VDOT Calculator and Chart

VDOT chart: race times for VDOT 30 to 85

Each row is one VDOT score with the 5K, 10K, half marathon and marathon times that earn it. Find your recent race time in its column and read the score on the left, or read across to see what the same fitness is worth at the other distances.

Times come straight from the Daniels and Gilbert equations, rounded to the second. Daniels’ printed table can differ by a few seconds (see the questions below).

VDOT training paces chart, per mile

Training paces per mile for each VDOT: the easy range, then marathon, threshold, interval and repetition pace. The per km chart is further down.

Swipe the table sideways for the interval and repetition columns.

How it works

VDOT is one number for your current running fitness, worked out from a race result. It comes from two equations that exercise physiologist Jack Daniels and Jimmy Gilbert published in 1979:

• Oxygen cost. The faster you run, the more oxygen each minute costs. The first equation turns your race speed into that cost.
• Share of your maximum. You can hold close to your maximum for a few minutes, but less for an hour or more. The second equation gives the share that can be held for a race of your duration.

Dividing the cost by the share gives the score. Daniels describes it as a pseudo VO2 max, one based strictly on performance, which is why he gives it its own name. It is not a lab measurement.

The same two equations then run backwards. Equivalent race times are the times at other distances that give the same score. Training paces are the speeds that cost a set percentage of the score:

• Easy: 59 to 74% of VDOT. Daniels puts easy running at about 59 to 74% of VO2 max.
• Marathon: the pace of the equivalent marathon.
• Threshold: 88% of VDOT. Daniels calls this comfortably hard running, a pace that a rested runner could race for about 60 minutes. Tempo runs are run at this pace.
• Interval: 97.5% of VDOT, the pace of his VO2 max intervals.
• Repetition: 6 seconds per 400 m faster than interval pace. This one is Daniels’ own rule of thumb and not a percentage. He adds that it fits faster runners best, and that the gap can be 7 or 8 seconds for runners with a VDOT in the 50s or 40s. This calculator uses 6 seconds throughout.

VDOT is a term from Jack Daniels’ work. The name is used by The Run SMART Project for its official VDOT Running Calculator. Plates & Pace is not affiliated with Jack Daniels or with The Run SMART Project.

The formula

v     = distance ÷ time, m/min
t     = race time in minutes

cost  = −4.60 + 0.182258 × v
        + 0.000104 × v²
a     = e^(−0.012778 × t)
b     = e^(−0.1932605 × t)
share = 0.8 + 0.1894393 × a
        + 0.2989558 × b
VDOT  = cost ÷ share

Training paces
easy       59 to 74% of VDOT
marathon   pace of the
           equivalent marathon
threshold  88% of VDOT
interval   97.5% of VDOT
repetition interval pace
           − 6 s per 400 m

pace at a percentage:
  the speed v whose cost
  is that share of VDOT

Worked example

A 10K in 50:00.

1. Speed: 10,000 m ÷ 50 min = 200 m per minute.
2. Oxygen cost: −4.60 + 0.182258 × 200 + 0.000104 × 200² = 36.01 ml/kg/min.
3. Share held for 50 minutes: 0.8 + 0.1894393 × 0.5279 + 0.2989558 × 0.0001 = 0.900, or 90.0%.
4. VDOT: 36.01 ÷ 0.900 = 40.0.
5. Threshold pace: 88% of 40.0 is 35.2 ml/kg/min. The speed that costs that much is 196.4 m per minute, which is 8:12 per mile or 5:05 per km.
6. Repetition pace: interval pace is 1:53 per 400 m, so repetition pace is 1:47 per 400 m, or 7:09 per mile.

At VDOT 40.0 the equivalent 5K is 24:06, the half marathon 1:50:52 and the marathon 3:49:34. Easy pace is 9:25 to 11:15 per mile, or 5:51 to 6:59 per km.

What a VDOT score can and cannot tell you

• It is not a lab VO2 max. A 2018 study compared the VDOT calculator with lab tests of collegiate and recreational runners after a 5 km time trial. VDOT came out lower than measured VO2 max in both groups, and the authors advise reading it with caution as a measure of VO2 max. In the same study the threshold pace matched the measured lactate threshold pace of the recreational runners but was faster than that of the collegiate athletes, and the interval pace matched the pace at VO2 max of the collegiate athletes but was slower than that of the recreational runners.
• Equivalent times assume equal training. For a 50:00 10K the equivalent marathon here is 3:49:34, almost the same as the 3:50:01 that Riegel’s formula gives. A 2016 study of 2,303 recreational runners found Riegel’s marathon times at least 10 minutes too fast for half of them. That study did not test VDOT, but with the two this close, treat an equivalent marathon as a best case unless you have trained for the distance.
• One race, one day. The score reflects the race you enter: the course, the weather and how you paced it. Train at the paces for the fitness you have now, and enter a new race result when you have one.
• Race length. The equations were built from races between about 1500 m and the marathon. The calculator still answers outside that range and marks the result as rough.

VDOT training paces chart, per km

The same training paces per kilometer.

Swipe the table sideways for the interval and repetition columns.

Questions

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Sources

1. Daniels J, Gilbert J. Oxygen Power: Performance Tables for Distance Runners. Tempe, AZ; 1979. The two equations behind VDOT.
2. Daniels J. Daniels’ Running Formula. 4th ed. Human Kinetics; 2022. The VDOT tables, the training intensities and the 6-second rule for repetition pace. Scanned copy at the Internet Archive.
3. Scudamore EM, Barry VW, Coons JM. An evaluation of time-trial-based predictions of VO2max and recommended training paces for collegiate and recreational runners. Journal of Strength and Conditioning Research. 2018;32(4):1137-1143.
4. Vickers AJ, Vertosick EA. An empirical study of race times in recreational endurance runners. BMC Sports Science, Medicine and Rehabilitation. 2016;8:26.
5. The Run SMART Project, LLC. VDOT Running Calculator, App Store listing: “The official VDOT Running Calculator, designed by Dr. Jack Daniels”.