VDOT Race Pace Calculator
VDOT is a running fitness index that turns one race result into an effective VO2max. It comes from the Daniels-Gilbert equations, which model two things: the oxygen cost of running at a given velocity, and the fraction of maximal oxygen uptake a runner can sustain for a given duration. Combining them yields VDOT, the oxygen cost divided by the sustainable fraction. This calculator takes a race distance in metres and a finishing time in minutes, computes velocity in metres per minute, evaluates the published equations, and returns your VDOT along with the intermediate velocity and percent-of-maximum values so you can see how the result is built.
Daniels-Gilbert VDOT formula
velocity (m/min) = distance (m) / time (min)
percent VO2max = 0.8 + 0.1894393*e^(-0.012778*t) + 0.2989558*e^(-0.1932605*t)
oxygen cost = -4.60 + 0.182258*velocity + 0.000104*velocity^2
VDOT = oxygen cost / percent VO2max
Worked example: 5,000 m in 21.5 min gives velocity = 232.56 m/min. Percent VO2max at t = 21.5 is about 0.9486. Oxygen cost = -4.60 + 42.39 + 5.62 = 43.41, so VDOT = 43.41 / 0.9486 = 45.76.
Notes on VDOT
- VDOT is an effective VO2max derived from performance, not a laboratory measurement.
- The percent-of-maximum term falls as race duration rises, reflecting that longer races are run at a lower fraction of maximum.
- Use a recent all-out race for the most representative result.
- The oxygen-cost term is calibrated for distance running on level ground.
- VDOT can be used to set training paces and to compare predicted times across distances.
VDOT: frequently asked questions
What is VDOT?
VDOT is a single number that summarises running fitness, popularised by coach Jack Daniels. It is derived from the Daniels-Gilbert equations, which estimate the oxygen cost of running at race velocity and the percentage of maximal oxygen uptake a runner can sustain for the race duration. Dividing the oxygen cost by that percentage yields a VDOT, an effective VO2max.
What equations does this calculator use?
It uses the published Daniels-Gilbert model: percent of VO2max equals 0.8 + 0.1894393 times e to the power of (-0.012778 times minutes) + 0.2989558 times e to the power of (-0.1932605 times minutes); oxygen cost equals -4.60 + 0.182258 times velocity + 0.000104 times velocity squared, where velocity is metres per minute; VDOT equals oxygen cost divided by percent of VO2max.
What do I enter?
Enter the race distance in metres and your finishing time in minutes. For example a 5 km race is 5,000 metres, and a 21 minute 30 second finish is 21.5 minutes. The calculator returns your velocity, the percent of VO2max sustained, and your VDOT.
Is VDOT the same as VO2max?
Not exactly. VDOT is an effective or pseudo VO2max derived purely from running performance. It bundles running economy and the fraction of maximum a runner can hold for the race into one performance index, so two runners with the same laboratory VO2max can have different VDOTs.
Why use VDOT for training?
A VDOT lets a runner set training paces (easy, marathon, threshold, interval, repetition) consistent with current fitness, and compare predicted times across distances. It turns a single race result into a structured set of effort levels.
Official sources
- National Center for Biotechnology Information (PubMed): Running economy and VO2max literature.
- U.S. Centers for Disease Control and Prevention: Physical activity basics.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.