How this calculator works
Running faster costs more oxygen. The Daniels and Gilbert equation gives the oxygen cost of a running velocity, and that cost is largely independent of fitness: two runners at the same speed use similar oxygen per kilogram per minute. What differs is the share of maximum uptake they can hold. A short race is run near 100 percent of VO2 max, while a marathon is run nearer 80 percent because the effort must last much longer. Dividing the oxygen cost by the sustainable share gives VDOT, a pseudo VO2 max that folds in running economy and threshold. It is an estimate, not a laboratory measurement, but it is available from any honest race.
Formula
Velocity v (m/min) = distance in metres / time in minutes. Oxygen cost = -4.60 + 0.182258 v + 0.000104 v squared. Sustainable share = 0.8 + 0.1894393 e^(-0.012778 t) + 0.2989558 e^(-0.1932605 t), with t in minutes. VDOT = oxygen cost / sustainable share. Race pace = 60000 / v seconds per kilometre.
Worked example
A 10 km in 50:00 gives v = 10,000 / 50 = 200 m/min. The oxygen cost is -4.60 + 36.4516 + 4.16 = 36.01 mL/kg/min. For 50 minutes the sustainable share is about 0.900, so VDOT is 36.01 / 0.900 = 40.0 mL/kg/min. The pace is 60,000 / 200 = 300 seconds per kilometre, or 5:00.
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Frequently asked questions
Is VDOT the same as VO2 max?
Not quite. VDOT is a pseudo maximum that includes running economy and the ability to hold a high share of uptake for a given duration. Laboratory VO2 max is a direct measurement of oxygen use. For most runners the two values land close together.
Why does the sustainable share change with race length?
The body cannot hold 100 percent of VO2 max for long. The share falls as duration rises, which is why a marathon is run at a lower fraction of maximum than a 5 km. The exponential terms in the equation model that decline.
Which distance gives the best estimate?
A hard effort between about 10 minutes and a half marathon is the sweet spot. Very short races depend on anaerobic capacity, and marathons add fuelling and pacing errors, so both widen the estimate.
Can I improve my VDOT?
Yes, through consistent aerobic volume and targeted threshold and interval work. The value usually moves slowly, so retest every six to twelve weeks rather than after every session.