What this calculator does
The Riegel formula predicts a time at a new distance from a known one: multiply the known time by the ratio of distances raised to the power 1.06. A 50 minute 10K predicts a 1:50:20 half marathon and a 3:50:02 marathon.
The exponent is what makes it work. If it were 1.0 the prediction would assume you hold the same pace at any distance, which nobody does. At 1.06 the predicted pace slows as distance rises, from 4:48 per km at 5K to 5:27 at the marathon for the same runner, which is roughly what actually happens.
The formula
The predicted time is the known time multiplied by the ratio of the new distance to the known distance, raised to the power of 1.06. The exponent was derived by Peter Riegel from race results across many distances. Predictions are most reliable when the two distances are close together, and least reliable when extrapolating from a short race to a marathon.
| Term | Meaning |
|---|---|
| Riegel formula | T₂ = T₁ × (D₂/D₁)^1.06, the standard race-time prediction relationship. |
| Fatigue exponent | The 1.06, which encodes how much pace slows as distance rises. |
| Extrapolation | Predicting far outside the known distance, which is where the formula is least reliable. |
The inputs explained
| Field | What to enter |
|---|---|
| Known distance (km) | The distance you have a time for, in kilometres. |
| Known time (min) | That time, in minutes. |
| Target distance (km) | The distance you want a prediction for, in kilometres. 21.1 is a half marathon and 42.2 a marathon. |
When to use it
Setting a goal time
A recent race at a shorter distance is the most common basis for a marathon goal, and this is the standard way of converting one to the other.
Choosing a pacing strategy
The predicted pace gives a target to hold rather than a finish time to hope for, which is the more useful form on race day.
Comparing performances across distances
A 10K and a half marathon run months apart can be compared by predicting one from the other and seeing which came out ahead.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What does a 50 minute 10K predict?
A 50 minute 10K projected to three other race distances.
| Target distance | Predicted finish time | Predicted pace | Predicted time (minutes) |
|---|---|---|---|
| 5 km | 23:59 | 4:48 /km | 24.0 min |
| 21.1 km | 1:50:20 | 5:14 /km | 110.3 min |
| 42.2 km | 3:50:02 | 5:27 /km | 230.0 min |
Questions
How accurate is the Riegel formula?
Reasonable between nearby distances, and progressively less so as the gap widens. Predicting a half marathon from a 10K is usually close. Predicting a marathon from a 5K is unreliable, because the marathon depends heavily on endurance training and fuelling that a 5K performance says nothing about.
Why 1.06?
Peter Riegel derived it empirically from race results across many distances in the 1970s. It represents the average rate at which pace declines with distance. Individual runners vary: those with more endurance base do better than 1.06 predicts at long distances, and speed-focused runners worse.
Does it work for the marathon?
Less well than for shorter distances, and it tends to be optimistic. The marathon introduces factors the formula cannot see, particularly glycogen depletion and the specific endurance that only long training builds. Many coaches use a higher exponent, around 1.07 to 1.10, for marathon predictions.
Can I predict a shorter race from a longer one?
Yes, the formula works in both directions, and predicting down is generally more reliable than predicting up. A marathon time predicts a 10K reasonably well, since the endurance required is already demonstrated and only the speed is in question.
For pace across a set distance, see the pace calculator. For training pace zones, see the training pace zones calculator.