# VDOT calculator > Markdown copy of https://pacewise.doughworks.dev/vdot-calculator, generated from the page. The page is canonical. The page has an interactive calculator; this copy carries its method, formulas and reference tables. Every page on this site has one; the index is https://pacewise.doughworks.dev/llms.txt. Your Daniels & Gilbert VDOT score from any race result, and the times it predicts at every distance. ## What VDOT actually is **One number for your current running fitness, worked out from a race you have already run.** Higher is fitter. It is not measured in a lab. **Why it beats a lab VO₂max (it already contains your economy)** Daniels and Gilbert introduced VDOT in *Oxygen Power* (1979) as a *pseudo*-VO₂max: not the oxygen uptake a lab would measure, but the VO₂max a runner would need in order to produce the race you just ran. A lab VO₂max is a ceiling. VDOT is a result, so it already contains your running economy and your fatigue resistance, which are what decide whether a big engine turns into a fast race. Two runners with identical lab numbers can have very different VDOTs, and the VDOT will tell you which one wins. ## The equations VDOT is a ratio of two fitted curves. Let `v` be your race velocity in metres per minute and `t` the race duration in minutes. **1. Oxygen cost of the velocity** `VO₂ = −4.60 + 0.182258·v + 0.000104·v²` **2. Fraction of maximum sustainable for that long** `%max = 0.8 + 0.1894393·e^−0.012778·t + 0.2989558·e^−0.1932605·t` **3. VDOT** `VDOT = VO₂ ÷ %max` **What the two curves mean, and a worked example (a 20:00 5K is VDOT 49.8)** The first curve says how much oxygen it costs to run at a given speed. The second says how much of your maximum you can hold for how long: near 100% for a very short race, falling towards 80% as the race lengthens. Divide one by the other and you have the maximum the runner must have. Going the other way, from a VDOT to the time it implies at another distance, has no closed form, because the duration sits on both sides. This page solves it numerically, exactly as the app does. For a fixed distance VDOT only falls as the time rises, so a bisection lands on the one realistic answer. A worked example. A 20:00 5K: velocity is 5000 m ÷ 20 min = `250 m/min`. - `VO₂ = −4.60 + 0.182258 × 250 + 0.000104 × 250² = 47.46` ml/kg/min - `%max = 0.8 + 0.1894393·e^−0.2556 + 0.2989558·e^−3.865 = 0.9529` - `VDOT = 47.46 ÷ 0.9529 = 49.8` ## VDOT reference table Race times by VDOT, straight from the equations above. Same table as *Daniels' Running Formula*, recomputed rather than copied. Race times by VDOT. | VDOT | 1500 m | Mile | 5K | 10K | Half | Marathon | | --- | --- | --- | --- | --- | --- | --- | | 30 | 8:30 | 9:10 | 30:41 | 1:03:49 | 2:21:17 | 4:49:49 | | 32 | 8:02 | 8:40 | 29:05 | 1:00:27 | 2:13:55 | 4:35:17 | | 34 | 7:36 | 8:13 | 27:38 | 57:25 | 2:07:17 | 4:22:11 | | 36 | 7:14 | 7:49 | 26:21 | 54:42 | 2:01:18 | 4:10:19 | | 38 | 6:54 | 7:27 | 25:10 | 52:15 | 1:55:51 | 3:59:30 | | 40 | 6:35 | 7:07 | 24:06 | 50:01 | 1:50:54 | 3:49:37 | | 42 | 6:18 | 6:49 | 23:08 | 47:58 | 1:46:22 | 3:40:33 | | 44 | 6:03 | 6:32 | 22:14 | 46:06 | 1:42:12 | 3:32:12 | | 46 | 5:49 | 6:17 | 21:24 | 44:23 | 1:38:21 | 3:24:29 | | 48 | 5:36 | 6:03 | 20:38 | 42:48 | 1:34:48 | 3:17:19 | | 50 | 5:24 | 5:50 | 19:56 | 41:20 | 1:31:31 | 3:10:40 | | 52 | 5:13 | 5:38 | 19:17 | 39:58 | 1:28:28 | 3:04:28 | | 54 | 5:02 | 5:27 | 18:40 | 38:42 | 1:25:37 | 2:58:40 | | 56 | 4:53 | 5:16 | 18:05 | 37:31 | 1:22:58 | 2:53:15 | | 58 | 4:44 | 5:06 | 17:33 | 36:24 | 1:20:28 | 2:48:09 | | 60 | 4:35 | 4:57 | 17:03 | 35:22 | 1:18:09 | 2:43:22 | | 65 | 4:16 | 4:37 | 15:55 | 33:02 | 1:12:54 | 2:32:35 | | 70 | 4:00 | 4:19 | 14:56 | 31:01 | 1:08:23 | 2:23:13 | | 75 | 3:46 | 4:04 | 14:04 | 29:15 | 1:04:26 | 2:14:59 | | 80 | 3:34 | 3:51 | 13:18 | 27:42 | 1:00:57 | 2:07:43 | | 85 | 3:23 | 3:39 | 12:37 | 26:19 | 57:51 | 2:01:15 | ## What VDOT does not tell you - **Nothing about age or sex.