Altitude Pace Calculator

What this page does

An altitude pace calculator answers one question in two directions. Going up: you know the pace you run at sea level, and you want the pace the same effort is worth at 2,000 m. Coming back: you ran 6:05 per kilometre at 2,000 m, and you want the sea-level equivalent of that run. Both directions are one multiplication by the same factor, and this page prints the factor as well as the pace so the arithmetic is visible rather than hidden behind a number.

The factor is not invented here. Lara B., Salinero J.J. and Del Coso J. (2014) compared marathon finishing times across 16 races held between about 0 and 2,800 m above sea level and reported that each 1,000 m of altitude added 10.8±0.6% to marathon race time in men, with 12.3±0.7% in women, after controlling for ambient temperature, the course's positive cumulative elevation gain and the number of participants. This page applies that measured rate to pace and to time, and prints the altitude, the multiplier, the pace per kilometre, the pace per mile and the marathon time at that pace side by side.

What it is not: an altitude course calculator. A hilly race and a high-altitude race are two different problems, and this site already prices the first one on the race time calculator and the marathon split calculator, which use a published energy-cost model per gradient. This page prices thin air, not gradient. If your race is both high and hilly, the two corrections are separate and neither page does the other one's job.

Everything runs in your browser. Nothing you type is sent to a server, there is no account and no upload, and the numbers never leave the page.

How the numbers are calculated

One rate, one multiplication. Let a be the altitude in metres and k the measured rate of change in race time per 1,000 m. The multiplier is:

m(a) = 1 + k × (a ÷ 1000)    k = 0.108

Because pace is time divided by a fixed distance, the same multiplier applies to pace and to finish time over any one distance. Going up, the altitude pace is p_alt = p_sea × m(a); coming back, the sea-level equivalent is p_sea = p_alt ÷ m(a). The reverse direction is the same equation divided rather than multiplied, which is why a pace that goes up by 21.6% comes back down to exactly where it started.

The rate itself is quoted, not derived. The abstract of the study says, in its own words: “On average, each increase of 1000 meters above sea level augmented marathon race time by 10.8±0.6% in men and 12.3±0.7% in women.” The study took the finishing times of runners placed 21st to 100th in each race, excluded the top 20 in each sex because elite fields cluster at low altitude, and used ambient temperature, positive cumulative elevation gain and field size as control variables. Its correlation between finishing time and race altitude was r = 0.78 for men and r = 0.73 for women, and against the Rotterdam marathon at 0 m the times were significantly higher at every race held above 700 m.

Why one rate for everybody

The study reports two rates. This page applies one, 0.108, to every visitor, because no page on this site converts a result by sex and this page is not going to be the first: a selector that changed the answer depending on who was reading it would be a grading system, and the site's standing position is that it does not ship one. The lower of the two reported rates is the one used, so the penalty printed here is the smaller of the two the study measured. The other number is written above, in the study's own sentence, for anyone who wants to multiply by it by hand. The single rate this page applies is 0.108; the study measured 12.3% in women, higher than that, so for a woman the answer here is the optimistic one — the effect is understated, not overstated, and the pace printed is faster than the study's own rate for women would give.

A worked example: 5:00 per kilometre at 2,000 m

At a = 2,000 m the multiplier is 1 + 0.108 × 2 = 1.216, which is 21.6% more time. A sea-level pace of 5:00 per kilometre is 300 s, so the altitude pace is 300 × 1.216 = 364.8 s, printed 6:05 per kilometre. The same pace per mile is 300 × 1.609344 = 482.80 s at sea level, printed 8:03, and 482.80 × 1.216 = 587.08 s at 2,000 m, printed 9:47. The speed falls from 12.00 km/h to 3600 ÷ 364.8 = 9.87 km/h. A marathon at that pace is 42.195 × 364.8 = 15,392.7 s, printed 4:16:33, against 3:30:58 at sea level.

The reverse: 6:05 per kilometre at 2,000 m is 365 s, and 365 ÷ 1.216 = 300.16 s, printed 5:00 per kilometre. The rounding to whole seconds is why the round trip reads 5:00 rather than 5:00.16 — one rounding, at the end, never halfway through the chain.

• a — altitude above sea level, in metres or feet. 0 to 2,800 m (0 to 9,186 ft).
• k — 0.108, the measured change in marathon race time per 1,000 m of altitude. Lara, Salinero and Del Coso (2014), High Altitude Medicine & Biology 15(1):64–69, DOI 10.1089/ham.2013.1060.
• m(a) — the multiplier. 1.000 at sea level, 1.108 at 1,000 m, 1.216 at 2,000 m, 1.302 at 2,800 m.
• 1,000 m = 3,280.84 ft — from 1 ft = 0.3048 m exactly, a definition.
• Marathon = 42,195 m — the measured race distance, the same number the rest of this site uses.

