Race Time Predictor

One race tells you something about every other race, because running speed falls away with distance in a way that is remarkably consistent between people. Peter Riegel put that into a power law in 1981 and almost every race predictor since has been the same equation with a different exponent in it. This page shows the exponent instead of hiding it, lets you swap between the three published values, and prints the one thing the studies agree the formula gets wrong: the marathon comes out too fast.

How it is calculated

predicted time = known time × (target distance ÷ known distance) ^ b

Everything rides on b, the fatigue factor. Riegel published sex-specific values of 1.055 for men and 1.08 for women; the pooled 1.06 is the number most calculators use without saying so, and modern refits of record data spread from about 1.04 to 1.12 depending on the discipline. At a fifty-minute 10 km the three values here separate the marathon prediction by more than eight minutes, which is a fair measure of how much confidence the method deserves.

Source: Karr JA Jr, Fryer RM, Darden B, et al., "NRCD: An Open Database of Collegiate Running with Unified Performance Standardization", arXiv:2608.14776, footnote 1 — "We adopt Riegel's gender-specific fatigue factors (b=1.055 men, 1.08 women), not a pooled population b. Classical Riegel and later predictors often use b=1.06; modern record refits vary by discipline (≈1.04–1.12)."

Questions people ask

Why is the marathon prediction optimistic?

Because the power law knows nothing about running out of fuel. A 2016 study of recreational endurance runners found the Riegel formula "well-calibrated for races up to a half-marathon, but dramatically underestimated marathon time, giving times at least 10 min too fast for half of runners". Treat the marathon row as a ceiling rather than a target.

Which fatigue factor should I pick?

The classical 1.06 if you want the number other calculators show, and the sex-specific 1.055 or 1.08 if you want the values Riegel actually published. The higher the exponent, the more the prediction slows you down over longer distances, which is why the women's figure gives the most conservative marathon.

Does it work in both directions?

Arithmetically, yes — feeding a marathon in gives shorter predictions, and the equation is symmetric. In practice the errors are not. Predicting down from a long race tends to be kinder than predicting up from a short one, because the thing the formula ignores only bites at the long end.

Why does the distance I entered come back unchanged?

Because the ratio of a distance to itself is one, and one raised to any power is one. That row is a free sanity check: if it does not match the time you typed, something in the input is wrong.

What does this not account for?

Hills, heat, wind, how long you have been training, and whether you have ever raced the distance before. The exponent is a population average fitted to race results, not a model of you. It is a starting point for a pace discussion, not a plan.

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