How this calculator works
Riegel scaling uses your time for a known distance to estimate a time for a different distance. The model assumes that performance declines with distance following a power law, with the exponent 1.06 fitted to running data. A prediction from 10 km to a half marathon therefore extends the time by the ratio of distances raised to 1.06, which is a little more than the straight ratio and reflects the extra fatigue of the longer race.
Formula
Predicted time = known time x (new distance / known distance)^1.06. Predicted pace per km = predicted time / new distance in km. Speed = new distance / predicted time.
Worked example
A 50:00 10 km is 3,000 seconds. A half marathon is 21,097.5 m, so the ratio is 2.10975. Raising it to 1.06 gives 2.2062, and 3,000 x 2.2062 = 6,618.6 seconds, which is 1:50:19. The pace is 6,618.6 / 21.0975 = 313.7 seconds per kilometre, or 5:14. A marathon from the same run predicts 3,000 x (42.195 / 10)^1.06 = 13,800 seconds, or 3:50:00.
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Frequently asked questions
What is the Riegel exponent?
The original Riegel model uses 1.06. A value near 1.05 to 1.08 is typical for trained runners, and endurance specialists sometimes use a lower value while fast-twitch runners may need a higher one. The page uses the published 1.06.
Which run should I use as the input?
Use a recent race or time trial at a similar effort, ideally within the last few weeks and on a comparable course. A training run usually understates race fitness because it is not all out.
Why is the prediction less reliable for a marathon?
The power law fits well over moderate changes in distance. Extrapolating from a 5 km to a marathon is a fourfold increase and ignores long-run endurance, fuelling and heat, so treat the number as a starting target rather than a forecast.
Does the prediction include transitions or stops?
No. It applies to running only. Add any planned walking, toilet stops or aid-station time separately if your race involves them.