VO2max estimator
A race result contains more information than a finish time. These are the Daniels and Gilbert equations that turn it into an estimate of aerobic fitness — the number coaches call VDOT — with the arithmetic printed rather than hidden.
Enter a recent race or time-trial result.
The Cooper 12-minute test
If you have no race result, this is the classic field test: run as far as you can in exactly 12 minutes, on a track, and read the distance.
VO2max ≈ (metres − 504.9) ÷ 44.73 — Cooper, JAMA, 1968. Run it on a measured 400 m track, not on the road.
VO2max from a 5K time
| 5K time | Pace /km | Estimated VO2max | Roughly |
|---|---|---|---|
| 15:00 | 3:00 | 69.6 | Competitive club level |
| 16:00 | 3:12 | 64.6 | Strong amateur |
| 17:00 | 3:24 | 60.2 | Strong amateur |
| 18:00 | 3:36 | 56.3 | Strong amateur |
| 19:00 | 3:48 | 52.9 | Well-trained recreational |
| 20:00 | 4:00 | 49.8 | Well-trained recreational |
| 21:00 | 4:12 | 47.0 | Well-trained recreational |
| 22:00 | 4:24 | 44.5 | Regular recreational |
| 23:00 | 4:36 | 42.3 | Regular recreational |
| 24:00 | 4:48 | 40.2 | Regular recreational |
| 25:00 | 5:00 | 38.3 | Regular recreational |
| 26:00 | 5:12 | 36.6 | Beginner / returning |
| 27:00 | 5:24 | 35.0 | Beginner / returning |
| 28:00 | 5:36 | 33.5 | Beginner / returning |
| 29:00 | 5:48 | 32.1 | Beginner / returning |
| 30:00 | 6:00 | 30.8 | Beginner / returning |
| 31:00 | 6:12 | 29.6 | Beginner / returning |
| 32:00 | 6:24 | 28.5 | Beginner / returning |
| 33:00 | 6:36 | 27.5 | Beginner / returning |
| 34:00 | 6:48 | 26.5 | Beginner / returning |
| 35:00 | 7:00 | 25.6 | Beginner / returning |
| 36:00 | 7:12 | 24.7 | Beginner / returning |
| 37:00 | 7:24 | 23.9 | Beginner / returning |
| 38:00 | 7:36 | 23.1 | Beginner / returning |
| 39:00 | 7:48 | 22.4 | Beginner / returning |
| 40:00 | 8:00 | 21.7 | Beginner / returning |
VO2max from a 10K time
| 10K time | Pace /km | Estimated VO2max |
|---|---|---|
| 30:00 | 3:00 | 72.8 |
| 32:00 | 3:12 | 67.5 |
| 34:00 | 3:24 | 62.8 |
| 36:00 | 3:36 | 58.8 |
| 38:00 | 3:48 | 55.2 |
| 40:00 | 4:00 | 51.9 |
| 42:00 | 4:12 | 49.1 |
| 44:00 | 4:24 | 46.5 |
| 46:00 | 4:36 | 44.1 |
| 48:00 | 4:48 | 42.0 |
| 50:00 | 5:00 | 40.0 |
| 52:00 | 5:12 | 38.2 |
| 54:00 | 5:24 | 36.6 |
| 56:00 | 5:36 | 35.0 |
| 58:00 | 5:48 | 33.6 |
| 1:00:00 | 6:00 | 32.3 |
| 1:02:00 | 6:12 | 31.0 |
| 1:04:00 | 6:24 | 29.9 |
| 1:06:00 | 6:36 | 28.8 |
| 1:08:00 | 6:48 | 27.8 |
| 1:10:00 | 7:00 | 26.8 |
| 1:12:00 | 7:12 | 26.0 |
| 1:14:00 | 7:24 | 25.1 |
| 1:16:00 | 7:36 | 24.3 |
| 1:18:00 | 7:48 | 23.5 |
| 1:20:00 | 8:00 | 22.8 |
Cooper test conversion table
| Distance in 12 min | Laps of a 400 m track | Estimated VO2max |
|---|---|---|
| 1,400 m | 3.50 | 20.0 |
| 1,500 m | 3.75 | 22.2 |
| 1,600 m | 4.00 | 24.5 |
| 1,700 m | 4.25 | 26.7 |
| 1,800 m | 4.50 | 29.0 |
| 1,900 m | 4.75 | 31.2 |
| 2,000 m | 5.00 | 33.4 |
| 2,100 m | 5.25 | 35.7 |
| 2,200 m | 5.50 | 37.9 |
| 2,300 m | 5.75 | 40.1 |
| 2,400 m | 6.00 | 42.4 |
| 2,500 m | 6.25 | 44.6 |
| 2,600 m | 6.50 | 46.8 |
| 2,700 m | 6.75 | 49.1 |
| 2,800 m | 7.00 | 51.3 |
| 2,900 m | 7.25 | 53.5 |
