How to calculate VO₂ max from running

A recent race, or 12 hard minutes on a track, can give you a VO₂ max estimate without a lab. The race version is a VDOT, from the Daniels-Gilbert equations. The 12-minute version is Cooper's 1968 equation. Both are useful. The calculator rounds them to whole numbers and shows a range, because a decimal would pretend you had been on a treadmill.

The running VO₂ max calculator runs both from a time or a distance you already have.

A race time

Jack Daniels and Jimmy Gilbert published the curves in Oxygen Power (1979). Pace becomes an oxygen cost. Velocity is meters per minute:

VO₂ = -4.60 + 0.182258 × velocity + 0.000104 × velocity²

Divide that by the fraction of VO₂ max a runner can hold for the minutes the race took:

0.8 + 0.1894393 × e^(-0.012778 × minutes) + 0.2989558 × e^(-0.1932605 × minutes)

Twenty minutes is about 95 percent. A marathon, which takes hours, sits closer to 80 percent. The same person can have two honest scores from two distances.

A 5K in 20:00 is 250 meters per minute, an oxygen cost of 47.5 ml/kg/min, and a VDOT of 49.8. The calculator shows 50. Pace is 4:00 per kilometer, 6:26 per mile. Daniels' tables are whole numbers. A few seconds either way is noise.

A 5K finish, scored as a VDOT

Runners who finish together share a VDOT even when a lab would split them, because economy and ceiling can trade off. Daniels started saying VDOT so the race score would stop being passed around as a measured VO₂ max (his short version).

A lab check found the race number reading low. After an indoor 5K and a treadmill test, the VDOT calculator was about 4.7 percent low in 11 collegiate runners and about 9.2 percent low in 9 recreational runners (Scudamore et al., 2018). On the 20:00 5K those average gaps land near 52 and near 54. Small samples, taken from the unrounded 49.8. A direction and a rough size. Your next test can sit outside it.

Heat, hills, and a first mile you cannot hold slow the clock, and the score falls with it. Enter a race you would call normal. The presets are the measured courses: 5,000 meters, 10,000, 21,097.5, and 42,195. A custom distance has to sit between 1,500 meters and 50 kilometers. Shorter than that, the effort is mostly anaerobic.

Twelve minutes

Kenneth Cooper needed a field test for US Air Force men. In 1968, 115 of them, ages 17 to 52, covered as much ground as they could in 12 minutes. Compared with a treadmill VO₂ max, the correlation was 0.897 (Cooper, 1968).

He published the line with distance as the result: miles = 0.3138 + 0.0278 × VO₂ max, residual variance a² = 0.00985. Turn it around and you have the estimate. The square root of 0.00985 is about a tenth of a mile. Divided by the slope, that is about 3.6 ml/kg/min either side.

Six laps of a 400 meter track is 2,400 meters. The line says 42.4, shown as 42, and Likely between 39 and 46. The edges come from 42.4, then get rounded. Round to 42 first and the low edge becomes 38.

That scatter is the original 115 men. In sedentary young men in Kolkata the same equation averaged 42.8 against a measured 39.8 (Bandyopadhyay, 2015). Women were not in that sample. Use a track, or any loop you have measured. Sprinting the first minute and walking the last three is a different test.

Where 50 sits at 35

FRIEND treadmill percentiles cover men and women ages 20 to 79, tested in a lab (Kaminsky et al., 2015). For men aged 30 to 39 the 50th percentile is 42.4 and the 75th is 49.2, so 49.8 lands near the 76th. A race score is only a place to stand on that chart.

Where this sits by age

About the 76th percentile for men aged 30 to 39

27.25th42.450th59.895th

Apple sorts cardio fitness the same way. Low, Below Average, Above Average, and High are age and sex bands in the Health app (Apple Support). A race and a watch can land in different bands. They measured different things.

