VDOT Calculator: Jack Daniels Training Paces and Race Times

VDOT is a running fitness score from Oxygen Power, a 1979 book of performance tables by the coach and exercise physiologist Jack Daniels and Jimmy Gilbert. It is worked out backward from a race: how fast you ran and for how long. The name comes from the way VO2 max is written, with a dot over the V, because the score plays the part of VO2 max in their equations. Researchers who model running describe it as an effective VO2 max rather than a measured one.

This VDOT calculator runs those equations for any race from 1500 m to the marathon. It turns the result into the five training paces Daniels uses, easy (E), marathon (M), threshold (T), interval (I) and repetition (R), and into equivalent times for eight race distances. Next to each number it shows what published studies say about how far that number can be trusted.

How the VDOT calculator works: two equations from 1979

Daniels and Gilbert described a race with two curves. One gives the oxygen cost of running at a given speed. The other gives the share of your aerobic capacity you can hold for a race of a given length. Dividing the first by the second gives the aerobic capacity your race implies, which is your VDOT.

1. Oxygen cost of your race pace. VO2 = −4.60 + 0.182258 × v + 0.000104 × v², with v your speed in meters per minute and the result in mL/kg/min.
2. Share of maximum you held. share = 0.8 + 0.1894393 × e^{−0.012778 × t} + 0.2989558 × e^{−0.1932605 × t}, with t your race time in minutes.
3. VDOT. VDOT = VO2 ÷ share.

For the default 5K in 25:00, your speed is 5,000 ÷ 25 = 200 meters per minute. The first equation gives an oxygen cost of 36.0 mL/kg/min. The second says a 25-minute race is run at 0.940 of your maximum. So your VDOT is 36.0 ÷ 0.940 = 38.3.

The share curve explains why VDOT can compare a mile with a marathon. It sits above 100 percent for races shorter than about 11 minutes, which draw on anaerobic energy as well, falls to 94.0 percent at 25 minutes and 88.8 percent at an hour, and levels off just above 80 percent for the longest marathons.

Oxygen Power was published by the authors themselves and is not online, so we checked every coefficient against two peer-reviewed papers that reprint the equations in full: Smyth et al. (2022), a study of recreational marathon runners in User Modeling and User-Adapted Interaction, and Lan et al. (2020), who used them to estimate the aerobic capacity of firefighter recruits in the Journal of Occupational and Environmental Medicine. Both cite Daniels' book for runners, Daniels' Running Formula, now in its fourth edition (Human Kinetics, 2022, ISBN 9781718203662). The calculator also reproduces two worked examples from V.O2, the company behind the official VDOT calculator: a 2:02:37 marathon scores 83.9 and a 3:17:17 marathon scores 48.

VDOT is Daniels and Gilbert's name for this score, and the official VDOT calculator is published by V.O2 (The Run SMART Project). FitCraft is not affiliated with or endorsed by Jack Daniels, Jimmy Gilbert, V.O2 or The Run SMART Project. We use the name only to say which published method this page runs.

Jack Daniels VDOT training paces: E, M, T, I and R

Daniels sets each training pace at a share of VO2 max, and in his system that means a share of your VDOT. This page uses the bands published with the official V.O2 calculator and works each pace out with the oxygen cost equation above, so the paces are computed here rather than copied from a printed pace table.

Two checks tie the bands to the equations. The share curve gives 88.8 percent for a 60-minute race, so threshold pace at 88 percent of VDOT sits close to the pace you could race for about an hour, which is how Daniels describes it in his notes on the V.O2 training intensities. The same curve crosses 100 percent between 10 and 12 minutes, the race length Daniels links to interval pace. The official calculator page also gives heart rate equivalents, such as 88 to 92 percent of maximum heart rate for threshold; the heart rate zone calculator works out those beats per minute for you.

The paces have been tested against lab measurements in one study we found. Scudamore, Barry and Coons (2018) gave 11 NCAA Division I runners and 9 recreational runners a hard indoor 5 km run and compared the official calculator's paces with their lab results. Threshold pace matched the measured lactate threshold pace in the recreational runners and came out faster than it in the Division I runners; the authors still judged it usable for threshold training at any level. Interval pace matched the speed at VO2 max in the Division I runners but was slower than it in the recreational runners. The samples were small, so treat both findings as a guide. Our guides to the tempo run and to an interval running workout show how to use T and I pace in a session.

