An index of running fitness in the same units as VO₂max, but worked out from a race result instead of measured on a treadmill. Because it comes from a performance, it captures running economy and race ability as well as aerobic capacity, which is what makes it useful for assigning training paces.

Can I enter a distance in miles?

Yes, select miles next to the distance field. That matters for a mile race, a 10-mile, or a half marathon quoted as 13.1, all of which had to be converted by hand before. Internally everything runs in kilometres at the exact factor of 1.609344.

Why does my 5K VDOT differ from my marathon VDOT?

Because the model assumes both were maximal efforts under comparable conditions, and a marathon rarely is in the same way a 5K is. A lower marathon VDOT usually reflects fatigue resistance, fuelling and pacing rather than less aerobic capacity. The gap between your two numbers is itself informative: a large one points at endurance or pacing, not at fitness.

What do the two exponential terms do?

They model how the sustainable share of VO₂max falls as a race gets longer. The term with the 0.1932605 coefficient decays within a few minutes and handles short races; the 0.012778 term governs the slow decline across long ones. At 25 minutes the model gives 94.0%; over a marathon it approaches the 0.8 floor the equation is built around.

Can I use a parkrun or a training run?

Only if it was genuinely all out. The equations were fitted to maximal race efforts, so a controlled tempo run or a social parkrun produces a slower time and therefore an artificially low VDOT. A time trial on a measured course under race-like conditions is the closest substitute.

How reliable is a single percentage of maximum as an intensity?

Less than it looks, and it is worth knowing that the assumption has been tested. In one study, subjects working at 80% of maximum heart rate were not under equal metabolic stress: 17 of 31 were past the point of metabolic acidosis and 14 were not. VDOT rests on a similar relative-percentage idea, which is why it compares your own races well and two different runners only roughly.

What happens outside 1500 m to the marathon?

The tool still returns a number and tells you the input sits outside the range the equations were fitted over. For a 400 m or a 100 km the arithmetic runs happily and the result stops describing anything useful, so the flag is there to stop a plausible-looking figure being taken at face value.

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Running

VDOT Calculator (Jack Daniels)

Estimate running fitness (VDOT) from a race result using the Daniels-Gilbert equations.

JCVerified Verified by Jobi Cheriyan, Founder & Builder

Updated 21 August 2026

What this tool does

This calculator estimates VDOT, Jack Daniels' index of running fitness, from a single race result. Enter the distance in kilometres or miles and the finish time, and it converts the performance to a velocity, estimates the oxygen cost of that velocity, works out what fraction of VO₂max is sustainable for a race of that duration, and divides one by the other. It shows those intermediate figures alongside the score. The model is fitted to race distances from roughly 1500 m to the marathon and flags results outside that band.

Enter values

Result

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Next steps

Training Pace Calculator (from VDOT) Calculate Easy, Marathon, Threshold and Interval paces from a VDOT score, in min/km and min/mile. Age-Graded Running Performance Calculator Express any race result as a percentage of a reference standard using the WMA ratio formula. Elevation-Adjusted Pace Calculator Estimate time cost of vertical gain using the 12 s/mile per 100 ft coaching heuristic. Continue in Guided Mode Run any calculator step by step. Your values carry across every tool in the session. Meal Planner Build a day of meals from a 300-food pantry and watch calories and macros land against your targets. Workout Planner Build a 7-day training week from 160+ exercises and see weekly hard sets per muscle against your volume target.

Formula Used

VDOT = \frac{- 4.6 + 0.182258 v + 0.000104 v ^{2}}{0.8 + 0.1894393 e ^{- 0.012778 t} + 0.2989558 e ^{- 0.1932605 t}}

d

Distance in km

t

Time in minutes

Disclaimer

This calculator is for educational and informational purposes only. It does not provide medical, nutritional, or training advice. Results are mathematical estimates and may not reflect individual circumstances. Consult a qualified coach, registered dietitian, medical professional, or physiotherapist for personal guidance.

How the VDOT Calculator works

VDOT is a fitness index in the same units as VO₂max but derived from a race rather than measured in a laboratory, which means it folds running economy and race ability into one number. This tool takes a race distance and time, converts them to a velocity, prices that velocity in oxygen, then divides by the fraction of maximum you could hold for a race that long. Enter the distance in kilometres or miles; both are common race units and the arithmetic converts internally at 1.609344 km per mile.

The formula, worked through

Velocity comes first: v = distance_m ÷ (minutes × 60). Oxygen cost at that velocity is VO₂ = −4.60 + 0.182258·V + 0.000104·V², with V in metres per minute. The sustainable fraction is a dual exponential in race duration: %VO₂max = 0.8 + 0.1894393·e^(−0.012778t) + 0.2989558·e^(−0.1932605t). Finally VDOT = VO₂ ÷ %VO₂max.

Working the default, 5 km in 25:00. Velocity is 5,000 ÷ 1,500 = 3.333 m/s, which is 200.0 m/min. Oxygen cost is −4.60 + 36.45 + 4.16 = 36.01 mL/kg/min. The fraction is 0.8 + 0.1376 + 0.0024 = 0.9400, so 94.0% of maximum is sustainable for a 25-minute effort. VDOT is 36.01 ÷ 0.9400 = 38.3. Race pace was 5:00 per kilometre, or 8:03 per mile.

