The Riegel formula predicts how fast a runner should complete one distance based on a known time at another distance. It was published by Robert Riegel in "Athletic Records and Human Endurance," American Scientist, Vol. 69, 1981.
Formula: T₂ = T₁ × (D₂ / D₁)^1.06
Where T₁ is the known race time, D₁ is the known distance, T₂ is the predicted time, and D₂ is the target distance. The exponent 1.06 was fitted to world record data across distances from 1 mile to 100 miles.
The exponent greater than 1 captures the fatigue premium at longer distances: doubling the distance costs more than doubling the time. A 10K runner who runs 40:00 does not simply run a marathon in 40:00 × (42.195/10) = 168:46 (2:48:46). The Riegel formula predicts 3:13:59 — significantly slower, reflecting the additional physiological toll of 42 km.
Known limitations: the formula was derived from competitive runners. The exponent may underestimate the fatigue premium for recreational runners who positive-split or hit the wall. It's also less accurate for very large distance gaps (predicting a marathon from a 1K or 5K) than for adjacent standard distances.