Race time predictor
Give it a recent race and it predicts another distance using Riegel's formula — and tells you when you have pushed the formula past where it was fitted, instead of quietly returning a number anyway.
A recent race
Prediction
T₂ = T₁ × (D₂ ÷ D₁)^1.06 — Peter Riegel's endurance formula, published in American Scientist in 1981. The 1.06 exponent is the rate at which pace decays as distance grows, fitted to world records between roughly 3.5 and 230 minutes.
A prediction assumes you have trained for the distance. Get the training paces that would earn it →
How the math works
T₂ = T₁ × (D₂ ÷ D₁)^1.06. Your known time, multiplied by the ratio of the distances raised to the fatigue exponent. If the exponent were exactly 1, doubling the distance would exactly double the time — the 0.06 is the penalty that reality charges for going further.
Riegel derived endurance coefficients across a range of sports — running, race walking, skating, cycling and swimming — rather than a single constant for all of them, and reported different values for different populations: nearer 1.08 for elite runners and around 1.05–1.06 for older recreational men. The 1.06 used here is the widely applied running figure, which is part of why it is only ever approximately right for any individual.
What the formula predicts from a 20:00 5 K
| Distance | Predicted | Confidence |
|---|---|---|
| 1500 m | 5:35 | Good — close to the known distance |
| 10 K | 41:42 | Strongest case for the formula |
| Half marathon | 1:32:00 | Reasonable with the endurance base |
| Marathon | 3:11:49 | Only with marathon-specific training |
Honest caveats
The formula assumes equivalent training for both distances, and that assumption does almost all of the damage. It is at its best predicting a neighbouring distance from a genuinely all-out effort — 5 K to 10 K is where it earns its reputation. It degrades as the gap widens, which is why this page warns you rather than staying silent when the ratio exceeds fourfold.
You will not find a made-up percentage margin here. Riegel published an exponent, not an error bar, and inventing one would be exactly the kind of false precision this site exists to avoid. If you want paces to train at rather than a time to aim for, the VDOT calculator is the better tool; to plan the race itself, use the pace calculator.
Common questions
Where does the 1.06 exponent come from?+−
Peter Riegel fitted it to world-record data and published it in American Scientist in 1981. It describes how much pace decays as distance grows: doubling the distance costs you about 4% more than simply doubling the time (2^1.06 = 2.085). He fitted it in what he called the endurance range, roughly three and a half minutes to just under four hours, and it has held up remarkably well for a formula with a single constant.
Why can I not predict a 100, 200 or 400?+−
Because they are a different energy system and Riegel has nothing honest to say about them. Sprints are powered largely anaerobically and are limited by neuromuscular power and technique rather than by the aerobic endurance the formula models. Plugging a 400 m time in would produce a number, and that number would be meaningless — so those distances are simply absent rather than quietly wrong.
Why is my actual marathon slower than the prediction?+−
Almost always because the formula assumes you are equally trained for both distances, and most people are not. A 10 K predicts a marathon accurately only if you have done the long runs and worked out your fuelling. Riegel models fatigue, not glycogen depletion, not gut tolerance and not the specific durability that marathon training builds.
Riegel or VDOT — which should I use?+−
Riegel to answer “what might I run”, VDOT to answer “how should I train”. They come at the same problem differently: Riegel is one exponent fitted to records, while Daniels’ VDOT models oxygen cost and the fraction of capacity you can hold. Their predictions are usually close. VDOT has the advantage of also handing you training paces.
A prediction is a hypothesis. Training is the test.
Twelve weeks built on the muscles that put force into the ground — periodized, with deload weeks, and a demo for every lift.