What is the Riegel formula for race prediction?
A power law that converts a race time at one distance into a predicted time at another: T₂ = T₁ × (D₂/D₁)^1.06. Roughly 80% accurate for general populations.
Peter Riegel proposed in 1981 that race times scale with distance according to a power law with an exponent of about 1.06. Double the distance and your time slightly more than doubles — the exponent above 1.0 captures the fact that you cannot hold a shorter race's pace over a longer one.
It works well between adjacent distances. Predicting a half marathon from a 10 km, or a 10 km from a 5 km, is generally accurate to within a few percent for trained runners. It also has the practical virtue of needing only one input, which is why every pace calculator in existence uses it.
It degrades in two directions. Predicting a marathon from a 5 km extrapolates a long way and systematically flatters the runner, because the marathon is limited by fuelling and durability rather than by the aerobic power that a 5 km tests. And it applies a single exponent to everyone, when in reality a high-mileage runner holds pace better over distance than a low-mileage one — a difference the formula cannot see.
Because of that, marathon predictions specifically deserve a higher exponent. This site uses about 1.08 whenever the marathon is one of the two distances, following work showing that a steeper exponent fits marathon results better.
Key numbers
| Formula | T₂ = T₁ × (D₂/D₁)^1.06 | |
|---|---|---|
| Marathon exponent | ~1.08 | when the marathon is in the pair |
| Accuracy | ~80% | general populations |
Work it out for yourself
Race time predictor — Convert any recent race result into predictions across every distance.
Frequently asked questions
How accurate is the Riegel formula for the marathon?
Less accurate than for shorter distances, and biased optimistic. The marathon is limited by glycogen, durability and pacing discipline as much as by aerobic power, none of which a 5 km or 10 km tests. Use a half marathon as the input where possible, and treat the output as a ceiling rather than a target.
Why does the exponent matter so much?
Because it compounds over the distance ratio. Predicting a marathon from a 10 km, changing the exponent from 1.06 to 1.08 shifts the prediction by several minutes — which is the difference between a realistic goal and a race that falls apart at 30 km.
Sources
- Riegel (1981). Athletic records and human endurance. American Scientist.
- Vickers & Vertosick (2016). An empirical study of race times in recreational endurance runners. BMC Sports Science, Medicine and Rehabilitation.
Related explainers
Glossary: Riegel Model