The table, and how to read it

The table under the tool holds one row every 500 m from sea level to 2,800 m, with the multiplier, the pace per kilometre, the pace per mile and the marathon time at that pace, all built from the sea-level pace you typed. The row nearest your altitude is highlighted, so the table doubles as a way of seeing how fast the penalty accumulates: the first 500 m costs 5.4%, the second 500 m costs another 5.4%, and by 2,800 m the multiplier is 1.302.

Two things about reading it. The multiplier is linear in altitude, which is what the study's single rate implies across the range it measured — it is not a curve, and this page does not add one. And the marathon column is there because the rate was measured on marathon times: it is the one distance where the number on this page and the number in the source are the same quantity, so it is the row to check the page against if you want to verify the arithmetic.

Below 700 m the study found no significant difference from a race at sea level, so the small multipliers in the first two rows are inside the noise of the data rather than a measured penalty. They are printed because the fit covers the whole range, and the page says so rather than hiding the first two rows.

Days at altitude: not modelled

The tool has no input for how many days you have been at altitude, and that is deliberate. The rate comes from race times measured at each city's own altitude; it is a single-day relationship between a race and the altitude of the course, not a time course of acclimatization. To turn days into a percentage you would need a study that measured the same runners repeatedly over the first weeks at altitude and reported the recovery of race performance day by day, and this site has no such source it can point at for a per-day figure.

So the page prints no acclimatization curve, no “day 3 you are at 80%” rule of thumb, and no recommendation about how many days to arrive early. A number invented for that column would look precise and be unfalsifiable, which is worse than an empty column. If you have been at altitude for two weeks and race on day fifteen, this page still returns the same pace for that altitude as it does for someone who landed yesterday — and that limitation is stated here rather than buried.

The sea-level equivalent

The second direction is the one visitors ask for after a trip. You ran 6:05 per kilometre at 2,000 m; what is that worth at sea level? Divide by the multiplier: 365 ÷ 1.216 = 300.16 s, printed 5:00 per kilometre. The number is not a prediction of what you would have run on the day — fitness, weather and the course all move that — it is the conversion of the time you did run into the time the same effort corresponds to at sea level, using the one measured rate.

Switch the direction with the two buttons above the answer, or just type the pace you have. The multiplier is the same in both directions; only the division changes. The table follows the direction too: in the reverse mode its sea-level row is the equivalent you just computed, and the rows above it show what the same run would have been worth at each lower altitude.

Racing at altitude: what the number does and does not say

It says one thing: at this altitude, the same effort is worth this much more time per kilometre, on the average of the races the study measured. It does not say how to pace the race, when to arrive, how to train for it, whether to enter it, or what your result will be. Those are decisions, and this page is a conversion.

It also does not combine with anything else automatically. If the race is high and hilly, the altitude correction and the gradient correction are two separate multiplications done on two different pages, and neither is aware of the other. If the day is hot, that is a third thing and this site does not model it at all. And if the question is what altitude does to a body rather than to a clock — breathing, sleep, headache, altitude illness — this page has nothing to say about it and the contact page says where medical questions belong.

The honest summary: treat the printed pace as the size of the altitude penalty, measured on marathon fields, applied to your pace. Treat everything else about racing up high as outside this page.

Supported range and limits

• Altitude: 0 to 2,800 m, or 0 to 9,186 ft. 2,800 m is the highest race in the study; above it the page refuses and says so instead of extrapolating the line.
• Pace: 2:00 to 20:00 per kilometre, or 3:13 to 32:11 per mile — the same range expressed in either unit. Typed as minutes and seconds.
• Direction: sea level to altitude, or altitude to sea level. One multiplier, applied or divided.
• Rounding: paces and times to the nearest second, the multiplier to three decimals, the change to one decimal. One rounding, at the end.
• Not a curve: the multiplier is linear in altitude because the rate is a single number per 1,000 m. No page on this site has a source for a curvature term, so none is added.
• Cost: none. No account, no email, no paywall, no request to a server.
• Privacy: every number is computed in your browser. Nothing you type is sent anywhere or stored — reload the page and it is gone.

What this page deliberately does not do

• No gradient or course-profile correction. A climb is not thin air. The race time calculator and the marathon split calculator price a course's own elevation with a published energy-cost model; this page does not touch that number and does not borrow that model.
• No acclimatization curve. No days-at-altitude input, no per-day percentage, no advice on when to arrive. There is no per-day source behind it, so there is no column for it.
• No sex split and no age grading. The study reports two rates; this page applies one to everybody and prints the other as a quotation. It does not grade your time, and it has no age-group table.
• No weather correction. Temperature, humidity and wind all move race times and none of them is priced here. That is a standing position across the site, not a gap on this page alone.
• No prediction from a previous race. Converting a pace between two altitudes is not the same as predicting a finish time. The predictor is the race time predictor on the home page.
• No race presets. There is no dropdown of real races and their altitudes, because a list like that would need a measured altitude for every course and would go stale. The altitude box is yours to fill.
• No medical content. Altitude illness, breathing, sleep and everything else about what altitude does to a body are outside this page and outside this site.
• No extrapolation past 2,800 m or below sea level. Both are refused with a message rather than clamped silently.

Questions