: the knob that stretches without changing

The model's third scale is a demonstration of independence: on the standard route, going from zero stops to thirty percent, the total runs from 240 to 312 minutes — more than an hour of difference — while the climb share stays nailed at 33.3 percent in all four rows. Breaks stretch the flat and the climb in the same ratio, and the route's character does not notice. The planning lesson is clean: stops are negotiated with the clock and the group, gradient is negotiated with training — and confusing them is the classic mistake of those who cut breaks to "make up time" on a route that was simply too long.

The grid's extremes: from twenty minutes to seventeen hours

The model's minimum — two flat kilometres at marching pace, no stops — closes at 20 minutes: the pier walk, the warm-up. The maximum — thirty kilometres with two thousand metres of climb, at the quiet pace and with contemplative breaks — closes at 1040 minutes: seventeen hours and twenty, a march no single day contains and that the model classifies, correctly, as an undertaking to split into two stages. And the maximum hides a subtlety: its climb share is only 25 percent — the band of the climb that accompanies, not of the scramble — because over thirty slow kilometres it is the flat that dominates the time. The grid's longest route is not its most vertical: hardness and character are two different axes, and that is why the calculator measures them with two different numbers.

The equivalence in practice: the route in a single number

Of the four outputs, the equivalent kilometres are the one born to be communicated. "Twenty equivalent kilometres" tells whoever stays in the valley, the friend deciding whether to come, the group discussing the plan, everything needed: what the route costs the legs, in a unit everyone owns — their own experience on flat routes. It also works in reverse, as an honesty filter on other people's route descriptions: an itinerary sold as "only twelve kilometres" with eight hundred metres of ascent is, in equivalents, a twenty-kilometre outing — and whoever tells it without the ascent is telling little more than half the route.

The planning walker's strategies

Four concrete moves follow from the model. Ask for the ascent first, the kilometres second: it is the climb that decides the route's character, and the ascent table shows it at constant distance. Measure your pace once, honestly: one timed hour on the flat with the pack is worth more than any optimistic guess — and it is the model's only personal input. Compare the total with the daylight hours, not with the enthusiasm: the eight-hour threshold does not reward keenness, it rewards those who leave at dawn. And add margin where the model is blind: technical terrain, altitude, steep descents and large groups are not in the count — the estimate is the reasonable minimum, and in the mountains you always round in the direction of prudence.

Frequently asked questions

What is the Naismith rule?

It is the empirical rule noted in 1892 by the Scottish mountaineer William Naismith: one hour per five kilometres on the flat plus one hour per six hundred metres of climb. This calculator uses it in parametric form: flat speed of your choice and ten minutes per hundred metres of ascent.

Why is the speed set in tenths of km/h?

To get fine steps without decimals in the input: 45 means 4.5 km/h. The scale runs from 30 (quiet pace, 3 km/h) to 60 (trained march, 6 km/h), in steps of 5, that is, half a kilometre per hour.

What are the equivalent kilometres?

The flat distance that would cost the same walking time: every hundred metres of climb are worth one kilometre on the flat. Twelve kilometres with eight hundred metres of ascent weigh like twenty flat kilometres — the right number to compare with your own experience.

What does the climb share of the time measure?

The percentage of the walking time written by the ascent. Below 15 percent it is a valley outing, between 15 and 30 the climb accompanies, between 30 and 50 it is real mountain, beyond 50 it is a scramble with some walking around it.

Why does the climb share not change with the breaks?

Because breaks stretch the flat time and the climb time in the same ratio: their proportion stays identical. The stops change how long the day lasts, not what character the route has.

Why does the climb share increase when walking faster?

It is the fast walker's paradox: speed shortens only the flat, while a hundred metres of ascent cost ten minutes to anyone. At 3 km/h the example's climb writes 25 percent of the time, at 6 km/h it writes 40: the climb is the great leveller of paces.

Does the descent count for nothing?

In the classic rule the moderate descent is walked at the flat pace, so it is already inside the distance. Steep descents, which actually slow you down, are one of the model's declared limits: on those routes the estimate should be read as a minimum and margin should be added.

When does the full-day warning trigger?

When the total time with breaks reaches 480 minutes, that is, eight hours. It is the perimeter of the useful daylight hours in mid-season: beyond that threshold you leave at dawn, the headlamp enters the pack and the backup plan is written before leaving.

Does the estimate hold with a heavy pack or at altitude?

The rule does not see pack, altitude or technical terrain. Above 2500 metres, with heavy loads or on boulder fields and cabled sections, the estimate should be read as a reasonable minimum and the margin is added, not removed.

How do I choose my flat speed?

With an honest test: time one hour of walking on flat terrain at the pace you actually keep on a hike, pack included. Most hikers sit between 40 and 50 tenths (4-5 km/h); 55-60 is a trained walker's pace.

How realistic are breaks at 10 percent?

They are the minimal physiological stop: water, photos, layers. With a packed lunch you go up to 20, with a contemplative day or a large group to 30. The choice does not change the route's character, only the return time.

Does the calculator work for mountain running?

No: the Naismith rule describes the hiking pace. Uphill running has different economies (lower climb/flat ratio, descents that are run) and uses its own models such as grade adjusted pace. Here the perimeter is walking, from 3 to 6 km/h.

Updated July 2026