VDOT running calculator: equivalent race times

An equivalent time is the finish time that gives back your VDOT at another distance. The calculator solves the two equations backward: for each distance it searches for the time whose speed and length produce your score. A 25:00 5K is equivalent to a 51:53 10K, a 1:55:04 half marathon and a 3:57:55 marathon. Because this works like a running equivalent calculator for any pair of distances, you can enter a 10K and read off a 5K just as easily.

This is a different method from Riegel's formula, which most race predictors use. Riegel stretches a time with a single exponent, while VDOT goes through oxygen cost and the share of maximum held, so the ratio between two distances shifts with your speed. To predict a marathon from a 10K in Riegel's terms, use our race time predictor.

Equivalent times assume you have trained for the new distance. A 5K runner whose longest run is 10 miles will not run the predicted marathon, and the accuracy section below shows how far marathon predictions miss even for runners who trained for both races.

What is a good VDOT?

There is no standard grading scale for VDOT in the research, so the clearest way to read a score is through the race times it stands for. On this calculator a 30:00 5K scores 30.8, a 25:00 5K scores 38.3, a 20:00 5K scores 49.8, a 40:00 10K scores 51.9 and a 3:15:00 marathon scores 48.7. At the top end, V.O2 puts Eliud Kipchoge's 2:02:37 marathon at 83.9, and this calculator agrees.

The more useful comparison is with yourself. VDOT puts a 5K and a half marathon on one scale, so it shows whether you are fitter this season than last even when you raced different distances. To compare yourself with runners of other ages, an age-graded score adjusts for age and sex; our age graded calculator does that. V.O2's own app grades VDOT levels by age and sex, from novice to elite.

How accurate is this VDOT calculator?

There are two questions here: whether the calculator runs Daniels' math correctly, and whether that math predicts your races. The first is settled. The coefficients match the peer-reviewed reprints exactly and the calculator reproduces two of V.O2's published examples. Printed tables and online calculators round differently, so equivalent times can differ by a few seconds from one to the next. Blödorn and Döring (2025) noticed about 10 seconds between Daniels' tables and the official online calculator over 5000 m.

How well VDOT-equivalent times match real races depends on how far you stretch them and on how fast you are. Between neighboring track distances they are close. Blödorn and Döring tested the official calculator on groups of men from world, national and regional all-time lists. It predicted the groups' average 3000 m times from their 1500 m times with an average error of 0.86 percent, and their 5000 m times from their 3000 m times with an average error of 0.80 percent, about 4 to 7 seconds at those times.

Stretching to the marathon is where it slips, and more so for slower runners. Oficial-Casado, Priego-Quesada and Pérez-Soriano (2026) took 7,663 runners who ran both the Valencia Half Marathon and the Valencia Marathon in the same year, 2022 or 2023. On a held-out fifth of them, they predicted each marathon from the half marathon with the VDOT tables in the fourth edition of Daniels' Running Formula. The average miss was 7.9 percent, and it grew steadily as finish times got slower:

The percentages are from Table 2 of the Valencia study; the minutes are our arithmetic for a runner in the middle of each band, and at 2:20 for the fastest group. The authors suggest the gap comes partly from VDOT being built on trained runners with a higher level of performance, and they point to durability, how well a runner holds up late in a long race, as one reason marathon predictions slip. The equations also give everyone the same endurance curve. Mulligan, Adam and Emig (2018) modeled how much realistic differences in endurance move the marathon pace a VDOT predicts: across a window of about 55 seconds per km for a runner with a VDOT of 40, 30 seconds at 60 and 20 seconds at 80.

Race conditions move the score too. Across seven marathons in the US and Canada, Ely et al. (2007) found the top men ran 1.7 percent slower than the course record in the coolest weather and 4.5 percent slower in the warmest, and slower runners lost more. A hot, hilly or windy race gives a VDOT below your real fitness.

