Key Takeaways
- Give it a race time, a 12-minute run, a 1.5-mile run, or all three. Each goes through its own published equation and the answers sit side by side. Expect them to disagree, because they are different equations built on different people.
- The race number is VDOT. The book it comes from calls it a rough estimate of the VO₂max behind a performance[1], and in one lab comparison it came out lower than measured VO₂max[2].
- Only the George 1.5-mile equation has a published cross-validated error, 3.9 mL/kg/min[5]. For the Cooper and time-only 1.5-mile equations none turned up, so none is shown.
- Your placement uses HUNT3, a Norwegian reference group of healthy adults tested on a treadmill[7]. It is not a table of runner standards.
How the Race Estimate Works
The oxygen cost of your pace, divided by the share of your VO₂max you can hold for that long.
The race estimate uses two equations printed in Daniels and Gilbert's Oxygen Power[1]. The first gives the oxygen cost of running at speed v, in metres per minute. The second gives the share of your VO₂max you can hold for t minutes.
cost = −4.60 + 0.182258 × v + 0.000104 × v²
share = 0.8 + 0.1894393 × e^(−0.012778 × t) + 0.2989558 × e^(−0.1932605 × t)
A faster pace costs more oxygen, and a longer race lets you use less of your maximum. Dividing one by the other puts both effects into a single number. The share never drops below 0.8, however long the race.
Worked example: a 22:00 5K
This is the calculator's own working for 5,000 m in 22:00:
Speed = 5000 m ÷ 22.00 min = 227.3 m/min
Oxygen cost = −4.60 + 0.182258 × 227.3 + 0.000104 × 227.3² = 42.19
Fraction of VO2max held = 0.8 + 0.1894393 e^(−0.012778 × 22.00) + 0.2989558 e^(−0.1932605 × 22.00) = 0.947
VDOT = 42.19 ÷ 0.947
The book prints these as Figures 1 and 2 and credits an earlier Daniels, Fitts and Sheehan book for them[1]. The pages that explain the method do not say how many runners the two curves came from, so that detail is unavailable.
The book also says its 800 m and 50 km times are not based on the same formula, and that the marathon was the longest distance in its data[1]. That is why the calculator takes races from 1,500 m to the marathon.
VDOT Is Not a Lab VO₂max
A good number for comparing your own races. A shaky one to quote as a measurement.
The book is upfront about this. It calls the number a rough estimate of the VO₂max that would allow the performance, and says it does not matter if it differs from a lab value[1]. What it cares about is that your times at different distances line up with each other.
One study checked the gap. Scudamore, Barry and Coons had 11 collegiate athletes and 9 recreational runners run indoor 5 km time trials, then compared Daniels' VDOT calculator with lab-measured VO₂max[2].
VDOT came out lower than measured VO₂max in both groups, and lower by more in the recreational runners. The abstract gives no size for the gap, and the authors advise reading VDOT with caution.
That is 20 people, so treat it as a warning and not a correction. No adjustment is applied. The study used the online calculator rather than these equations directly, and the two have not been compared here.
In practice, if you set a race-based number beside a lab result or the HUNT3 table below, expect the race number to sit low.
What Sits Behind the Other Estimates
Same quantity, four equations, very different amounts of published evidence.
| Estimate | Built from | Published error |
|---|---|---|
| Race result (VDOT)[1] | The two Daniels and Gilbert equations above | Unavailable. It is a reference value, not a prediction of lab VO₂max |
| 12-minute run[3][4] | Cooper 1968: 115 US Air Force men, average age 22, r = 0.897 with treadmill VO₂max. The paper fits distance to VO₂max, and the calculator turns the line around | Unavailable. The paper prints a correlation, not a standard error |
| 1.5-mile run, time only[4] | The Cooper Institute formula, 483 ÷ minutes + 3.5, which it treats as interchangeable with the 12-minute run | None found |
| 1.5-mile run, with weight and sex[5][6] | George 1993: 149 fit college students aged 18 to 29 were measured. The 1.5-mile model was fitted on 49 and cross-validated on 47 | 3.9 mL/kg/min in cross-validation, 2.8 in the fitting group |
What each estimate on this page is based on and what error is published for it
George's abstract confirms the three inputs and the error figures, then cuts off before the coefficients[5]. An open-access 2019 paper prints the same equation[6], but it credits the Cooper test and not George. The coefficients could not be checked against George's full text.
A review of 123 studies found a pooled correlation of 0.79 with lab VO₂max for the 1.5-mile test and 0.78 for the 12-minute test[8]. That says these tests rank people well. It does not say how close your own number is.
Why Your Estimates Will Not Match
Different equations, fitted to different people.
Take a man who runs 1.5 miles in 11:40. Treated as a race, the Daniels equations give 37.8. The time-only 1.5-mile formula gives 44.9, a gap of 7.1.
