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Race time predictor (Riegel formula)

Short answer

Riegel's formula predicts a time for a new distance as T₂ = T₁ × (D₂ ÷ D₁)^1.06. From a 25:00 5K it predicts 52:07 for 10K, 1:55:00 for the half marathon and 3:59:47 for the marathon. A study of 2,303 recreational runners found it well calibrated up to the half but often 10 minutes or more too fast for the marathon.

Last reviewed 27 October 20262 published sourcesNot medical advice

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Race time predictor

Use a recent, all-out race or time trial.

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Enter a recent race distance and time to see your predictions.

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The formula

Riegel fitted world-record times across endurance sports and found time rises as a power of distance: T₂ = T₁ × (D₂ ÷ D₁)^k, where k is a fatigue factor a little above 1 (Riegel, 1981).

Vickers and Vertosick note Riegel cited k of about 1.08 for elite runners and 1.05–1.06 for male recreational runners aged 40–70, and that a widely used online calculator uses 1.06 (Vickers & Vertosick, 2016). This page shows 1.06, 1.07 and 1.08 side by side.

Predictions from a 5K time (k = 1.06)
5K10KHalf marathonMarathon
20:0041:421:32:003:11:49
22:3046:551:43:303:35:48
25:0052:071:55:003:59:47
27:3057:202:06:304:23:45
30:001:02:332:18:004:47:44
35:001:12:582:41:005:35:41
T₂ = T₁ × (D₂ ÷ D₁)^1.06. From a 25:00 5K the marathon prediction is 3:59:47 at k = 1.06, 4:04:57 at k = 1.07, 4:10:14 at k = 1.08.

Why marathons run slower than predicted

In the same study, adding typical weekly mileage to a prior race time cut the marathon prediction error substantially compared with Riegel alone, which suggests training volume matters most over 42 km (Vickers & Vertosick, 2016).

Turn a goal time into a per-km or per-mile pace with the pace calculator, and check your aerobic fitness with the VO2 max calculator.

Train for the time you want

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Common questions

How accurate is the Riegel formula?

Vickers and Vertosick tested it on 2,303 recreational runners. It was well calibrated for 10K and half-marathon predictions, but for the marathon it was 10 minutes or more too fast for about half of runners, and more than 20 minutes too fast for nearly a quarter.

What fatigue factor should I use?

Riegel cited about 1.08 for elite runners and 1.05–1.06 for male recreational runners aged 40 to 70; popular calculators use 1.06. For the marathon, the slower 1.07 and 1.08 columns are the safer pacing guide.

What race should I predict from?

A recent all-out race or time trial, ideally the longest you have run, run on a flat course in good conditions. A training run at an easy pace will give predictions that are far too slow.

Sources

Figures on this page were checked against these publications on 27 October 2026.

  1. Riegel PS. Athletic records and human endurance. American Scientist. 1981;69(3):285–290. www.jstor.org/stable/27850427
  2. Vickers AJ, Vertosick EA. An empirical study of race times in recreational endurance runners. BMC Sports Science, Medicine and Rehabilitation. 2016;8:26. doi.org/10.1186/s13102-016-0052-y

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