Race time predictor: equivalent times across distances

Predictions use Riegel's formula (1981): T2 = T1 × (D2/D1)^1.06. The exponent is empirical and drifts at ultramarathon distances.

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Enter a recent race result and this page predicts the equivalent times at 5K, half marathon and marathon distance, with the pace each one requires. The prediction comes from Riegel's formula — one line of arithmetic, documented on /sources — and it is worth understanding its limits before you use the numbers.

The formula

T₂ = T₁ × (D₂/D₁)^1.06

T₁ is a known time over distance D₁; T₂ is the predicted time over distance D₂. The exponent 1.06 is empirical: it was fitted to record performances (Riegel, 1981) and captures the fact that doubling the distance costs you more than double the time.

Read the table from left to right and the arithmetic is doing three jobs at once: scaling the time, converting the distance, and giving you the pace that follows. The row marked as your input is not a prediction — it reproduces the result you entered, which is a useful check that the distances were read the way you intended.

Where it works

Riegel's formula is a good description when:

• the two distances are within a factor of about four of each other (5K to half marathon, 10K to marathon);
• both results come from comparable efforts on comparable surfaces;
• you are comparing fitness, not predicting a specific race day.

It is a bad description when:

• the distances are far apart. Stretching a 5K to a marathon assumes endurance you may not have built; the formula does not know about fuelling or the last 10 km of a marathon.
• the surface or terrain differs. A road 10K says little about a mountain ultra.
• the input came from a training run. A tempo run is not a maximal effort, so the prediction will be conservative by however much you held back.
• you are looking at ultramarathon distances. Beyond the marathon the exponent tends to understate the slowdown.

The formula also has a well-known asymmetry: predicting down from a long race to a short one is usually more reliable than predicting up, because speed is easier to retain than endurance.

Using a prediction sensibly

A predicted time is a description of what your current fitness implies, not a target you are owed:

1. Compare, do not commit. A predicted marathon of 3:05 does not mean 3:00 is impossible — it means the gap is about seven seconds per kilometre at your current fitness.
2. Cross-check with a second distance. If a 10K predicts 1:28 and a half marathon predicts 1:40, the inconsistency is information: one of the two was not a maximal effort.
3. Re-run it after a real race. The prediction is only as good as the result you feed it.

For training intensities around a predicted result, use the VDOT calculator. For the pace of any finish time, the pace calculator and the three charts (5K, half marathon, marathon) cover the common cases exactly.