Neither is a mistake. One turns a pace and a duration into a reference number, and the other is a field estimate for a single distance. VDOT coming out lower fits the lab comparison above[2], but that study did not test the 1.5-mile equation, so it is a pattern and not proof.
The calculator flags a gap larger than 3.9 mL/kg/min. That is the George cross-validated error, borrowed because it is the only published one here. It is a flag for a big gap, not an error for the other methods.
Comparing your own results over time sidesteps most of this, because the same method's quirks apply every time. Pick one test, run it the same way, and watch the change.
Where Your Number Sits: HUNT3
Lab-measured VO₂max by sex and decade, from a Norwegian population study.
HUNT3 tested around 3,800 healthy Norwegian adults aged 20 to 90 on a treadmill[7]. The calculator places your estimate against the group that matches your sex and age.
| Age | Men, mean (SD) | Women, mean (SD) |
|---|---|---|
| 20 to 29 | 54.4 (8.4) | 43 (7.7) |
| 30 to 39 | 49.1 (7.5) | 40 (6.8) |
| 40 to 49 | 47.2 (7.7) | 38.4 (6.9) |
| 50 to 59 | 42.6 (7.4) | 34.4 (5.7) |
| 60 to 69 | 39.2 (6.7) | 31.1 (5.1) |
| 70 and over | 35.3 (6.5) | 28.3 (5.2) |
HUNT3 mean VO2max in mL/kg/min with standard deviation, by age group and sex
These are averages for healthy adults at every fitness level, not for runners. Being above the average says little about how you rank among runners.
Runner-specific bands for a "good" or "elite" VO₂max are unavailable here, because no sourced table is used. A field estimate also carries its own error, so your true gap to the average could be bigger or smaller than shown.
Other Running and Fitness Tools
For questions this page does not answer.
- Race predictions and training paces: Running Performance calculator.
- One test in depth: Cooper 12-Minute Test calculator or 1.5 Mile Run Test calculator.
- A walking test instead of a hard run: Rockport Walking Test calculator.
- A heart-rate estimate, or converting a lab value: VO₂ Max calculator.
- A fitness age from the same HUNT3 data: Fitness Age calculator.
Limits
What these numbers cannot tell you.
- None of them is a measured VO₂max. Only a lab test with gas analysis measures it.
- Every estimate assumes an honest, full effort. The book behind VDOT notes that terrain, footing and weather all affect performance[1].
- The Cooper equation came from men, and the George equation from fit students aged 18 to 29. Outside those groups the calculator warns you and keeps the number.
- The Cooper Institute says the 12-minute and 1.5-mile runs are for apparently healthy, regularly active people. It suggests a walking test if you are obese, relatively inactive or get joint pain while running[4].
- Input limits such as ages 18 to 99 and weights 30 to 250 kg only stop typing mistakes. They are not physiological claims.
Frequently Asked Questions
Sources & References
- Oxygen Power: Performance Tables for Distance Runners (scanned PDF; the two equations are Figures 1 and 2, PDF pages 97 and 99). Daniels J, Gilbert J. Oxygen Power, 1979 (reproduced at vivamarathon.com) (1979)
- An evaluation of time-trial-based predictions of VO2max and recommended training paces for collegiate and recreational runners (abstract). Scudamore EM, Barry VW, Coons JM. Journal of Strength and Conditioning Research 32(4):1137-1143 (2018)
- A means of assessing maximal oxygen intake. Correlation between field and treadmill testing (citation only; the full text is not freely available). Cooper KH. JAMA 203(3):201-204 (1968)
- 50 Years of the Cooper 12-Minute Run. The Cooper Institute. cooperinstitute.org (blog post)
- VO2max estimation from a submaximal 1-mile track jog for fit college-age individuals. George JD, Vehrs PR, Allsen PE, Fellingham GW, Fisher AG. Medicine & Science in Sports & Exercise 25(3):401-406 (abstract) (1993)
- Multiple fitness improvements found after 6 months of high intensity functional training (open access; its Methods print the 1.5-mile equation with weight and sex, crediting Cooper). Cosgrove SJ, Crawford DA, Heinrich KM. Sports 7(9):E203 (2019)
- Aerobic capacity reference data in 3816 healthy men and women 20-90 years. Loe H, Rognmo Ø, Saltin B, Wisløff U. PLoS ONE 8(5):e64319. A correction to Table 2 was published in November 2013 (2013)
- Criterion-related validity of the distance- and time-based walk/run field tests for estimating cardiorespiratory fitness: a systematic review and meta-analysis. Mayorga-Vega D, Bocanegra-Parrilla R, Ornelas M, Viciana J. PLoS One 11(3):e0151671 (2016)
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Disclaimer: This calculator is for informational and personal journaling purposes only. It logs measurements and compares them to published reference values. It is not health, medical, or nutrition advice.