How it works
VO2 max is the most oxygen your body can use per minute, per kilogram of body weight. Labs measure it with a mask on a treadmill. This calculator estimates it from a race instead, using equations that exercise physiologist Jack Daniels and Jimmy Gilbert published in 1979. The same equations sit behind the pace tables in Daniels’ Running Formula.
It works in two steps:
- Oxygen cost. The faster you run, the more oxygen each minute costs. The first equation turns your race speed into that cost.
- Share of your maximum. You can hold close to your maximum for a few minutes, but less for an hour or more. The second equation estimates the share you held for a race of your duration.
Dividing the cost by the share gives the estimate. The equivalent times come from running the same equations backwards for other distances.
The formula
v = distance (m) ÷ time (min)
cost = −4.60 + 0.182258 × v + 0.000104 × v²
share = 0.8 + 0.1894393 × e^(−0.012778 × t) + 0.2989558 × e^(−0.1932605 × t)
VO2max = cost ÷ share
t = race time in minutes, results in ml/kg/minWorked example
A 5K in 25:00.
- Speed: 5000 m ÷ 25 min = 200 m per minute.
- Oxygen cost: −4.60 + 0.182258 × 200 + 0.000104 × 200² = 36.01 ml/kg/min.
- Share held for 25 minutes: 0.8 + 0.1894 × 0.7265 + 0.2990 × 0.0080 = 0.940, or 94.0%.
- Estimate: 36.01 ÷ 0.940 = 38.3 ml/kg/min.
At that level, the equivalent 10K is 51:53 and the equivalent half marathon is 1:55:04.
Questions
Is this my real VO2 max?
It is an estimate from performance. A lab test measures the oxygen you use directly. A race also depends on running economy, pacing and conditions, so two runners with the same lab VO2 max can race differently. The race-based number is useful for tracking your own fitness over time.
Why does my watch show a different number?
Watches estimate VO2 max from heart rate and pace during training runs, using their own models. They often disagree with race-based estimates by a few points. Compare numbers from the same source over time rather than across sources.
What counts as a good VO2 max?
It depends a lot on age and sex, and published norms vary between studies. The most useful comparison is with your own earlier results: if the number climbs after a training block, your fitness improved.
Why are the equivalent times a few seconds off Daniels’ tables?
The times here come straight from the equations. Daniels’ printed tables were prepared from the same model but round and smooth some values, so they can differ by a few seconds, a little more in the marathon.
Which race gives the best estimate?
A recent all-out effort on a flat, accurately measured course in mild weather. Races from 5K to the half marathon are a good middle ground. Heat, hills and poor pacing all pull the estimate down.
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Sources
- Daniels J, Gilbert J. Oxygen Power: Performance Tables for Distance Runners. Tempe, AZ; 1979.
- Daniels J. Daniels’ Running Formula. 3rd ed. Human Kinetics; 2014.