** A VDOT of 45 is the same number at 25 and at 65, which makes it a poor way to compare two runners. Use an [age grade](https://pacewise.doughworks.dev/age-grade-calculator) for that. - **The marathon column assumes marathon training.** The equations extrapolate a duration, not an endurance base. A VDOT off a 5K names a marathon time you can only run if you have done the long runs behind it. - **It is a snapshot.** VDOT describes the race you ran on the day you ran it. A result from a year ago is a fact about last year. **Why there are no training paces here (that is coaching, and this is a calculator)** Most VDOT calculators finish by handing you easy, marathon, threshold, interval and repetition paces. This one stops short of that. Prescribing training is coaching, and PaceWise is a calculator: it tells you what your numbers are and leaves what to do about them to you and whoever you train with. *Daniels' Running Formula* gives the paces for each VDOT alongside the context that makes them safe to use, which a web page can't. ## Questions **What is VDOT?** One number for your current running fitness, from Jack Daniels and Jimmy Gilbert. It is a pseudo-VO₂max: the VO₂max you would need to produce the race you just ran, given how much of their maximum a runner can hold for that long. Because it comes from a race result rather than a lab, it already includes your running economy and your fatigue resistance. **How is VDOT calculated?** From two equations. The oxygen cost of your race velocity v in metres per minute is VO₂ = −4.60 + 0.182258v + 0.000104v². The fraction of maximum you can hold for t minutes is 0.8 + 0.1894393·e^(−0.012778t) + 0.2989558·e^(−0.1932605t). Divide the first by the second. A 20:00 5K is 250 m/min for 20 minutes, which comes out at VDOT 49.8. **Is VDOT the same as VO2 max?** No, and the difference matters. VO₂max is a measured ceiling: the most oxygen your body can use, established in a lab. VDOT comes from a race, so it also reflects your running economy and how much of that ceiling you can actually hold. Two runners with the same lab VO₂max can have very different VDOTs, and the VDOT is the better guide to how they will race. **What is a good VDOT score?** VDOT is a fitness scale, not a grade, and it takes no account of age or sex, so comparing yours with someone else's tells you little. For rough orientation: a 30-minute 5K is about VDOT 30, a 25-minute 5K about 38, a 20-minute 5K about 50, a 15-minute 5K about 70. For a comparison that does allow for age and sex, use an [age grade](https://pacewise.doughworks.dev/age-grade-calculator). **Does this VDOT calculator give training paces?** No. It gives you your VDOT and the race times it implies, and stops there. Prescribing easy, threshold, interval and repetition paces is coaching, and PaceWise is a calculator, not a coach. *Daniels' Running Formula* sets out the training paces for each VDOT, along with the context that makes them safe to use. ## Other calculators - [**Race time predictor** VDOT next to Riegel and Cameron.](https://pacewise.doughworks.dev/race-time-predictor) - [**Age grade calculator** The age- and sex-adjusted comparison VDOT is not.](https://pacewise.doughworks.dev/age-grade-calculator) - [**Pace calculator** Pace, time, distance and splits.](https://pacewise.doughworks.dev/pace-calculator)