Training Pace Calculator (from VDOT)

How the Training Pace Calculator works

Enter a VDOT, Jack Daniels’ index of running fitness, and the tool returns four training paces. It first solves the Daniels-Gilbert oxygen-cost equation VO₂ = 0.000104·v² + 0.182258·v − 4.6 for the velocity v, in metres per minute, whose oxygen cost equals your VDOT. That velocity is vVDOT. Each zone is then a fixed percentage of it: Easy 70%, Marathon 80%, Threshold 88%, Interval 98%. Results are shown per kilometre and per mile, since Daniels’ own tables are printed in miles. Repetition pace is omitted because Daniels defines it by repeat duration rather than as a fixed fraction of vVDOT.

The formula, worked through

Rearranged for the quadratic formula the equation is 0.000104·v² + 0.182258·v − (4.6 + VDOT) = 0. At VDOT 45 that solves to v = 239.4 m/min, which is 4:11 per kilometre or 6:43 per mile. Pace for a zone is then 60,000 ÷ (v × percentage) seconds per kilometre. Easy at 70% gives 60,000 ÷ 167.6 = 358 seconds, or 5:58 per kilometre. The same VDOT produces 5:13 for Marathon, 4:45 for Threshold and 4:16 for Interval.

Percentages of velocity, not of VO₂max

This distinction is worth stating because it is easy to misread. The 70, 80, 88 and 98 figures are percentages of velocity at vVDOT, and because the oxygen-cost curve is quadratic rather than straight, a given fraction of velocity is a smaller fraction of oxygen uptake. Feeding each zone velocity back through the equation at VDOT 45 gives oxygen costs of 28.9, 34.1, 38.4 and 43.9 mL·kg⁻¹·min⁻¹, which are 64.2%, 75.8%, 85.4% and 97.5% of the VDOT. Those land inside the intensity ranges Daniels describes for the four zones, but they are not the same numbers as the velocity percentages, and quoting one where the other is meant is a common source of confusion.

A fixed-ratio approximation, not the published tables

Daniels’ printed VDOT tables are built from his own zone definitions rather than from one constant percentage of vVDOT, so figures taken from a table will not always match what this tool returns, particularly at the harder end. Treat the output as a transparent approximation whose every constant is stated above, and check it against the tables in the book or the Run SMART VDOT calculator before building a season around it (Daniels, Running Formula; Run SMART Project VDOT calculator).

Where this method is most accurate

The VDOT system was developed on competitive distance runners with steady training backgrounds, and the oxygen-cost model fits best across roughly 1500 m to marathon race paces. It is less suited to sprint distances or ultra efforts where the metabolic picture differs. VDOT also assumes a recent race run in good conditions: heat, altitude, a stale result, or a bad day all decouple your true fitness from the number you type in. The zone percentages are population averages and individual lactate profiles vary.

What this tool does not do

It does not derive VDOT from a race time; you need a VDOT first, from the VDOT calculator on this site or from a table. It does not prescribe workout structure, weekly mileage, or progression, and it does not give Repetition pace. The paces are estimates: running economy, lactate profile, terrain and weather all move the intensity a given pace actually represents.

Disclaimer

This calculator is an educational tool that applies published formulas to user-supplied data. It does not constitute training advice, medical guidance, or performance guarantees. Numbers produced here are estimates based on population-derived models and may not reflect individual physiology. Consult a qualified coach or healthcare provider before beginning or modifying any training programme.