Race time prediction

What it's for

You ran a 10K and want to know your possible half-marathon time? The Riegel formula predicts your time over a different distance from a known performance.

Note

It's an estimate assuming proper training for the new distance. The closer the two distances, the more reliable the prediction.

What Riegel's formula says

Time does not grow in proportion to distance: doubling the kilometres more than doubles the time, because the same pace cannot be held. Riegel measured that «more» across thousands of performances and found an exponent close to 1.06 or so, that is time grows as distance raised to 1.06.

In practice it means that at every doubling of distance the pace lengthens by about four per cent. From a 10 km it therefore predicts a half marathon slightly slower per kilometre, and a marathon slower still. The formula works both ways, but downwards it is less interesting: nobody needs to be told they could run a fast 5,000.

Where the prediction holds, and where it does not

It holds well between nearby distances: 5 to 10 km, 10 km to half marathon. It starts to err when the jump is large, and it errs above all towards the marathon, which is the distance where the prediction is systematically optimistic for most people.

The reason is not in the mathematics but in the physiology: the marathon brings in glycogen depletion, hydration and muscle damage, things that do not exist over ten kilometres. Anyone who has never run beyond twenty-five kilometres in training will not hit the predicted time, however fast they are over ten.

The assumption almost everyone forgets

The formula assumes training appropriate to the new distance, and that clause is what makes it a wrong prediction most of the time. Someone running twenty kilometres a week who gets a good ten-kilometre time does not have the mileage to hold that same rhythm over twenty-one.

Hence a more honest use: the prediction says what you are capable of if you train for that distance, not what time you would run next Sunday. As the target of a programme it is a good number; as a cold forecast it is optimistic nearly always.

How it is used in a race

The most useful number it yields is not the finishing time but the pace to hold: dividing it by the distance gives the target rhythm, and the race is built on that. The rule that works is starting the first kilometres slightly slower than target pace, and taking it back in the second half if the legs are there.

The opposite, that is banking time at the start, almost never works: the time gained in the first kilometres is paid back multiplied in the last ones, which is why races won with a faster second half are the norm at the top and the exception among amateurs.

Nearby tools

For pace there is Pace calculator and for conversion Pace and speed converter. For training zones Heart rate zones and for aerobic capacity VO2max with the Cooper test.