Body FormulaFitness

Race Time Predictor

One race result, two published models, and the gap between them printed rather than hidden. Predicting a marathon from a half, they disagree by four minutes.

A race you have actually run, and the one you are aiming at

A hard, recent effort. A training run at conversational pace predicts a training run.

Every distance is worked out in the table below whichever you pick here.

Predicted marathon3:41:01

from Half marathon in 1:45:00 — Riegel says 3:38:55, Cameron says 3:43:08

Riegel (1977) 3:38:55
Cameron (1998) 3:43:08
They differ by 4:13 min:sec

Distance Riegel Cameron Mean Pace / km
Mile 6:52 6:39 6:45 4:12
5K 22:50 22:52 22:51 4:34
10K 47:35 47:37 47:36 4:46
10 miles 1:18:48 1:18:44 1:18:46 4:54
Half marathon 1:45:00 1:45:00 1:45:00 4:59
Marathon 3:38:55 3:43:08 3:41:01 5:14

Riegel raises the distance ratio to the power 1.06; Cameron uses a fitted coefficient at each distance. Both extrapolate from a single performance and neither knows whether you have trained for the target.

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The two formulas, written out

Riegel (Peter Riegel, 1977; refined 1981). The one almost every other predictor uses, usually without naming it:

T₂ = T₁ × (D₂ ÷ D₁)1.06

The exponent 1.06 is a fatigue factor fitted across world-class performances. If running were free of fatigue the exponent would be 1.00 and doubling the distance would exactly double the time; 1.06 says doubling the distance costs about 4.2% more than double. Riegel stated the fit holds for efforts of roughly three and a half minutes to about four hours — a range this page will happily let you leave, while telling you when you have.

Cameron (Dave Cameron, 1998). A different shape entirely, fitting a coefficient at each distance rather than a single exponent:

a(x) = 13.49681 − 0.000030363x + 835.7114 ÷ x0.7905
T₂ = (T₁ ÷ D₁) × (a(D₁) ÷ a(D₂)) × D₂

with x in metres. Cameron is generally the gentler of the two when extrapolating upward from a short race, and the harsher when extrapolating down.

Worked example: half marathon in 1:45:00

  1. Distance ratio = 42,195 ÷ 21,097.5 = exactly 2
  2. Riegel: 6,300 s × 21.06 = 6,300 × 2.0849 = 13,135 s = 3:38:55
  3. Cameron: a(21,097.5) = 13.1752 and a(42,195) = 12.4001, so (6,300 ÷ 21,097.5) × (13.1752 ÷ 12.4001) × 42,195 = 13,388 s = 3:43:08
  4. Mean of the two = 3:41:01, and the two models are 4:13 apart

Four minutes on a marathon is a whole pacing band. A runner shown only the Riegel figure would set out at 5:11 / km; one shown only Cameron would set out at 5:17. That is the reason both are printed here.

The error nobody prints, and it dwarfs both models

Riegel and Cameron differ by about 2% over a doubling. The difference between a runner who has done twenty-week marathon training and one who has not, at the same half-marathon time, is far larger — commonly ten to twenty minutes over a marathon, and occasionally much more.

This is the single most important thing to understand about race prediction: both formulas assume you are equally well trained for both distances. Neither knows your longest run. Neither knows whether you have practised taking on fuel, or ever been past 30 km. A 5K time is an excellent predictor of a 10K and a poor predictor of a marathon, not because the arithmetic degrades but because the assumption does.

Practically: predictions upward past a doubling are optimistic for anyone whose training is not built for the longer race, and the marathon prediction from a 5K is the most optimistic figure this page produces. Predictions downward towards a mile are unreliable for the mirror-image reason — short races are decided by speed and running economy at high velocity, which endurance training does not develop.

Which race to enter, and how recent

Use a hard, recent, evenly-paced effort at a distance that took you at least about ten minutes. Three things spoil the input:

A training run. A parkrun taken at conversational effort predicts a conversational marathon. The models assume a maximal effort.

An old result. Fitness moves. A result more than about eight weeks old is describing a runner who no longer exists, in either direction.

A badly paced race. A race where you blew up at 8 km understates you; one where you had a great deal left understates you differently. Even pacing is what the models were fitted on.

Using a prediction to set a target

The sensible use is as a ceiling and a starting point, not a goal. Take the mean of the two models, then decide honestly whether your training supports it. If the target race is more than twice the distance of the one you ran, treat the prediction as the time you would run if your endurance base matched your speed, and add time if it does not.

Then convert it to a pace and check that against your actual training paces and your heart-rate zones. A marathon prediction that lands you at threshold effort from kilometre one is telling you the prediction is wrong, not that you should try harder.

Limitations, stated plainly

Both models were fitted on flat, well-paced, well-trained performances in reasonable weather. They know nothing about hills, heat, altitude, wind, whether you have raced the target distance before, or how your training is structured. Riegel's own stated range of validity is roughly three and a half minutes to four hours, so a marathon prediction for anyone slower than about four hours is already an extrapolation past the fit, and a mile prediction is below it.

Neither model is a plan and neither is a promise. This is a fitness estimate for planning a race, not medical advice, and nothing here is a judgement about what you should be capable of running.

Common questions

What is the Riegel formula?

T₂ = T₁ × (D₂ ÷ D₁)1.06, published by Peter Riegel in 1977. The exponent 1.06 is a fatigue factor: doubling the race distance costs about 4.2% more than doubling the time. It is the model behind almost every race predictor on the web, usually unnamed.

How accurate is a race time prediction?

Accurate within a couple of per cent when the two distances are close and you are equally trained for both — a 5K to a 10K prediction is usually good. It degrades badly as the ratio grows, and the degradation is not in the arithmetic but in the assumption: a marathon predicted from a 5K assumes you have done marathon training, and if you have not, the prediction can be twenty minutes fast or worse.

Why do Riegel and Cameron disagree?

Because they are different curves fitted to different performance data. Riegel uses one exponent for every distance; Cameron fits a coefficient that varies with distance. Over a doubling they land about 2% apart, which is four minutes on a marathon. Neither is the right answer — the gap between them is a fair picture of how much confidence any single prediction deserves.

Can I predict a marathon from a 5K?

You can, and the number will be optimistic unless your endurance training genuinely matches your speed. That is an eight-fold extrapolation, well outside the range Riegel described his own fit as covering. Use a half marathon if you have one; it is by far the best single predictor of a marathon, because it is close enough in distance that the training assumption mostly holds.

Should I use my best-ever time or a recent one?

Recent. The models predict what you can run now from what you could run recently, and a personal best from three years ago describes a different runner. Something within the last six to eight weeks, run hard and paced evenly, gives the most useful answer.

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