Running VO₂ max calculator
Enter a recent race time, or the distance you covered in 12 minutes. A race uses the Daniels-Gilbert equations and comes back as a VDOT. The 12-minute test uses Cooper's 1968 equation. Both show a range, because a single decimal would pretend to be a lab test.
Free. No account required.
A 20:00 5K, drawn out
Same equations as the calculator. The dot is 20:00. For a man aged 35, that score sits near the 76th percentile of the treadmill reference.
A 5K finish, scored as a VDOT
Where this sits by age
About the 76th percentile for men aged 30 to 39
How the calculation works
A race has two steps, from Daniels and Gilbert's Oxygen Power (1979). First, turn pace into an oxygen cost. Velocity is in meters per minute: VO₂ = -4.60 + 0.182258 × velocity + 0.000104 × velocity². Second, divide by the fraction of VO₂ max a person can hold for that many minutes: 0.8 + 0.1894393 × e^(-0.012778 × minutes) + 0.2989558 × e^(-0.1932605 × minutes). The result is a VDOT. Daniels uses that name so it is not mistaken for the VO₂ max a lab would measure. The curves assume a common running economy. Two people with the same lab number and different economy race at different speeds, and this page only sees the speed.
The page rounds VDOT to the nearest whole number. Daniels' tables are whole numbers, and a race moved by a few seconds does not deserve a decimal. The line under the result is not a confidence interval. In one study of indoor 5K time trials, the VDOT calculator read lower than a treadmill test: about 4.7 percent lower in 11 collegiate runners, and about 9.2 percent lower in 9 recreational runners (Scudamore, Barry, and Coons, 2018). For a 20:00 5K the race score is 49.8, shown as 50. Those average gaps land near 52 and near 54. A hot day, a hilly course, or a bad start moves the race itself, and the score moves with it.
The 5K is 5,000 meters, the 10K is 10,000, the half marathon is 21,097.5, and the marathon is 42,195. A custom distance has to sit between 1,500 meters and 50 kilometers. Shorter than that, the effort is mostly anaerobic and the fraction curve was not built for it. The same course entered in kilometers or miles uses one conversion, 1,609.344 meters to the mile.
The Cooper test is the distance you can cover in 12 minutes. Kenneth Cooper's 1968 paper compared 115 US Air Force men, ages 17 to 52, with a treadmill test. The correlation was 0.897. He published the line the other way around: distance in miles = 0.3138 + 0.0278 × VO₂ max, with a residual variance a² of 0.00985 (113 degrees of freedom). This page solves that line for VO₂ max. The square root of 0.00985 is about a tenth of a mile of scatter. Divided by the slope, 0.0278, that is about 3.6 ml/kg/min either side. A 2,400 meter test is 42.4, shown as 42, and the scatter rounds to 39 through 46. That spread is the original sample. It is not a personal error bar.
Other groups do not sit on that line the same way. In sedentary young men in Kolkata, Cooper's equation averaged 42.8 against a measured 39.8 (Bandyopadhyay, 2015). The original sample was men. Women can use the same arithmetic, and the page does not pretend the 1968 scatter was measured on them. The reference chart underneath is separate. It places the result on treadmill percentiles from the FRIEND registry (Kaminsky et al., 2015), by age and sex, from 20 to 79. A race VDOT is not one of those laboratory tests. The percentile is a place to stand.
A worked example
A 5K in 20:00 is 250 meters per minute. The oxygen cost is 47.5 ml/kg/min, about 95 percent of max for 20 minutes, and the VDOT is 49.8, shown as 50. The collegiate gap in Scudamore's study would put a lab test near 52, and the recreational gap near 54. For men aged 30 to 39, 49.8 sits near the 76th percentile of the FRIEND treadmill standards. Covering 2,400 meters in the Cooper test is 42.4, shown as 42, with the 1968 scatter reading Likely between 39 and 46.
Sources checked October 29, 2026: Daniels and Gilbert, 1979; Daniels, on VDOT; Scudamore et al., 2018; Cooper, 1968; Bandyopadhyay, 2015; Kaminsky et al., 2015; Apple, VO₂ max white paper; Apple, cardio fitness; Lambe et al., 2025; Caserman et al., 2024; Swain, 2000.
Common questions
Is a VDOT the same as VO₂ max?
It is in the same units, ml/kg/min, and it is a rough estimate of the VO₂ max that would produce that race if your economy matched the curve. Daniels and Gilbert said a lab test can disagree, because people differ in how much oxygen they use at a given speed. Scudamore, Barry, and Coons tested the VDOT calculator against a treadmill. It read low in collegiate runners and lower still in recreational runners. Use the whole number. The 52 and 54 next to a VDOT of 50 are those average gaps, from 11 and 9 runners, not a promise about your next lab visit.
Why does the Cooper result have a range?
Cooper's paper gives the scatter around the line, not a single true value. The residual variance of distance was 0.00985. Spread through the slope of the line, that is about 3.6 ml/kg/min either side of the unrounded estimate, and the page rounds those edges. For 2,400 meters the estimate is 42.4, and the edges are 39 and 46. Rounding 42 first and then adding the scatter would show 38 on the low side. The range is the original group of 115 men. A later study of sedentary young men found the equation high, on average, by about 3 ml/kg/min.
Which race should I enter?
A recent one you actually raced, on a measured course, in weather you would call normal. Heat, hills, and a reckless first mile all slow the clock, and the VDOT falls with the time. A 5K and a marathon can disagree for the same person because the fraction of VO₂ max you can hold changes with the minutes, and so does your pacing. Enter the distance you have. The 5K, 10K, half marathon, and marathon presets are the certified distances, including 21,097.5 and 42,195 meters.
How does this compare with Apple Watch cardio fitness?
Apple estimates cardio fitness from heart rate during outdoor walks, runs, and hikes on ground flatter than about a 5 percent grade, with a usable GPS fix. A first workout does not produce a number, and the watch needs to have been worn for a day. Apple's validation set had an average error of 1.4 ml/kg/min, with a standard deviation of 4.7. Independent checks have been wider: one study of 30 adults found the watch 6.07 ml/kg/min low on average, and a Series 7 study found a mean gap of about 4.5. The watch is answering a different question from a race time. It never sees the finish clock. Rides do not count. Apple says indoor workouts and gym equipment do not either.
What does Zolt do with a run?
On iPhone and Apple Watch, Zolt files an estimate from the run itself. It looks for steady minutes, turns pace into an oxygen cost with the ACSM running equation, and extends heart rate up to your max. That is a different method from the race math on this page, and the sheet shows the range and what was missing when a run has no estimate. The write-up of the ride version, which uses the same heart-rate line, is linked below.