Altitude-adjusted pace

How to use

This calculator allows you to estimate an “altitude-adjusted pace” for workouts and races at various elevations above sea level. To use the calculator, you need three things:

1. A recent race performance, or a training pace (e.g. your threshold pace)
2. The altitude where you ran that performance
3. Your home altitude (which may or may not be sea level)

By default, the calculator is set up to calculate the sea-level equivalent for a 5k race run at 5,000 feet above sea level, for a sea-level resident, but all of these parameters are adjustable.

You can enter a performance as a race result (18:40 for 5k) or a pace (6:00/mi pace for 5k); the button swaps between the two modes. Training paces are always entered as a pace, though you can select the units (/mi, /km, /400m, /200m) as you prefer.

Pace/result mode versus effort mode

There are two ways to use the calculator. First, pace/result mode: you can take a known performance at altitude, and convert it to its sea-level or home-altitude equivalent.

Pace/result mode is useful when you have already been training and racing at altitude, and you want to know what you should expect at sea level (or some other altitude). For example:

18:40 for 5k at an altitude of 5,000 ft, for an athlete living at 4,000 ft, is the same effort as 17:55 at sea level.

Second, in effort mode, you can take your home-altitude effort, and use it to predict what you will run at some other altitude. This is useful when, for example, you live and train at sea level, and are going to race at altitude and want to know what pace your usual effort will produce:

An 18:40 sea-level effort for 5k, when running at an altitude of 5,000 ft, results in a time of 19:34 for an athlete living at sea level.

Acclimation and training at altitude

After traveling to a new altitude, your body adapts over a period of several weeks. This adaptation process reduces, but never eliminates, the negative effects of altitude on performance.

This calculator accounts for acclimation by allowing you to specify your home altitude—which might be the same as the altitude you competed at. For example, if you want to run 16:00 for 5k in Boulder, Colorado (5,400 ft / 1,650 m) and you live at sea level, you need to be in 15:11 sea-level 5k fitness to do it. However, an athlete who lives and trains in Boulder only needs to be in 15:20 sea-level 5k fitness to run 16:00 in Boulder, because they are less severely affected by the altitude.

For altitude residents, you can also calculate your performance equivalent at any other elevation, using the Other home-altitude option. For example, maybe you live and train in Boulder, but you want to know what your training pace should be in Flagstaff (7,000 ft / 2,100 m) in the first few weeks after you arrive. Continuing our example above, the 16:00 5k runner in Boulder would only run about 16:21 in Flagstaff soon after arrival.

The same technique works for racing at a lower, but not-quite-sea-level, altitude.

One note: acclimation to altitude takes at least three to four weeks. So far, this calculator does not model the partial acclimation that occurs in the first several days at altitude—it assumes you are fully adapted to your home altitude, and assumes that the “new” altitude you are running or competing at is fairly early on in the adaptation period—roughly within the first few days. See the limitations section for more.

How this calculator works

Running performances are slower at altitude because of the lower oxygen availability at high elevations. This reduction in oxygen availability hampers your body’s ability to produce energy aerobically, so your VO2max goes down and so does your performance in middle- and long-distance events.

There are two ways to estimate how the lack of oxygen affects running performance: the first way is to measure how VO2max changes at different altitudes using experimental data, then predict performance changes from VO2max. The second is to directly look at how performance changes in athletes who live at one altitude but race at another. The statistical model that powers this calculator uses the latter approach.

Under the hood, the calculator relies on a statistical model fit to a large dataset of track performances across many different altitudes and events, for athletes who live and train at a wide variety of altitudes. In effect, every time an athlete races at an altitude that is different from the altitude they live at, we have a natural experiment, and we can examine how much they slow down or speed up.

The model has two parts: first, it calculates the “full-size” penalty of altitude for an athlete who lives at sea level. Then, if the athlete is a resident of another altitude, it calculates the “discount” that gets applied to the altitude penalty as a result of the athlete’s home-altitude acclimation. These calculations can be run forward or in reverse, which is how the pace and effort modes work.

The altitude penalty for a sea-level resident looks like this:

And the discount looks like this (shown for racing a 5k at a given elevation, for a sea-level athlete versus an athlete who lives and trains at the same altitude as the race):

As you can see, the practical impact of being acclimated to a given altitude increases markedly as the elevation of the event goes up.

Notably, the statistical model powering this calculator is built so that it factors out the effects of heat, humidity, wind speed, and track geometry (e.g. a 200m banked indoor track is faster than a 200m flat track at the same altitude). The calculator itself does not adjust for any of these factors—it assumes conditions are otherwise identical (same weather, same surface, etc.).

Half marathon, marathon, and training paces

So far, I do not have a large, reliable dataset on marathon and half marathon times at various altitudes (though I am working on it!). So, when you calculate marathon and half marathon paces, the calculator applies the same percentage slowdown that it applies to the 10k.

This assumption is not as implausible as it sounds: long track events are already so aerobically dominated that the altitude effects at 10k are practically indistinguishable from the effects at 5k and even 3k, so I think the effects will be fairly comparable (especially for the half marathon). Still, the calculator pops up a warning to let you know that you are beyond the distances this model was built on.

