How it works
T₂ = T₁ · (D₂/D₁)^1.06 (Riegel; + Cameron and VDOT)
All three models translate the fitness shown by one race into an equivalent time at another distance. **Riegel** raises the distance ratio to a fatigue exponent of 1.06: T₂ = T₁·(D₂/D₁)^1.06 — the de-facto standard predictor. **Cameron** uses a velocity-fade factor fitted to world-best times, accurate across 800 m to the marathon. **VDOT** (Daniels & Gilbert) finds the time at the target distance that shares your race’s VDOT, the pseudo-VO₂max behind Daniels’ equivalent-performance tables. The headline number is the mean of the three; the range shows the fastest and slowest model. Predictions are most reliable when the target distance is close to the one you raced — the further apart they are, the more the models must extrapolate.
Sources
- Riegel endurance model Riegel, P. S. (1981). “Athletic Records and Human Endurance.” American Scientist 69(3), 285–290. Exponent 1.06 for adult runners.
- Cameron model David F. Cameron, race-time prediction model (1998), fitted to world-best times across 800 m–marathon.
- Daniels & Gilbert VDOT Jack Daniels & Jimmy Gilbert, “Oxygen Power: Performance Tables for Distance Runners” (1979); Jack Daniels, “Daniels’ Running Formula” (Human Kinetics).
FAQ
How does a race time predictor work?
It takes the time you ran at one distance and scales it to another using a model of how runners slow down as distance grows. This calculator runs three respected models at once and averages them, so you get a balanced estimate rather than relying on a single formula.
Which recent race gives the best prediction?
Use a recent, hard effort at a distance close to your target. Predicting a 10K from a 5K is very reliable; predicting a marathon from a 5K is far less so. The nearer the two distances, the tighter the model agreement and the more you can trust the number.
Why do the three models disagree?
Riegel, Cameron and VDOT each describe endurance fade slightly differently and were fitted to different data. Small disagreements are normal and healthy — the range between them tells you how confident to be. Tight cluster: trust it. Wide spread: treat it as a rough guide.
How accurate are race predictions?
They assume similar training, even pacing and good conditions. They are realistic targets for a well-prepared runner, not guarantees. Heat, hills, fuelling and race tactics can all move your actual time, especially over longer distances.
Can I predict a shorter race from a longer one?
Yes. The models work in both directions — predict a fast 5K from your half-marathon fitness, or a marathon from a 10K. Just remember that endurance and speed are not perfectly interchangeable, so cross-distance predictions are estimates.
What is VDOT and why is it one of the models?
VDOT is Jack Daniels’ measure of running fitness — a pseudo-VO₂max derived from race results. Including it alongside Riegel and Cameron adds a physiology-based view to the two empirical models. See the VDOT calculator to find your score directly.
Race predictions are mathematical estimates from published models (Riegel, Cameron, Daniels & Gilbert), not guarantees of performance. Training, pacing, weather and course all affect the result. General information for training, not medical or coaching advice.