VO₂max Calculator

How VO₂max is estimated

Every method here answers the same question — how much oxygen your body can take in and use per minute at full effort — and none of them measures it. Measuring means a mask, a gas analyser and a test to exhaustion. A calculator infers the number from something you can do on a track, and each method infers it in its own way.

VO₂ = −4.60 + 0.182258 × v + 0.000104 × v² — Daniels and Gilbert, v in metres per minute

%VO₂max = 0.8 + 0.1894393 × e^(−0.012778 × t) + 0.2989558 × e^(−0.1932605 × t) — t in minutes

The first equation gives the oxygen cost of running at a given speed; the quadratic term is why running faster costs disproportionately more. The second gives the fraction of your maximum you can hold for a given duration — close to 1 over three minutes, around 0.8 over a marathon. Dividing the first by the second gives VDOT, the number Jack Daniels built his training tables on. Strictly it is not VO₂max but a pseudo-VO₂max with running economy folded in. For a runner that is a feature: two people with identical laboratory VO₂max but different economy race differently, and VDOT already knows it.

VO₂max = (distance in metres − 504.9) / 44.73 — Cooper 12-minute test

VO₂max = 483 / time in minutes + 3.5 — 2.4 km (1.5 mile) test

Both are linear regressions that Kenneth Cooper fitted in 1968 by testing 115 US Air Force personnel on a laboratory treadmill and then in the field. The correlation was high (r ≈ 0.90) but the standard error is about 3–3.5 ml/kg/min: two runners in three land within ±3 of their true value, and one in twenty is out by 6 or more. Pacing matters enormously — a test run too fast for the first four minutes reads several units low.

VO₂max ≈ 15.3 × HRmax / HRrest — heart rate ratio method

Uth, Sørensen, Overgaard and Pedersen (2004) derived the factor from the Fick principle and published maximum-to-rest ratios for stroke volume and arteriovenous oxygen difference, on well-trained subjects. It is the only method here that needs no maximal effort, and the only one whose error is not bounded by a regression on real running. It reads high on untrained people and on anyone whose resting heart rate is low for reasons other than fitness.

Worked example

A runner covers 5 km (3.1 mi) in 25:00. Daniels and Gilbert give VDOT 38.3. Put that same VDOT back through the model and the same runner covers 2506 m (2741 yd) in a 12-minute test — a distance Cooper's formula turns into 44.7. The 2.4 km test, which this runner would finish in 11:31, gives 45.4.

That is a spread of 6.4 ml/kg/min for one person on one day, with no change in fitness at all. It is not noise. Cooper's regressions were fitted on young military men in 1968 and read high on trained distance runners, while VDOT is anchored to what this runner actually held for 25:00. The practical rule follows: pick one method and stay with it. Comparing this month's Cooper number against last month's VDOT tells you about the formulas, not about your training.

VDOT, race times and training paces

Every row is one VDOT value: the race times it corresponds to, and the threshold pace it implies. The table is computed with the same functions as the calculator above, not copied from a book.

Find a recent race time in its column and read VDOT on the left — that is your number without any arithmetic. Times in a single row are equivalents, not promises: they assume you are equally prepared for every distance, which is why a marathon read off a 5K is optimistic unless the weekly volume is there. The threshold column is roughly the pace you could hold for an hour, in minutes per kilometre.

What counts as a good VO₂max

Percentiles of measured VO₂max from maximal treadmill tests with gas analysis, by age and sex. Column headings are percentiles: the 50th is the median of the group, the 95th is the top twentieth.

Source: Kaminsky LA, Arena R, Myers J. Reference Standards for Cardiorespiratory Fitness Measured With Cardiopulmonary Exercise Testing: Data From the Fitness Registry and the Importance of Exercise National Database (FRIEND). Mayo Clinic Proceedings 2015;90(11):1515–1523, Table 3. Values are from maximal treadmill tests on 4,611 men and 3,172 women aged 20 to 79 without cardiovascular disease.

One number means different things depending on who holds it: VDOT 38.3 is the 34th percentile for a man of 35 and the 81st for a woman of the same age. Two further cautions. These values were measured on a treadmill — a cycle ergometer reads several units lower for the same person, because you drive a smaller muscle mass. And a watch reports an estimate built from heart rate and pace, not a measurement; it is useful for tracking your own trend and close to meaningless for comparing yourself with someone else.

Why the methods disagree

Because they were built from different people doing different things. Daniels and Gilbert fitted their equations to distance runners and expressed the result as the pace a runner can hold, so economy of movement is inside the number. Cooper fitted his to military recruits in a field test and expressed the result as oxygen uptake, so anything that makes you a more economical runner reads as a higher VO₂max. The heart rate method never watches you run at all. Averaging the four would produce a tidier single figure and would hide exactly the information you need: the range is how much the question is actually worth arguing about.

Turning the number into paces

This is where VDOT earns its keep. At VDOT 38.3 the marathon prediction is 3:57:55, which is 5:38 per kilometre (9:04 per mile), and threshold work sits at 5:16 per kilometre (8:29 per mile). Easy running is deliberately given as a wide band, because hitting it exactly does not matter; interval pace is given as a narrow one, because a few seconds per kilometre there changes the training effect. Note that marathon pace here is not a fixed share of VDOT but the pace of the predicted marathon: taking 84 % of VDOT would give about six seconds per kilometre too fast, which over 42 km compounds into more than four minutes.

What VO₂max does not tell you

It is a ceiling, not a result. Two runners with the same VO₂max finish minutes apart over a half marathon if one holds a higher fraction of that ceiling for longer, and that fraction — lactate threshold — responds to training faster than VO₂max does. Economy matters as much again: the cost of carrying yourself a kilometre differs between runners by well over ten per cent. VO₂max also has a strong hereditary component and a ceiling of its own; trained runners often see it plateau while their race times keep improving for years. If your number stops rising and your times keep falling, nothing is wrong.

This is a fitness calculator, not a medical device or a medical opinion. Estimates from field tests carry errors of several units, and a maximal effort is itself a stress. If you have a heart or lung condition, take medication that affects heart rate, are pregnant, or have been inactive for a long stretch, talk to a doctor before running any all-out test — and use the heart rate method, which requires no maximal effort, if you want a number in the meantime.

Using it

The field tests below require an all-out effort, so read the caution above before running one — and if you would rather not, the heart rate ratio needs no maximal effort at all. If you have raced in the past few weeks, use that: it is the most informative input you own. If not, run the 12-minute test on a track, even-paced, on a day you are rested — start too fast and the number is wrong in a way no formula can correct. The 2.4 km test is the same idea over a fixed distance and suits people who pace better against a known finish. If you cannot run flat out at all, use the heart rate ratio, measure your resting pulse lying down before getting up, and treat the result as an order of magnitude. Then read the percentile with your age and sex, and take the paces from the table below the calculator.

Frequently asked questions