VO₂max
VO₂max calculator: beep test, PACER or Cooper
Pick the test, enter your result and your age. For the beep test and the PACER, the calculator applies the equation of Léger and colleagues (1988): VO₂max = 31.025 + 3.238 × S − 3.248 × age + 0.1536 × age × S, where S = 8 + 0.5 × level, with age set to 18 for adults. For the Cooper test it applies the 1968 equation: (distance in metres − 504.9) ÷ 44.73.
On the beep test and the PACER, the equation uses the last level announced by the recording, the one during which you stopped, not the last level you completed. Age plays no part in the Cooper equation.
Your estimate
The two equations, as published
Léger, Mercier, Gadoury and Lambert published the 20 metre shuttle run test and its equation in 1988. The runner stops when they can no longer keep up with the beeps; the number of the last level announced gives a speed, S = 8 + 0.5 × level in km/h. The equation adds age, because a child uses more oxygen than an adult at the same running speed. It was derived from 188 boys and girls aged 8 to 19. In adults aged 18 to 50, the authors showed that the same equation could be used with age held at 18, which is what the calculator does from 18 onwards.
The FitnessGram PACER is run on the same 20 m chart. The calculator finds the level in which your last lap falls, from the site’s chart (7 laps at level 1, then 8, 8, 9…), then applies Léger’s equation to that level. FitnessGram publishes its own estimate, which can give a different figure.
Kenneth Cooper published in 1968 the relationship between the distance run in 12 minutes and VO₂max measured on a treadmill, in US Air Force men. The equation is VO₂max = (distance − 504.9) ÷ 44.73. 2,400 m gives 42.4 ml/min/kg and 2,800 m gives 51.3.
What the figure is worth
It is a statistical estimate, not a laboratory measurement. Each equation was fitted on a specific group, and a real person can sit several ml/min/kg away from it. To follow progress, keep the same test and the same equation from one session to the next. At level 1 the equation counts 8.5 km/h, as in the 1988 protocol, while the site’s 8 km/h chart starts at 8 km/h; from level 2 onwards the speeds are the same.
Further reading
Sources
- Léger L. A., Mercier D., Gadoury C., Lambert J., « The multistage 20 metre shuttle run test for aerobic fitness », Journal of Sports Sciences, 1988; 6(2): 93-101, résumé PubMed — checked 2026-10-11
- Cooper K. H., « A means of assessing maximal oxygen intake: correlation between field and treadmill testing », JAMA, 1968; 203(3): 201-204, via BrianMac Sports Coach — checked 2026-10-11
- Topend Sports, Cooper 12 minute run test — checked 2026-10-11