Marathon Time Predictor from a Recent Race (Riegel Formula)

How to use it

Choose the Recent race distance you ran. For any other length, choose Custom distance and type it in kilometres.
Type your finishing time in Recent race time, such as 50:00 or 1:45:30.
Read the Predicted marathon time and the Marathon pace per km.
Open Predicted times for each race distance to see the 5 km, 10 km and half marathon times and their paces.

How Riegel's formula works

Peter Riegel published the formula in 1981 in the article "Athletic Records and Human Endurance" in American Scientist. It assumes that the time for a new distance follows the same power law as the recent race: the new time is the known time multiplied by the ratio of the distances raised to the power 1.06.

The pace per km is the predicted time divided by the distance. Because the exponent is above 1, the pace slows as the distance grows: the longer the race, the more seconds each kilometre takes.

T2 = T1 × (D2 ÷ D1)^1.06

T1  your recent race time
D1  your recent race distance (km)
D2  the distance to predict (km)
1.06  the endurance exponent of Riegel's formula

Why a short race predicts a marathon too fast

The formula uses one exponent for every distance. A marathon asks for more endurance, more long training runs and more fuelling than a 5 km or 10 km race tests. A runner who has not trained for the length of a marathon often runs it slower than the prediction, so the marathon figure from a short race is optimistic.

The effect is smaller for a half marathon, which is closer in length to the marathon than a 5 km race is. A recent all-out race of 10 km or more is usually the better basis for a marathon prediction.

What this calculator does not include

Training, sleep, heat, hills and the course. One race is a sample of your fitness on one day.
Your own endurance. The exponent is an average for runners; a stronger or weaker endurance than average changes the real time.

Worked example: 10 km in 50:00

The 5 km time is 50:00 × (5 ÷ 10)^1.06 = 3,000 × 0.479640 = 1,438.9 seconds, which is 23:59. The pace is 288 seconds per km, or 4:48.

The half marathon is 3,000 × (21.0975 ÷ 10)^1.06 = 6,619 seconds, which is 1:50:19 at a pace of 5:14 per km.

The marathon is 3,000 × (42.195 ÷ 10)^1.06 = 13,801 seconds, which is 3:50:01 at a pace of 5:27 per km. A runner who has not trained for the full distance would usually be slower than this on race day.

Race	Predicted time	Pace per km
5 km	23:59	4:48
Half marathon	1:50:19	5:14
Marathon	3:50:01	5:27

Frequently asked questions

What is Riegel's formula?

It predicts the time over a new distance from a recent race: the race time is multiplied by the ratio of the distances raised to the power 1.06. Peter Riegel published it in 1981 in American Scientist.

Is a marathon time predicted from a 5K accurate?

It is usually too fast, because a 5K does not test the endurance and long training runs a marathon needs. A recent race of 10 km or more gives a more realistic marathon prediction.

Which race should I type in?

Use a recent race you ran all out, on a course and in weather you can compare with your goal race. A race of 10 km or the half marathon usually gives a better basis for a marathon than a 5 km race.

Does the prediction allow for heat or hills?

No. The formula uses only the race time and the distances. Heat, hills, wind and the course change the result, so adjust the time yourself if your race will be very different from the one you ran.

What does the exponent 1.06 mean?

It is the endurance factor in Riegel's formula. A larger exponent predicts a slower time over a longer distance from the same short race, so 1.06 is the value that the calculator uses for every prediction.

How accurate is the prediction?

It estimates what you could run on a good day with training for that distance. It cannot know your training, so compare the predictions with times you have already run.

Sources

Figures and text last checked on Tuesday, November 10, 2026.

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