Riegel’s formula
Race time predictor
Put in a recent race and see what it suggests for other distances, from the mile to the marathon.
Predicted times
Predicted half marathon
1:55:00
exponent 1.06 (Riegel’s default)
| Distance | Time | Pace |
|---|---|---|
| 1 mile1.6093 km · 1.00 mi | 7:31 | 4:40 /km 7:31 /mi |
| 5K5 km · 3.11 miYour race | 25:00 | 5:00 /km 8:03 /mi |
| 10K10 km · 6.21 mi | 52:07 | 5:13 /km 8:23 /mi |
| 10 miles16.0934 km · 10.00 mi | 1:26:19 | 5:22 /km 8:38 /mi |
| Half marathon21.0975 km · 13.11 mi | 1:55:00 | 5:27 /km 8:46 /mi |
| Marathon42.195 km · 26.22 miLikely too fast unless trained for it | 3:59:47 | 5:41 /km 9:09 /mi |
How the prediction works
Riegel’s formula scales your time by the ratio of the distances, raised to a power: T2 = T1 × (D2 ÷ D1)1.06. A 25:00 5K suggests 52:07 for 10K, a little slower per kilometre, because nobody holds 5K pace for twice as long.
The exponent sets how much you slow down as races get longer. Riegel’s formula uses 1.06; move the slider up if your longer races fade more than that, or down if you hold pace well.
When to trust it
It is most useful between nearby distances, from races you have trained for. In a study of recreational runners it was well calibrated up to the half marathon but predicted marathons too fast, by 10 minutes or more for half of them. A 5K time only predicts a marathon if your training has been built for the marathon too, and past the marathon the formula is least reliable. Heat, hills and a crowded start all cost time it cannot see.
Sources
- The formula and its exponent of 1.06: Riegel PS. Athletic Records and Human Endurance. American Scientist 69(3), 285–290 (1981).
- Accuracy for recreational runners: Vickers AJ, Vertosick EA. An empirical study of race times in recreational endurance runners. BMC Sports Science, Medicine and Rehabilitation 8, 26 (2016).
- Half marathon 21.0975 km and marathon 42.195 km: World Athletics, Terms and Abbreviations (July 2023); 1 mile = 1.609 344 km: NIST SP 811, Appendix B.8.
Questions
How accurate is Riegel’s formula?
Close between nearby distances, such as 5K to 10K, and less so as the gap grows. For recreational marathon runners it tends to be too optimistic, so treat a marathon prediction as a best case.
Which exponent should I use?
Start with 1.06. With two recent races you can work out your own: divide the natural log of the time ratio by the natural log of the distance ratio, and set the slider to that.
Can it predict an ultramarathon?
You can add a distance up to 100 km, but treat anything past the marathon as a rough guess: walking breaks, terrain and fuelling matter more there than any formula.