Riegel's formula ran 10 minutes fast for half of 2,303 recreational runners

Runners often use Riegel’s formula to estimate their marathon finish based on a recent half marathon. The formula is simple, and for recreational runners it is optimistic: in the one large study that checked it, half the runners finished at least 10 minutes slower than it predicted [4]. Here is what the numbers show, where the formula works, and where it breaks down.

What Riegel’s Formula Claims

Riegel’s formula lets runners predict a finish time for a longer race based on a shorter one, using the equation:

T₂ = T₁ × (D₂ / D₁)¹·⁰⁶

where T₁ is the time for distance D₁, and T₂ is the predicted time for distance D₂. For marathon and half marathon, the ratio D₂ / D₁ is 2 (since a marathon is twice a half marathon in distance: 42.195 km vs 21.0975 km) [1, 2].

The exponent 1.06 is Riegel's published value; it encodes how pace slows as distance grows, 4.25% per doubling [5]. For a two-hour half marathoner, Riegel's formula predicts a marathon of 4:10:12, computed two ways on the site's data page: doubling the distance at exponent 1.06 slows the pace by 4.25% [5].

The Reality for Amateur Runners

Vickers and Vertosick surveyed 2,303 recreational endurance runners and tested the formula against their race times: it was well calibrated for races up to a half marathon, but dramatically underestimated marathon time, giving times at least 10 minutes too fast for half of runners [4]. Their models built from one or two prior races did better: a mean squared error of 228 and 208 against Riegel's 381 [4].

For the two-hour half marathoner, that means 4:10:12 is a floor rather than a forecast: half of recreational runners would finish at 4:20:12 or later [5]. The study also found that sex, age, BMI and race training were associated with race velocity at every distance, and that typical weekly mileage and interval training mattered at all distances [4]; the formula knows none of that.

Why the Prediction Misses for Most Amateurs

The formula's single exponent fits runners whose endurance scales evenly with distance; the survey found weekly mileage and training type associated with velocity at every distance [4], and recreational runners vary in both. In practice, many amateur runners:

• Race the half marathon with a higher relative effort than is sustainable for double the distance
• Have less marathon-specific endurance, so pace drops more sharply after 30 km
• May lack experience in fuelling and pacing over 42 km

Pacing and fuelling errors over the marathon distance add time the formula cannot foresee; the study's figure, at least 10 min too fast for half of runners, is a lower bound for that half, not a ceiling [4].

Across the range of half-marathon times

The formula scales the same way at every level: a 1:30:00 half predicts 3:07:39, a 1:45:00 half 3:38:55, a 2:15:00 half 4:41:28 and a 2:30:00 half 5:12:44, each computed two ways on the data page [5]. Adding the study's 10 minutes gives the time at least half of recreational runners would need [4,5].

How to Adjust Your Own Prediction

If you are an amateur runner aiming for your first marathon, treat Riegel's prediction as a best-case scenario, not a target: half of the recreational runners in the study finished at least 10 minutes slower than it [4], and the ones who matched it had the mileage and the pacing to hold the second half.

How to use the formula in practice:

1. Use your half marathon time for the prediction, but be realistic about your training.
2. Add at least 10 minutes to the predicted time unless you have strong marathon experience; the study's models from a prior race predicted better than the formula [4].
3. Use the formula to plan pacing, but listen to your body and adjust for conditions on race day.

Questions readers ask

Does Riegel’s formula work for other distances?

The formula works best for distances between 5 km and a marathon, especially for runners with a strong aerobic base [3]. For ultramarathon or shorter sprint distances, the exponent (1.06) often underestimates the slowdown.

Can I improve my prediction accuracy?

Yes. The study's own models, built from one or two prior races, predicted marathon time with a mean squared error of 228 and 208 against Riegel's 381 [4]: a recent race tells you more than the formula. As an example, a tune-up race of 30 km shows whether your pace holds late; marathon-specific long runs help close the gap.

Should I use my training run times or race times in the formula?

Race times are more reliable, as most runners push harder in races and conditions are more controlled. Training runs often include stops, slower pacing, and less optimal nutrition.

How the numbers work

These figures were computed for this article, not estimated by its writer. Inputs come from the numbered sources or are assumptions, labelled as such; change an assumption and the results change with it.

*Corrected 2026-11-07: Two sentences cited the study for figures it does not print (the exponent 1.06, which the data page states, and 42 km); they now cite the data page for the exponent and drop the distance figure.*

Sources

1. Marathon - Wikipedia
2. Half marathon - Wikipedia
3. Long-distance running - Wikipedia
4. Vickers, A. J. and Vertosick, E. A. (2016). An empirical study of race times in recreational endurance runners. BMC Sports Science, Medicine and Rehabilitation 8:26
5. Our own calculation (2026-11-07): Riegel's marathon prediction from a half, two ways, and the recreational-runner gap