Why a VDOT is not your lab VO2 max

Race speed depends on more than aerobic capacity. In their review of what makes endurance champions, Joyner and Coyle (2008) describe three factors working together: VO2 max, the share of it you can sustain (tied to the lactate threshold) and efficiency, the oxygen it costs to run a given speed. Conley and Krahenbuhl (1980) tested 12 men who placed in the top 19 of a nationally prominent 10 km race and had a similar VO2 max, about 71.7 mL/kg/min on average. VO2 max did not predict who ran faster (r = −0.12), while running economy accounted for 65.4 percent of the differences in their 10 km times. Daniels himself wrote in 1985 that economy differs both between runners and within one runner over time.

VDOT folds all three into one number by giving every runner the same oxygen cost curve and the same endurance curve, which is how Mulligan and colleagues describe the model. A runner who is more economical than that curve gets a VDOT above their lab VO2 max, and a less economical runner gets one below it. In Scudamore's lab comparison, VDOT from the 5 km run came out below measured VO2 max in both groups, and further below in the recreational runners. In 23 masters runners with an average age of 57, Lee, Snyder and Lundstrom (2020) found VDOT from a goal race and lab-measured VO2 peak were closely related (r = 0.85) but not the same number.

That is why our VO2 max calculator leaves race times out and sticks to field tests with published equations and known error ranges. Use this page for training paces and race equivalents, and that one if you want an estimate of VO2 max itself. Our review of the running economy research covers what changes the oxygen cost of your stride.

Worked examples: a VDOT chart for nine race results

Nine race results run through the calculator. Paces are per milekm, and easy and interval pace are ranges because Daniels publishes them as bands.

The equivalent times for the same nine results follow. The time in bold is the race that was entered.

Two patterns hold across all nine. Threshold pace comes out 25 to 27 seconds per mile (15 to 17 seconds per km) slower than the equivalent 5K race pace, in line with the usual coaching rule of thumb. Marathon pace lands at 80.5 to 81.8 percent of VDOT, inside Daniels' 75 to 84 percent band, and the faster the runner, the higher the share.

How to raise your VDOT

Your VDOT rises when your race times drop, so anything that makes you faster over the distance raises it. The paces above are built for that: most of the week at easy pace, with one or two harder sessions at threshold, interval or repetition pace. Recalculate after each race you run all out on a fair course, because paces from an old result go stale as you get fitter.

Running economy is the part that a lab VO2 max misses and VDOT does not. In a meta-analysis of five controlled studies with 93 highly trained middle- and long-distance runners, Balsalobre-Fernández, Santos-Concejero and Grivas (2016) found that 8 to 12 weeks of strength work, two or three times a week, improved running economy with a large effect. Most programs used two to four lower-body lifts at moderate loads plus jumps and short sprints. Better economy means a lower oxygen cost at the same speed, which shows up as faster races and a higher VDOT. If you want to add the lifting side at home, a dumbbell workout app can plan and progress those sessions for you.

When to ignore this calculator

The equations describe a fair race by a runner trained for it. In these cases, read the numbers loosely or not at all:

• Hot, hilly or windy races. Heat slows marathon times, and slower runners lose more (Ely et al. 2007). Use a result from a fair course in mild weather.
• Distances under 1500 m or over the marathon. Daniels' system is designed for races from 1500 m to the marathon, as Blödorn and Döring note, so the calculator does not score shorter or longer races.
• Run-walk races and VDOTs under about 30. Below that, the slow end of easy pace comes close to walking speed. Run easy days by feel; our guide on how to pace yourself running explains the talk test.
• Heart conditions, chest pain or dizziness during exercise. Interval and repetition paces are hard efforts. Talk to a doctor before hard running, and stop at once if you feel chest pain, faintness or unusual breathlessness.
• Pregnancy. Pace by how you feel rather than by a number from a pre-pregnancy race, and follow the advice of your obstetric care team.
• Coming back from injury or a long break. An old personal best overstates your current fitness. Wait for a new race or hard effort before you set paces.

