You run a 5K, put the time into a predictor, and it hands you a marathon time. The number looks plausible. Whether you should believe it depends on something the calculator has no way of knowing.

The Riegel formula

The most widely used model comes from Pete Riegel in the late 1970s:

T2 = T1 × (D2 / D1)^1.06

Your predicted time at the new distance is your known time, scaled by the distance ratio raised to a fatigue exponent. The exponent is the whole model. If it were 1.0, you would hold the same pace forever; at 1.06 you slow slightly as distance grows, which is what actually happens.

Riegel fitted that exponent to performance data from well-trained runners. It is a good average. It is also a single number standing in for something that varies substantially between individuals.

A runner with a strong aerobic base and high weekly mileage has a lower personal exponent — they hold pace better as distance grows. A fast runner with limited endurance has a higher one. Two people with identical 5K times and different training histories have genuinely different marathon potential, and Riegel cannot tell them apart.

Where it works and where it fails

The formula is at its best over modest extrapolations. From 5K to 10K, or 10K to half marathon, it is usually close. The physiological demands are similar enough that the fatigue curve holds.

It degrades as the gap widens, and 5K to marathon is where it most often overpromises. That prediction asks a model built on pacing decay to also account for glycogen depletion, fuelling, thermoregulation over several hours, muscular durability, and the simple fact that the marathon punishes inadequate long-run training in a way that no shorter race does. None of that is in the equation.

The honest framing is this: Riegel predicts what you could run at another distance if you were equally well trained for it. Equally well trained is doing enormous work in that sentence. A runner doing 30 km a week can produce a sharp 5K and is not going to hit the marathon time that follows from it.

Cameron and the alternatives

Other formulas fit the curve differently. The Cameron model uses a more complex relationship that many runners find more realistic at longer distances, where Riegel tends toward optimism.

Daniels VDOT takes a different route entirely. Rather than scaling one time to another directly, it maps your performance to a single fitness value derived from oxygen cost modelling, then reads equivalent performances and training paces off that value. The practical appeal is that it produces training paces as well as predictions, which makes it a system rather than a single answer.

All three agree closely at short distances and diverge as distance grows — which tells you something useful. Where the models disagree is where the prediction is least trustworthy. Running your time through several and comparing the spread is more informative than any single number. A tight cluster means the extrapolation is well behaved; a wide spread means you are asking the models to guess.

What a prediction assumes

A predicted time carries silent assumptions, and most disappointments come from one of them failing:

  • That you have trained for the distance. The single biggest one. Marathon prediction from a 5K assumes marathon training you may not have done.
  • That the input was a genuine maximal effort. A tempo run or a parkrun where you eased off produces a soft input and a soft prediction.
  • That conditions are comparable. Heat, wind, hills and altitude all cost time, and the model knows about none of them. A prediction from a cool, flat 10K does not transfer to a hot, hilly marathon.
  • That you will pace it properly. A perfectly accurate prediction still requires you to execute. Go out too fast and the model was right while you were not.
  • That the input is current. Fitness from three months ago predicts a race you would have run three months ago.

Using predictions well

Three uses that hold up:

Setting a realistic target. Predict from a recent race at a distance close to your goal, not a distant one. For a marathon, a recent half is a far better input than a 5K.

Checking whether training is working. Run the same predictor off successive time trials over a training block. The trend is more informative than any single value, and it is measured in your own terms.

Finding the model that describes you. Once you have raced two distances, compare the actual results to what each model predicted from the other. Whichever fits your results best is the one to trust going forward, because it has been calibrated on you rather than on a population.

That last one is the most valuable and the least used. If your marathon came in slower than Riegel predicted from your half, that is not a failure — it is a personal fatigue exponent that is higher than average, and now you know it.

The marathon-specific warning

It is worth stating plainly because it causes more ruined races than anything else on this page: a marathon prediction from a short race is the least reliable number in the sport.

The marathon is the distance where factors absent from every model dominate the outcome. Fuelling, which the model has never heard of. Long-run volume in training, which it cannot see. Heat accumulated over three or four hours. The mechanical durability of legs asked to do something for far longer than they have practised.

Runners who take a 5K-derived marathon time as a target and pace the first half to it very often walk the last ten kilometres. The prediction was not lying about their speed — it was silent about their endurance.

If you are targeting a marathon, predict from a half marathon run in the same training block, build in a margin, and treat the first half of the race as the place where the prediction gets tested rather than the place where it gets proved.