Training paces carry a similar caveat: all performances used to power this model are maximal effort performances; there is some scientific data to suggest that submaximal performances may not be affected as badly as an all-out effort. For easy run paces, threshold workouts, and the like, you may find that this calculator is too conservative (i.e. it predicts an altitude pace somewhat slower than you can actually run).

Limitations

By far the biggest limitation of this calculator is the fact that individual responses to altitude can vary significantly according to your physiology. This calculator predicts how an average runner will run at a given altitude. You, in particular, may run faster or slower than average.

This calculator estimates how your race or workout would have unfolded at a different altitude, all else equal (weather, surface, etc.). Often, all else is not equal; for example, one reason why Boulder, Flagstaff, Iten, and other altitude training locations are so popular is that they have excellent weather for much of the year (Flagstaff is quite nice for training in July; Texas, not so much). A race at altitude might go better than expected simply because the cool, dry air is more conducive to performance.

As noted earlier, the transition from “new to altitude” to “fully adapted” is gradual, and is not accounted for in this calculator (in this app you are either “new” to any altitude other than your home altitude, or you are “fully adapted,” never halfway in between).

Very high altitudes

In the data I used to build this calculator, there are not very many competitions with recorded performances at altitudes above about 7,200 ft (2,200 m). Doubly so for sea-level athletes competing that high. So, for altitudes above 8,000 ft or 2,400 m, the calculator will show an alert to inform you that you are beyond the range of the data. I expect the calculator to perform reasonably well up to about 8,000 ft (2,400 m) or so, but above that it just extrapolates in a straight line—all bets are off if we’re talking 10,000+ ft (3,000+ m) elevation.

Middle-distance races

One thing you might notice is that if you run a 400m race at moderate altitude, the calculator predicts you can go a little faster! That’s because the lower air pressure slightly reduces drag forces, which play a much bigger role in performance at high speeds. Interestingly, this effect works against you at very high altitudes, and 400m gets slower again (perhaps because the aerobic contribution to the event starts getting severely hampered at very high elevations).

For 800m, altitude’s effects are small, but negative (on average). The calculator does not take the absolute speed into account, so it may well be that extremely fast 800m times are not affected very much at all (because of the air resistance component), while slower typical 800m times are affected more.

In general, though, I expect results for middle-distance races to be less precise than for longer distance races, because of the individual variation in aerobic and anaerobic energy contributions to those race distances. Something like the 3k, in contrast, is so aerobically dominated that the effects of altitude are more stable.

How this calculator compares to the NCAA altitude conversions

The now-retired NCAA altitude conversion factors were developed in the 1980s by Dr. Bill Adams, a physiology researcher at UC Davis. For a long time, they were used to give a “bonus” to performances run at altitude, for the purposes of determining who could run at various championship meets.

The underlying formula was a simple quadratic function, with different coefficients for each event (800m, 1500m/mile, etc.) that was only applied at elevations above 3,000 feet above sea level.

The NCAA factors are somewhat more conservative than my altitude-adjusted pace calculator, especially at 3k and 5k (shown here at 5,400 ft (1,650 m), which is the elevation of Boulder, Colorado):

There were a few issues with the old NCAA conversion factors. Aside from the implausible 3,000-foot threshold, the underlying quadratic function implied nonphysiologic values: if you extrapolated the trend down to sea level, you would get “faster than sea level” results! Additionally—and this was by design—they didn’t account for where an athlete lived, so they weren’t that helpful for predicting what a sea-level native would run at altitude.

Here are a few examples of how my calculator differs from the old NCAA conversion factors, for an athlete living at the same altitude as the race.

At 5k, the differences are most stark, with my calculator being consistently more generous:

At one mile, you actually see the two conversions converge at high altitudes—in Flagstaff, AZ (7,000 ft / 2,100 m) they are nearly the same.

And the same thing happens at 10k:

While these similarities and differences are a useful cross-check of the model, I would not recommend using my altitude-adjusted calculator as a tool for determining who gets to run at various championship meets—such a decision requires a consideration of many factors beyond just the physiology of altitude.

Calculator settings

This calculator will remember your race time or pace, the race distance, the pace-versus-effort switch, and your altitude settings in your browser’s local storage, so when you come back later you can pick up where you left off. You can reset everything to the defaults using the button, and turn off remembering with the “Remember settings” switch.

Support my work

If you want to find out when I have new apps and research coming out, sign up for my email list below! It's the best way to follow my work. I have several major projects coming out soon that you won't want to miss.

If you're training for the marathon, be sure to check out my new book, Marathon Excellence for Everyone. It covers the modern approach to marathon training, including training plans, racing strategies, and the latest science on training.

If you live outside of the United States, there is also a Metric Edition of Marathon Excellence available, with all workouts and paces in kilometers!

If you want to learn more about the science of running, you can also check out my first book, Modern Training and Physiology - it covers a scientific approach to training for events from 800m to the 10k. It's available on Amazon as both an eBook and paperback.

This app is 100% free. If you find it useful, you can share it with your friends or post about it on social media. I also offer coaching services for those interested.

Contact

If you've got feedback on this web app, or if you've found a bug, please reach out! You can reach me at john@runningwritings.com.

I'm also on Instagram and on X, but the best way to follow my work is my email list!