Predict a running time across race distances, work backward from a goal, or use two performances to calculate a personal fatigue exponent.
How the Race Time Predictor Works
The predictor scales a known performance by the ratio between target and source distance. A fatigue exponent accounts for the slowing that normally appears as races get longer.
Use one-race mode for a quick projection, reverse mode for a qualifying target, or personal mode when two recent comparable efforts are available.
Formula and Method
Formula: T2 = T1 x (D2 / D1)^k
A conventional default exponent is 1.06; it is not a universal physiological constant. Personal mode derives k from two results with k = ln(T2 / T1) / ln(D2 / D1), then anchors the projection on the longer race.
Choosing the Right Inputs
Use performances that reflect similar fitness and race effort. Distances are converted to meters before the formula runs. Enter times as decimal seconds, minutes or hours: 20 minutes 30 seconds is 20.5 minutes. Distance suggestions include a mile, 5K, 10K, half marathon and marathon; custom values are accepted. Clock results round to the nearest second, while subsecond estimates use decimal seconds. Pace and speed always describe the target race, including reverse mode.
| Exponent | Typical use | Effect at longer distances |
|---|---|---|
| 1.06 | Standard Riegel starting value | Fastest of these example projections |
| 1.08 | More fatigue allowance | Moderately longer prediction |
| 1.10 | Still more fatigue allowance | Longest prediction |
Understanding Your Results
The primary time is followed by kilometer and mile pace, speed, distance ratio, time multiplier, and the exponent used.
A higher exponent produces a slower long-distance prediction. The number is a performance model, not a promise.
Worked Example
A 20:00 5K with k = 1.06 predicts a 41:42 10K. A 45:00 10K predicts a 1:39:17 half marathon.
Common Mistakes
Do not compare unequal-effort races in personal mode, reverse the distance ratio, or reuse rounded pace as an input to another step.
Assumptions and Limitations
Riegel's original endurance range was approximately 3.5 to 230 minutes. Recreational marathon outcomes can be slower than a fixed-exponent projection because training, fueling, weather, terrain, and durability are not inputs.
Sources
Peter S. Riegel. Athletic Records and Human Endurance. American Scientist, 1981.
Andrew J. Vickers and Emily A. Vertosick. An Empirical Study of Race Times in Recreational Endurance Runners. BMC Sports Science, Medicine and Rehabilitation, 2016.