Why the two exponentials matter

The dual-exponential term is the part doing the real work, and it is why the same runner can post different VDOTs from different distances. The fast-decaying term, with its coefficient of 0.1932605, falls away within the first few minutes; the slow term with 0.012778 governs how much intensity ebbs across a long race. At 25 minutes the model says 94.0% of VO₂max; over a marathon it drops toward the 0.8 floor the equation is built around. Enter the same fitness at two distances and any gap between the answers is telling you about your fatigue resistance and pacing, not about a change in aerobic capacity.

The one-number assumption, and its limits

Reducing intensity to a single fraction of maximum is a modelling convenience rather than a physiological fact. Work testing exactly that assumption found that people exercising at the same relative percentage of maximum heart rate were not under equivalent metabolic stress: at 80% of maximum heart rate, 17 of 31 subjects were above the point of metabolic acidosis while 14 were at or below it (Katch, Weltman, Sady and Freedson, 1978). VDOT inherits that caution. It is a good comparator between your own races and a rough one between two different runners.

Where this method is most accurate

The equations were fitted to competitive distance runners racing standard distances, so accuracy is best for all-out efforts on flat, measured courses in temperate conditions between about 1500 m and the marathon. Sprints and ultra distances sit outside that band and the tool says so when you cross it. Heat, altitude, wind and cold all depress a race time without touching true aerobic capacity, so a hard day in bad conditions reads as lost fitness that was never lost. Once you have a VDOT, the training-pace calculator turns it into Easy, Marathon, Threshold and Interval paces, and the published tables give the same mapping for every distance (Daniels, Running Formula).

What this tool does not do

It estimates a number from a race result. It does not prescribe training, diagnose anything, or predict future races on its own. VDOT is model output, not a measurement, and the tool cannot tell whether the time you entered was a maximal effort, a paced group run, or a bad day. It knows nothing about your injury history, training background, or race-day pacing.

Disclaimer

This tool is provided for educational and informational purposes only. It is not a substitute for professional coaching, medical advice, diagnosis, or treatment. All calculations are estimates based on published mathematical models and may not reflect individual physiological variation. Consult a qualified coach or healthcare provider before making decisions about training, competition, or health based on calculator output.

Questions

What is VDOT?: An index of running fitness in the same units as VO₂max, but worked out from a race result instead of measured on a treadmill. Because it comes from a performance, it captures running economy and race ability as well as aerobic capacity, which is what makes it useful for assigning training paces.
Can I enter a distance in miles?: Yes, select miles next to the distance field. That matters for a mile race, a 10-mile, or a half marathon quoted as 13.1, all of which had to be converted by hand before. Internally everything runs in kilometres at the exact factor of 1.609344.
Why does my 5K VDOT differ from my marathon VDOT?: Because the model assumes both were maximal efforts under comparable conditions, and a marathon rarely is in the same way a 5K is. A lower marathon VDOT usually reflects fatigue resistance, fuelling and pacing rather than less aerobic capacity. The gap between your two numbers is itself informative: a large one points at endurance or pacing, not at fitness.
What do the two exponential terms do?: They model how the sustainable share of VO₂max falls as a race gets longer. The term with the 0.1932605 coefficient decays within a few minutes and handles short races; the 0.012778 term governs the slow decline across long ones. At 25 minutes the model gives 94.0%; over a marathon it approaches the 0.8 floor the equation is built around.
Can I use a parkrun or a training run?: Only if it was genuinely all out. The equations were fitted to maximal race efforts, so a controlled tempo run or a social parkrun produces a slower time and therefore an artificially low VDOT. A time trial on a measured course under race-like conditions is the closest substitute.
How reliable is a single percentage of maximum as an intensity?: Less than it looks, and it is worth knowing that the assumption has been tested. In one study, subjects working at 80% of maximum heart rate were not under equal metabolic stress: 17 of 31 were past the point of metabolic acidosis and 14 were not. VDOT rests on a similar relative-percentage idea, which is why it compares your own races well and two different runners only roughly.
What happens outside 1500 m to the marathon?: The tool still returns a number and tells you the input sits outside the range the equations were fitted over. For a 400 m or a 100 km the arithmetic runs happily and the result stops describing anything useful, so the flag is there to stop a plausible-looking figure being taken at face value.

Sources & Methodology

Uses the Daniels-Gilbert equations. Velocity v = distance ÷ time; oxygen cost VO₂ = −4.60 + 0.182258·V + 0.000104·V² with V in metres per minute; sustainable fraction %VO₂max = 0.8 + 0.1894393·e^(−0.012778t) + 0.2989558·e^(−0.1932605t) with t in minutes; VDOT = VO₂ ÷ %VO₂max. Distance is accepted in kilometres or miles and converted at 1.609344 km per mile. Results outside roughly 1.5 km to the marathon are flagged as outside the range the equations were fitted over.

› Daniels J. Daniels' Running Formula. 4th ed. Human Kinetics; 2021.
› Katch V, Weltman A, Sady S, Freedson P. Validity of the relative percent concept for equating training intensity. Eur J Appl Physiol Occup Physiol. 1978;39(4):219-27.
› Daniels J, Gilbert J. Oxygen Power: Performance Tables for Distance Runners. Oxygen Power; 1979. Source of the oxygen-cost and fractional-utilisation equations; out of print and not available online.

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VDOT Calculator (Jack Daniels)

What this tool does

Export Report

How the VDOT Calculator works

The formula, worked through

Why the two exponentials matter

The one-number assumption, and its limits

Where this method is most accurate

What this tool does not do

Disclaimer

Questions

Sources & Methodology

More in Running

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