Related reading

References

1. Daniels J, Gilbert J. Oxygen Power: Performance Tables for Distance Runners. Tempe, AZ: J. Daniels and J. Gilbert; 1979. Published by the authors and not online; listed in the references of Mulligan et al. 2018 and Lee et al. 2020 below.
2. Daniels J. Daniels' Running Formula. 4th ed. Champaign, IL: Human Kinetics; 2022. ISBN 9781718203662. Publisher's page
3. Smyth B, Lawlor A, Berndsen J, Feely C. "Recommendations for marathon runners: on the application of recommender systems and machine learning to support recreational marathon runners." User Model User-Adapt Interact. 2022;32(5):787-838. doi:10.1007/s11257-021-09299-3, PMC9701182. Equations 7 to 9 reprint the VDOT equations.
4. Lan FY, Fernandez-Montero A, Yiannakou I, et al. "A Mediterranean lifestyle is associated with lower hypertension prevalence and better aerobic capacity among New England firefighter recruits." J Occup Environ Med. 2020;62(7):466-471. doi:10.1097/JOM.0000000000001868, PMC7765687
5. V.O2 (The Run SMART Project). "V.O2 Running Calculator," with its training pace definitions. vdoto2.com/calculator, accessed October 29, 2026.
6. Daniels J. "Running intensities built into V.O2: what and why?" V.O2. vdoto2.com/learn-more/training-definitions, accessed October 29, 2026.
7. V.O2. "Age-graded VDOT levels." August 14, 2019. news.vdoto2.com, accessed October 29, 2026.
8. Oficial-Casado F, Priego-Quesada JI, Pérez-Soriano P. "Performance prediction equation for the Valencia Marathon based on time and pacing in the half marathon." Front Physiol. 2026;16:1718298. doi:10.3389/fphys.2025.1718298, PMC12856576
9. Blödorn W, Döring F. "Special endurance coefficients enable the evaluation of running performance." Sci Rep. 2025;15:20184. doi:10.1038/s41598-025-06009-6, PMC12181339
10. Scudamore EM, Barry VW, Coons JM. A study of the VDOT calculator's VO2 max and training pace predictions in collegiate and recreational runners. J Strength Cond Res. 2018;32(4):1137-1143. doi:10.1519/JSC.0000000000001942, PubMed 28426511
11. Lee EJ, Snyder EM, Lundstrom CJ. "Predictors of long-distance race performance in master runners." J Hum Sport Exerc. 2020;15(2):355-366. doi:10.14198/jhse.2020.152.10, PMC10695480
12. Mulligan M, Adam G, Emig T. "A minimal power model for human running performance." PLoS One. 2018;13(11):e0206645. doi:10.1371/journal.pone.0206645, PMC6239296
13. Joyner MJ, Coyle EF. "Endurance exercise performance: the physiology of champions." J Physiol. 2008;586(1):35-44. doi:10.1113/jphysiol.2007.143834, PMC2375555
14. Conley DL, Krahenbuhl GS. "Running economy and distance running performance of highly trained athletes." Med Sci Sports Exerc. 1980;12(5):357-360. doi:10.1249/00005768-198025000-00010, PubMed 7453514
15. Daniels JT. "A physiologist's view of running economy." Med Sci Sports Exerc. 1985;17(3):332-338. doi:10.1249/00005768-198506000-00006, PubMed 3894870
16. Balsalobre-Fernández C, Santos-Concejero J, Grivas GV. "Effects of strength training on running economy in highly trained runners." J Strength Cond Res. 2016;30(8):2361-2368. doi:10.1519/JSC.0000000000001316, PubMed 26694507
17. Ely MR, Cheuvront SN, Roberts WO, Montain SJ. "Impact of weather on marathon-running performance." Med Sci Sports Exerc. 2007;39(3):487-493. doi:10.1249/mss.0b013e31802d3aba, PubMed 17473775

How this calculator differs from typical VDOT calculators

Most online VDOT calculators print a score and a pace table without showing the math or naming a source for the equations. Many call VDOT your VO2 max, and most present the equivalent marathon time as a forecast with no word on how often it misses, or for whom.

This calculator prints both equations with coefficients checked against two peer-reviewed reprints, and shows the oxygen cost and the share of maximum behind your score. It works each training pace out from the intensity bands Daniels publishes instead of copying a table, and shows easy and interval pace as the full bands. It reports the published accuracy next to the result: within about 1 percent between neighboring track distances, and a marathon miss from about 1 to 18 percent depending on finish time. It separates VDOT from lab VO2 max with the studies that compared them, and it flags inputs outside the 1500 m to marathon range the equations were built for instead of scoring them.