| 3,000 m | 7.50 | 55.8 |
| 3,100 m | 7.75 | 58.0 |
| 3,200 m | 8.00 | 60.3 |
| 3,300 m | 8.25 | 62.5 |
| 3,400 m | 8.50 | 64.7 |
The equations
Two of them, from Jack Daniels and Jimmy Gilbert's Oxygen Power (1979) — the pair that underlies the VDOT tables in Daniels' Running Formula. The first gives the oxygen cost of running at velocity v, in metres per minute:
VO₂ = −4.60 + 0.182258·v + 0.000104·v²
The second gives the fraction of VO2max a runner can sustain for t minutes — because a 5K is run at a far higher percentage of maximum than a marathon:
%VO₂max = 0.8 + 0.1894393·e−0.012778·t + 0.2989558·e−0.1932605·t
Divide the first by the second and you have VDOT. Worked example: a 20:00 5K is 250 m/min, giving an oxygen cost of 47.5 ml/kg/min; 20 minutes of running sits at about 95.3% of maximum; 47.5 ÷ 0.953 gives a VDOT of about 49.8.
What to do with the number
On its own, nothing. Its value is as a training-pace key: easy running at roughly 1.3 to 1.45 times your race pace per kilometre, threshold work at around 1.08 times, and intervals close to it. A VO2max number that does not change how you run on Tuesday is trivia.
It is also the honest counterweight to the Riegel predictor. Both start from the same race result; the predictor tells you what you might run, and this tells you what engine produced it. If the two disagree with how your training has actually felt, believe the training.
Questions
What is a good VO2max?
For an untrained adult, roughly 30–40 ml/kg/min; a regular recreational runner typically lands between 42 and 52; a competitive amateur between 55 and 65; elite distance runners run above 70. It falls with age at roughly 1% a year from the thirties onward, and training slows that decline substantially.
How accurate is estimating VO2max from a race time?
As an estimate of your running fitness it is very useful; as a laboratory measurement of oxygen uptake it is approximate. The Daniels and Gilbert equations derive oxygen cost from running velocity and how long you sustained it, so what they really measure is race performance. Two runners with the same lab VO2max can have different running economy and produce different estimates here.
What is VDOT?
Jack Daniels' term for the VO2max-equivalent number derived from a race result rather than measured in a lab. It bundles true VO2max and running economy into a single number that predicts race performance better than either alone, which is exactly what a runner wants.
What is the Cooper test?
Run as far as you can in exactly 12 minutes on a flat track, then estimate VO2max as (distance in metres − 504.9) ÷ 44.73. Kenneth Cooper published it in JAMA in 1968 as a field test for the US Air Force. It is crude, free, and needs nothing but a track and a watch.
Every time, pace and physiological figure on this site is computed from a published formula, and the formula is named and shown on the method page. Nothing here is predicted by a model you cannot check. Race details change — always confirm dates, routes and entry with the official organiser. Training guidance is general information, not individual coaching or medical advice.