Race Time Predictor

Pete Riegel published the endurance formula T2 = T1 * (D2 / D1)^1.06 in a 1981 paper titled Athletic Records and Human Endurance. He observed that across runners, swimmers, and cyclists, finish time scales with distance to a power slightly above 1, reflecting the fact that pace gets slower as the race gets longer. The 1.06 exponent fit the data for adult endurance athletes covering a few minutes to a few hours of effort, and it has held up well enough that it is still the default in most race-prediction calculators 40-plus years later.

Riegel is most reliable when the target distance is within roughly half to double the known distance. A 5K time predicts a 10K time fairly well, and a 10K time predicts a half marathon reasonably. Predictions tend to drift past 2x: a marathon predicted from a 5K usually reads several minutes optimistic because the formula does not model glycogen depletion, hydration loss, pacing decline, or training base. Use predictions as a starting point, not a goal time guarantee, and recalibrate after you actually race the longer distance.

The Riegel exponent assumes physiological decline scales smoothly with race duration, but the marathon adds problems that 5K does not have. Glycogen stores run out around mile 18 to 20 for runners who have not trained long enough to push that wall back, and pace falls off sharply after that. Heat, hydration, and pacing errors compound at the marathon distance. Most coaches recommend using 1.07 or 1.08 instead of 1.06 when projecting from a short race to a marathon, or using a marathon-specific calculator like Daniels' VDOT tables that adjust for distance more aggressively.

Jack Daniels' VDOT tables (used in the Daniels Running Formula book) map each race time to an equivalent VO2max-style score, and then read off the same score at any other distance. The VDOT system is more conservative than Riegel for long predictions because it accounts for training intensity zones. The Cameron formula, published by David Cameron in 1998, uses a slightly different power curve and tends to predict faster marathons than Riegel. Pete Riegel's own later work also explored a piecewise formula with different exponents for different distance ranges, which can be more accurate than a single 1.06 across the board.

The exponent is the fatigue factor: how much slower you get as the distance doubles. With exponent 1.06, doubling the distance increases your time by 2^1.06, or about 2.085 times, so you slow down by roughly 4.2% per doubling. A 1.0 exponent would mean perfectly even pace at every distance (impossible in reality). An exponent of 1.15 would mean a 10.9% slowdown per doubling, which fits ultra-distance runners better than 5K-to-marathon road racing. Trained, well-paced runners often see a fit closer to 1.05, while less-experienced runners with weaker endurance bases fit 1.07 or 1.08 better. Adjust the exponent if your past races show a consistent over- or under-prediction.