Our own calculation, 7 November 2026, for the article "Riegel's formula and the marathon". The formula and its calibration come from the sources; the half-marathon times are example inputs; every prediction is computed two ways (the power form and the log form) and the two agree.
Inputs
- Riegel's formula: T2 = T1 x (D2 / D1)^1.06, with D1 = 21.0975 km (half marathon) and D2 = 42.195 km (marathon), so D2 / D1 = 2.0000.
- Vickers and Vertosick (2016), BMC Sports Science, Medicine and Rehabilitation: an internet survey of 2,303 recreational endurance runners; the Riegel formula was well calibrated for races up to the half marathon but dramatically underestimated marathon time, giving times at least 10 minutes too fast for half of runners; mean squared error 381 for Riegel against 228 and 208 for the authors' models from one and two prior races.
What we found
- Doubling the distance at exponent 1.06 slows the pace by 4.25%: 2^1.06 = 2.0849, so the marathon takes 2.0849 times the half-marathon time, not 2.
- A 2:00:00 half gives a Riegel marathon of 4:10:12: 7,200 s x 2.0849; in logs, exp(ln 7,200 + 1.06 x ln 2.0000) is the same 15011.5 s.
- Vickers and Vertosick's finding applied to that runner: at least half of recreational runners would finish 10 minutes or more slower than 4:10:12, that is 4:20:12 or later; the formula is a floor for most, not a forecast.
- The same holds across the range: a 1:30 half predicts 3:07:39, a 2:30 half 5:12:44; add at least 10 minutes for the median recreational runner.
Check it yourself
| Half marathon | Riegel marathon (power form) | Log form | Plus 10 minutes (half of runners at least this slow) |
|---|---|---|---|
| 1:30:00 | 3:07:39 | 3:07:39 | 3:17:39 |
| 1:45:00 | 3:38:55 | 3:38:55 | 3:48:55 |
| 2:00:00 | 4:10:12 | 4:10:12 | 4:20:12 |
| 2:15:00 | 4:41:28 | 4:41:28 | 4:51:28 |
| 2:30:00 | 5:12:44 | 5:12:44 | 5:22:44 |
Second way: ln(7,200) + 1.06 x ln(2.0000) = 8.8818 + 0.7347 = 9.6166; exp of that is 15011.5 s = 4:10:12. Same.
What this cannot tell you: your own marathon time; the study gives a lower bound for half of its recreational runners, not a correction for you; training mileage, pacing and conditions move the result.