VO2max: definition, formula, example

VO2max is the highest rate at which you can take oxygen from the air and use it in your muscles. It is measured in litres per minute, or more usefully for runners in millilitres per kilogram per minute, since a heavier body costs more to carry. A. V. Hill described the plateau of oxygen uptake in the 1920s, and VO2max has been the headline number of endurance physiology ever since. It sets the size of your aerobic engine. It does not, on its own, decide how fast you race.

What sets VO2max: the Fick equation

Oxygen uptake is the product of how much blood the heart pumps and how much oxygen the muscles extract from it:

At maximal effort, extraction differs less between trained and untrained people than cardiac output does, and maximum heart rate does not rise with training. What separates a 40 from a 70 is mostly stroke volume, the amount of blood pushed out at each beat, which is why Bassett and Howley (2000) conclude that in trained athletes VO2max is limited mainly by oxygen delivery rather than by the muscles.

How it is measured or estimated

The reference is a lab test: an incremental run on a treadmill with a mask that analyses the air you breathe, until oxygen uptake stops rising despite a higher speed. Everything else is an estimate:

• The Cooper test (Cooper, 1968): distance run in 12 minutes, then VO2max = (distance in metres − 504.9) / 44.73.
• The heart rate ratio (Uth et al., 2004): VO2max ≈ 15.3 × HRmax / HRrest. Quick, but it needs a real maximum heart rate and ignores how fast you actually run.
• Race performance: Daniels’ VDOT turns a race time into an “effective” VO2max that includes your economy.
• Watches: Garmin, Polar, COROS and others estimate it from heart rate against pace or power during runs, with models they do not fully publish.

A worked example

Take a runner who covers 2,900 m in the Cooper test, has a resting heart rate of 48 and a maximum of 188, and recently ran a 10K in 45:00.

• Cooper: (2,900 − 504.9) / 44.73 = 53.5 ml/kg/min
• Heart rate ratio: 15.3 × 188 / 48 = 59.9 ml/kg/min
• VDOT from the 10K: 45.3

Three numbers from 45 to 60 for the same person. None is wrong; they measure different things. The ratio method looks only at the heart, the Cooper test at a 12-minute effort, VDOT at what the runner actually produces over 45 minutes. A gap like this usually says the runner has a decent engine and room to improve economy and endurance.

For the lab version, plug in plausible values: a cardiac output of 25 litres per minute and an extraction of 160 ml of oxygen per litre of blood give 4,000 ml/min, or 57 ml/kg/min for a 70 kg runner.

VO2max, VMA and running economy

On flat ground, running costs roughly 3.5 ml/kg/min of oxygen for each km/h of speed (Léger and Mercier, 1984). Divide VO2max by that cost and you get an approximate VMA (maximal aerobic speed): 53.5 / 3.5 ≈ 15.3 km/h, close to the 15 km/h this runner gets from a 6-minute test. A runner who uses less oxygen per km/h, the more economical one, reaches a higher speed with the same VO2max. Joyner and Coyle (2008) describe endurance performance as three factors working together: VO2max, the fraction of it you can sustain (linked to lactate threshold) and economy.

How to use it in training

VO2max responds to work close to it: 4 to 6 repetitions of 3 to 5 minutes at 95 to 100% of VMA, with recoveries of about the same length, or shorter formats like 30/30. It also rises with easy volume, through a bigger stroke volume. For setting paces, VMA and VDOT are more practical, since they are speeds. In OpenAthlete, VO2max is a metric that can be imported from Garmin, Polar or COROS or entered by hand, and you can follow it on the metrics page next to HRV and resting heart rate. The VMA calculator gives you the paces.

Limits

Among runners of a similar level, VO2max predicts race results poorly: economy and sustainable fraction matter as much. Watch values move with heat, hills, fatigue and a wrong maximum heart rate, so read them as a trend over weeks. Genetics set a large part of the ceiling, and gains slow down after the first years of training, while threshold and economy can keep improving for a long time.