How it works
T_marathon = T_race · (42.195 km / D_race)^1.06 (Riegel; + Cameron, VDOT)
Each model answers the same question — what marathon matches your current race fitness — a different way. **Riegel** scales time by distance raised to a fatigue exponent of 1.06: T₂ = T₁·(D₂/D₁)^1.06. **Cameron** applies a velocity-fade factor fitted to world-best times, which tends to hold up well from 5K to the marathon. **VDOT** (Daniels & Gilbert) finds the marathon time that shares your race’s VDOT — its pseudo-VO₂max — by matching oxygen cost to the fraction of VO₂max you can sustain. The headline figure is the mean of the three; the range spans the fastest and slowest model so you can see how much they agree. The further your input distance is from the marathon, the wider that spread tends to be — predicting 26.2 miles from a 5K asks a lot of any model.
Sources
- Riegel endurance model Riegel, P. S. (1981). “Athletic Records and Human Endurance.” American Scientist 69(3), 285–290. The exponent 1.06 is Riegel’s value 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
Which race should I enter to predict my marathon?
A recent, hard half marathon gives the most reliable marathon prediction because it stresses the same endurance systems. A 10K or 15K also works well. The closer the input distance is to the marathon, the tighter and more trustworthy the prediction.
Why are there three different predictions?
Riegel, Cameron and VDOT each model endurance fade differently, so they rarely agree exactly. Showing all three plus a consensus and a range is more honest than a single number — if the models cluster tightly, you can trust the estimate more; if they spread out, treat it with caution.
How accurate is a marathon prediction?
Predictions assume marathon-specific endurance, good fuelling and even pacing — none of which a shorter race fully tests. They are realistic targets for a well-trained runner, not guarantees. Many first-time marathoners run slightly slower than predicted because the last 10 km exposes gaps in long-run training.
Can I predict a marathon from a 5K?
You can, but expect a wider range and more uncertainty. A 5K barely taps marathon endurance, so the models extrapolate a long way. Use it as a rough ceiling and re-check with a longer race as your training builds.
Does this account for the wall or fuelling?
No model can — they predict from race fitness alone. Hitting the wall, dehydration, heat and poor pacing can all add minutes. Use the predicted time to set a goal, then train your long runs and fuelling so you can actually hold it.
How do I turn the prediction into a pacing plan?
Take the predicted finish time to the marathon pace calculator for per-mile and per-kilometre splits, or plan a controlled second half with the negative split calculator.
Marathon predictions are mathematical estimates from published models (Riegel, Cameron, Daniels & Gilbert), not a guarantee of performance. Training, fuelling, weather and course all affect the result. General information for training, not medical or coaching advice.