Predicting one time from another
You have just run 10 km in 50 minutes and wonder what might be possible in a marathon? That is exactly the question the Riegel formula answers. US engineer Peter Riegel derived it in the late 1970s from record times in several endurance sports. It is still the best-known rule of thumb for finish-time predictions.
The formula
The Riegel formula is: T₂ = T₁ × (D₂ ÷ D₁)^1.06.
1. T₁ is your known time, D₁ the matching distance.
2. D₂ is the distance you want a prediction for.
3. The exponent 1.06 makes the pace slower over longer distances.
Without the exponent you would simply scale up your pace, as if you could hold your 10K speed for 42 km. Nobody can. With 1.06, doubling the distance does not double the time but multiplies it by about 2.08.
Worked example
Your 10K time is 50:00, or 3,000 seconds. For the half marathon:
1. Distance ratio: 21.0975 ÷ 10 = 2.10975.
2. To the power of 1.06: 2.10975^1.06 ≈ 2.2064.
3. Time: 3,000 seconds × 2.2064 ≈ 6,619 seconds, or about 1:50:19.
For the marathon the same steps give a factor of about 4.60, or roughly 3:50:00. The pace calculator shows these predictions for 5K, 10K, half marathon and marathon as soon as you enter a run.
| Your run | Predicted 10K | Predicted half | Predicted marathon |
|---|---|---|---|
| 5K in 25:00 | ≈ 52:07 | ≈ 1:55:00 | ≈ 3:59:46 |
| 10K in 45:00 | – | ≈ 1:39:17 | ≈ 3:27:00 |
| 10K in 50:00 | – | ≈ 1:50:19 | ≈ 3:50:00 |
| Half marathon in 1:45:00 | ≈ 47:35 | – | ≈ 3:38:55 |
When the formula fits well
The Riegel formula works best between about 1.5 km and the half marathon, and when you are similarly well trained for both distances. If you run 40 to 50 km a week and raced a 10K all-out, you will often get a fairly accurate estimate for the half marathon.
What matters is that your starting time comes from a real race or an honest time trial. An easy training run underestimates your potential; a run with a tailwind and a downhill course overestimates it.
Why the marathon prediction is often too optimistic
In the marathon many recreational runners finish well above the Riegel prediction. The reasons:
1. Energy stores: from about 30 km, carbohydrate stores run low. If you did not do enough long runs in training, you slow down markedly.
2. Training volume: the formula assumes you are prepared for the long distance. On 20 km a week, a marathon at the predicted pace is hardly achievable.
3. Experience: in a first marathon, the feel for the right pacing is often missing. Starting too fast costs many minutes at the end.
Some coaches therefore use a slightly higher exponent for the marathon, such as 1.07 or 1.08. From 50:00 over 10 km that gives roughly 3:53 to 3:57. For a first marathon this is often the more realistic target.
How to use the prediction sensibly
Treat the Riegel time as the upper limit of what would be possible with ideal preparation, not as a promise. For pacing, choose a slightly slower target pace and run the second half faster if things go well. How to calculate your pace and pace a race is explained in How to Calculate Your Running Pace, and how to split the two halves in Negative Split.
The prediction is a mathematical estimate, not training or health advice. If you are preparing for a marathon, build up your volume gradually and seek medical advice if you have any complaints.