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.

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.

An example with numbers

From a 10 km run in 50 minutes the formula predicts 1:50:19 for the half marathon (21.0975 km), that is a pace of 5:14 per kilometre. From the same race it predicts 3:50:01 for the marathon, at 5:27 per kilometre.

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.

The pace table is the slip of paper to carry with you

The number you need during a race is not the finishing time, it is the split at each kilometre: at the marker you glance at your watch and in a second you know whether you are on track. It is the only way to correct before it is too late, because the sense of effort deceives in the early kilometres, when everything feels easy.

Many people write it on a paper wristband or on tape around the forearm, and big races hand it out at the entrance. It matters above all in the first half: in the second the body decides by itself, and all that is left to do is hold on.

Here the table comes already written under the predicted time: a split at every kilometre up to the half marathon, one every five kilometres over distances such as the marathon. It is worked out at an even pace, which is the reference and not the tactic: the section below explains why it pays to start a little slower.

Starting slow is the strategy that wins

There is a surprising regularity in race times: the best performances almost always come from running the second half equal to or faster than the first. In marathons a faster second half is the norm among the front runners and the exception among amateurs, and it is the main difference between the two populations.

The reason is physiological: starting above the sustainable rhythm burns reserves that never come back and produces a slowdown at the end far larger than the time banked. The practical rule is running the first kilometres ten or fifteen seconds slower than target pace, and not one second faster.

Gradient, wind and the other thieves of seconds

A climb costs more than the descent gives back: on a rolling course the time is nearly always worse than on the flat, even when total elevation gain is zero. The most used practical figure is about fifteen to twenty seconds per kilometre for every hundred metres of climb, and half of that in your favour downhill.

The wind works the same way: against you it slows a lot, behind you it helps little. And heat is the most underrated factor: above twenty degrees the sustainable rhythm drops, above twenty-five it drops considerably, and over a marathon the difference between twelve and twenty-eight degrees is measured in tens of minutes.

Not all kilometres are alike

In road races the first kilometre is nearly always slower than planned, because of the crowd at the start, and it should not be made up: anyone trying to get back on schedule in the second kilometre makes exactly the mistake of starting too fast. The time comes back by itself if the rhythm is right.

Watch the measured distance too: certified courses are measured along the shortest possible line, and anyone running wide through bends or weaving through people covers a good many extra metres. Over a marathon, a personal watch reading forty-two and a half instead of 42.195 is not a fault of the device: it is the extra road actually run.

Nearby tools

For pace there is Running pace, to convert into kilometres per hour Pace ⇄ speed and to find the third number among speed, time and distance Speed, Time & Distance. For training Training paces (VDOT), which estimates times with a different model, the one by Jack Daniels, so the two predictions may not match to the second. For training zones Heart rate zones and for aerobic capacity VO2max (Cooper). All the running pages read and write pace and speed the same way: 5:00 min/km and 12 km/h are the same pace, and a pace is always written in minutes and seconds, like 5:14.