Running

Race Time Predictor

Enter a recent race and get predicted times for the mile, 5K, 10K, half marathon and marathon, based on Peter Riegel’s formula.

Updated · Sources

Units
km
Your time
km
More options

Riegel’s value is 1.06. A higher number assumes you slow down more as the distance grows, which gives more cautious predictions for long races.

RunningRace predictor

Predicted Half marathon

1:50:19

Pace /km
5:14
Speed
11.5 km/h
Exponent
1.06
Working50:00 × (21.098 ÷ 10)^1.06 = 1:50:19

Predictions from 10 km in 50:00

RaceTimePace /km
1 mile7:134:29
5K23:594:48
10K50:005:00
Half marathon1:50:195:14
Marathon3:50:015:27

How it works

Peter Riegel, an engineer and runner, noticed that world records at different distances followed a simple pattern. As the distance goes up, time goes up a little faster than distance does, because you cannot hold the same pace for longer. He described it with one equation, published in 1981, which is still one of the most widely used race predictors.

The key number is the exponent, 1.06. If it were exactly 1, doubling the distance would double your time. At 1.06, doubling the distance multiplies your time by about 2.085, so a runner who does 25:00 for 5K is predicted to run about 52:07 for 10K.

The prediction assumes you are equally well trained for both distances. If you have done the endurance work for a half marathon, the number is a fair target. If your training is built around 5K races, the longer predictions will be too optimistic.

The formula

Formula
T2 = T1 × (D2 ÷ D1) ^ 1.06

T1 = your race time        D1 = your race distance
T2 = predicted time        D2 = distance to predict

Worked example

You ran a 10K in 50:00 and want a half marathon prediction.

  1. Distance ratio: 21.0975 ÷ 10 = 2.10975.
  2. Raise it to the power 1.06: 2.109751.06 = 2.2065.
  3. Multiply by your time: 50 minutes × 2.2065 = 110.32 minutes.
  4. That is a predicted half marathon of 1:50:19, or about 5:14 per km.

The same method predicts a 3:50:00 marathon from that 10K.

A note on marathon predictions

Riegel fitted his formula to world records, and those athletes are trained for the distances they race. Most recreational runners are not. A 2016 study by Vickers and Vertosick of 2,303 recreational runners found the Riegel formula well calibrated for races up to the half marathon, but its marathon predictions were at least 10 minutes too fast for about half of the runners.

If you are using a short race to set a marathon goal, treat the prediction as a best case. A half marathon result gives a better starting point than a 5K. You can also raise the exponent under More options to get a more cautious number.

Questions

Which race should I enter?

Use a recent race or time trial that you ran at full effort on a flat course, in normal weather. The closer it is in distance to your goal race, the more reliable the prediction.

What exponent should I use?

Keep 1.06 unless you have a reason to change it. It is the value Riegel found in world records. Raising it, for example to 1.08, assumes you slow down more as races get longer, which suits newer runners or big jumps in distance.

Can I predict a shorter race from a longer one?

Yes. The formula works in both directions, so a half marathon time also predicts your 5K. The same limits apply: the prediction assumes similar training and conditions.

How is this different from the VO2 max calculator?

The VO2 max calculator uses a different model, from Jack Daniels and Jimmy Gilbert, based on the oxygen cost of running. For common race distances the two methods usually land close together, so a big gap between them is a sign to check your input.

Does it work for trail races or hilly courses?

Not well. Hills, surface, altitude and heat all change how long a race takes, and the formula knows nothing about them. It works best between road races on similar courses.

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Sources

  1. Riegel PS. Athletic records and human endurance. American Scientist. 1981;69(3):285-290.
  2. Vickers AJ, Vertosick EA. An empirical study of race times in recreational endurance runners. BMC Sports Science, Medicine and Rehabilitation. 2016;8:26.