Apple Watch cardio fitness

The watch estimates VO₂ max from heart rate on outdoor walks, runs, and hikes, on ground flatter than about a 5 percent grade, with GPS and a real rise in heart rate. The first workout does not count, and the watch needs a day of wear before that. Indoor runs, gym equipment, and rides are out. How Zolt estimates VO₂ max from a bike ride is why a rider's history can sit still, and the cycling calculator scores one effort if you have the watts.

Apple's validation reported an average error of 1.4 ml/kg/min in the held-out group, standard deviation 4.7 (white paper). A spread of 4.7 means plenty of people were several points off.

Independent checks have been wider. After 5 to 10 days of wear and a maximal treadmill test, the watch was 6.07 ml/kg/min low on average in 30 adults, mean absolute error 6.92 (Lambe et al., 2025). A Series 7 study with a short wear found the lab about 4.5 ml/kg/min higher (Caserman et al., 2024). Apple followed people for close to a year. A weekend of runs is thinner, and a wrong age, sex, weight, or unlisted heart-rate medicine in the Health app moves the number too.

The watch sees heart rate at a pace you can sustain. A VDOT sees the finish clock. Keep one of them when you want a trend.

What is worth doing

Repeat one test. A 5K you race twice a year, or a 12-minute run on the same track, beats a drawer of mismatched numbers. A 5K and a marathon can disagree because they ask for different fractions of your max, and because marathon day includes fueling.

The score moves when the performance moves. Easy running fills most of a sensible week, and some faster running is what changes the next finish. If the shoes are done, settle that before you rewrite the plan: how many miles running shoes last, or the mileage calculator for a pair you already log.

On a daily run, Zolt uses the run itself: steady minutes, the ACSM running equation for oxygen cost, and heart rate extended toward your max. The ride article includes that running version. You need enough steady minutes, with heart rate between 70 and 95 percent of max. Intervals often get no estimate, and the sheet says what was missing. The calculator is for a finish time, when you do not have those minutes.

Common questions

Is a 5K a better input than a marathon?

Use the race you actually ran. A 5K sits close to the top of what you can hold. A marathon sits nearer 80 percent, for much longer, and it adds fueling mistakes. Switching distances is weak evidence that you got fitter.

Why doesn't this match my Apple Watch?

The watch never sees your finish time, and a VDOT never sees your heart rate. Heat, a sloppy course, or a wrong weight in the Health app widens the gap. Compare two races, or two months of the same watch.

Should I race more often just to raise the number?

One honest race, or one evenly paced 12-minute test, places you. The number moves when the next performance does. If the figure you distrust is calories, that is a different measurement: how accurate Apple Watch calories are.

References

1. Apple. Using Apple Watch to Estimate Cardio Fitness with VO₂ max. PDF
2. Apple. Track your cardio fitness levels. support.apple.com/en-us/108790
3. Bandyopadhyay A. Validity of Cooper's 12-minute run test. Biology of Sport. 2015;32(1):59-63. doi:10.5604/20831862.1127283
4. Caserman P, et al. Apple Watch Series 7 VO₂ max. JMIR Biomedical Engineering. 2024;9:e59459. PMC11325102
5. Cooper KH. A means of assessing maximal oxygen intake. JAMA. 1968;203(3):201-204. doi:10.1001/jama.1968.03140030033008
6. Daniels J, Gilbert J. Oxygen Power: Performance Tables for Distance Runners. 1979.
7. Kaminsky LA, Arena R, Myers J. FRIEND treadmill reference standards. Mayo Clinic Proceedings. 2015;90(11):1515-1523. doi:10.1016/j.mayocp.2015.07.026
8. Lambe R, et al. Apple Watch VO₂ max validation. PLOS ONE. 2025;20(5):e0323741. doi:10.1371/journal.pone.0323741
9. Scudamore EM, Barry VW, Coons JM. Time-trial predictions of VO₂max. Journal of Strength and Conditioning Research. 2018;32(4):1137-1143. doi:10.1519/jsc.0000000000001942