VO2 max is the most oxygen the body can use in a minute, per kilogram of body weight, written in mL/kg/min. Only a laboratory test with gas analysis measures it; field tests estimate it from a timed run. Take a runner who covers 2,400 m in exactly 12 minutes, which is a Cooper test as it stands. Cooper's equation puts that run at 42.4 mL/kg/min. Daniels and Gilbert's race formula, applied by us to the same run, gives 36.3. The 1.5-mile formula, 483 ÷ time + 3.5, gives 43.5 with the time scaled to the full 1.5 miles (2,414 m), or 43.8 with 12 entered as it stands. One run, 7.2 mL/kg/min apart, on our arithmetic. Each method turns running speed into oxygen with a different line.
Such comparisons are not new. In a 2014 paper, Kayihan and colleagues applied three one-mile equations to 351 male police officers in Turkey, aged 20 to 23, and found the results differed significantly.
Common field formulas put the same run at least seven mL/kg/min apart
We ran the three methods for 15 times, every 30 seconds from 9:00 to 16:00 over 2.4 km. For Cooper's we assumed the same pace held for 12 minutes, a conversion of our own. The 1.5-mile formula used the time scaled to 2,414 m. Figures in mL/kg/min.
| 2.4 km time | Daniels and Gilbert | Cooper | 483 ÷ t + 3.5 | Gap |
|---|---|---|---|---|
| 9:00 | 50.3 | 60.3 | 56.9 | 9.9 |
| 11:00 | 40.1 | 47.2 | 47.2 | 7.1 |
| 12:00 | 36.3 | 42.4 | 43.5 | 7.2 |
| 14:00 | 30.4 | 34.7 | 37.8 | 7.4 |
| 16:00 | 25.9 | 29.0 | 33.5 | 7.6 |
The gap never fell below 7.05 at any of the 15 times. Its widest value depends on the conversion: 9.9 at constant pace, or 8.3 if the 12-minute distance is chosen to match the Daniels and Gilbert figure instead. Daniels and Gilbert always read lowest.
The split reaches the fitness groups Mandsager and colleagues drew from 122,007 adults referred for treadmill testing, their fitness estimated from treadmill performance. For a hypothetical man of 25, the three figures fell in more than one group at 12 of the 15 times. A group is a position within that clinical cohort and passes no judgement on anyone.
The 1.5-mile formula matches the treadmill running equation at race pace
Websites credit 483 ÷ time + 3.5 to Cooper, Balke or nobody. A 2023 study in Nutrients applied it to a 2,400 m run and cited the NSCA's 2012 Guide to Tests and Assessments, which we have not opened. Its origin remains unknown.
The ACSM running equation for level ground is 0.2 × speed in metres per minute + 3.5. Over 1.5 miles, speed is 2,414 ÷ t, so the first term becomes 482.8 ÷ t, within 0.05% of the formula on our arithmetic. That says nothing about authorship, but it shows the assumption: an all-out 1.5 miles is run at VO2 max. In 99 active adults, a 2023 study in Sports found the ACSM equation, applied at the last treadmill stage completed, overestimated measured VO2 max by 9.8 mL/kg/min on average.
An oxygen-cost curve from Daniels and Gilbert places the race estimate lowest
VDOT, Daniels's race-based index, takes two steps: an oxygen-cost curve for running speed, then division by the share of VO2 max that can be held for the race's duration. At 200 m per minute, the 12:00 pace, the curve gives 36.0 mL/kg/min where the ACSM line gives 43.5. That difference is why VDOT reads lowest. Cooper's equation, (metres − 504.9) ÷ 44.73 as Soares and colleagues give it, is a regression from distance to measured VO2 max, with no oxygen-cost model inside.
The divisor matters less. Under about 11.03 minutes the sustainable share exceeds 1.0 (1.021 at 9:00), lowering VDOT by 1.1 mL/kg/min at most; above that it nudges VDOT up. We could not obtain Daniels and Gilbert's 1979 book to see what range they intended.
Until 16 October 2026 the race method in our VO2 max calculator accepted 1 to 50 km despite its "5K to marathon" label, and for 2.4 km in 9:00 printed "the model assumes you held 102% of your VO2 max". It also called Soares's limits of agreement individual errors, graded an empty age as 30, and told readers to "confirm zero outbound requests". The revision that day refuses races under 5 km or over 42.195 km, and any time that would push the share to 1.0 or above. To re-run it, enter 2,400 m by the Cooper method for 42.4, or 5 km in 22:30 by the race method for 43.4.
Validation studies place each equation within a narrow group of volunteers
| Study | Method | Who | Reported error |
|---|---|---|---|
| Uth et al. 2004 | Heart-rate ratio | 46 well-trained men, 21–51 | SEE 2.7 mL/kg/min, in the other 36 men |
| Kline et al. 1987 | Rockport one-mile walk | 343 adults, 30–69 | SEE 0.325 L/min |
| Larsen et al. 2002 | 1.5 miles, "somewhat hard" | 101 students, 18–26 | SEE 3.37 |
| Burger et al. 1990 | 2.4 km run | 20 young military volunteers, plus a check group | SEE 2.24–2.91 mL/kg/min |
| Soares et al. 2026 | Cooper, tested | 73 varsity team-sport athletes | Mean −6.0 mL/kg/min |
SEE is the typical error of an estimate (Larsen's has no printed unit). The first four built equations; Soares tested Cooper's against gas analysis and reported 95% limits of agreement of −19.8 to +7.9 mL/kg/min, the band expected to hold 95% of individual differences. Kline's walk uses heart rate at the end of the mile. Larsen's subjects held a submaximal effort, so the equation does not fit an all-out run. No equation here has a term for heat or humidity.
Small changes in resting heart rate displace the Uth estimate widely
Uth's method multiplies the ratio of maximum to resting heart rate by 15.3. Holding the maximum at 190 beats a minute, a resting rate of 60 gives 48.5 mL/kg/min and 70 gives 41.5, on our arithmetic. Between resting rates of 50 and 80, each 10-beat step moved the estimate by 5.2 to 9.6 mL/kg/min. The authors wrote that use in other groups "will have to await direct validation".
IPPT scoring puts a 2.4 km run on a points scale
The Individual Physical Proficiency Test (IPPT) is the SAF's fitness test. MINDEF's release of 24 July 2014 gave the 2.4 km run up to 50 of 100 points. Its Pass example, an NSman (operationally ready national serviceman) aged 25 to 27, ran 12:40 for 31 points; the run leg of its Gold example, a serviceman aged 34 to 36, took 10:40 for 41. Those are 2014 figures, and we did not open current tables. The release converts no time into VO2 max.
For NAPFA, the National Physical Fitness Award school test, the Mandsager groups are no help: they start at 18. In 2015 Chen, Wong, Or and Quek compared two field estimates in the same 187 Singapore Secondary 2 students aged 14. The 2.4 km run-walk gave a mean of 36.70 and the multistage fitness test 33.60 (correlation 0.78). The abstract prints the unit as L/min, evidently meaning mL/kg/min, and does not say which equation converted the run.
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