The Riegel formula, explained without the maths headache

The first time someone told me I could predict my marathon from a 10K, I rolled my eyes. Running a marathon is not just six and a bit 10Ks stapled together. And yet here we are, and the little formula that does it is genuinely useful once you know what it can and cannot do.

It is called the Riegel formula, named after Pete Riegel, an engineer who wrote it up in 1981. Here it is:

predicted time = your time x (new distance / old distance) ^ 1.06

That little ^ 1.06 is doing all the work, so let's talk about it.

What the 1.06 actually means

If running were perfectly efficient, the exponent would be 1.0. Double the distance, double the time. A 20 minute 5K would mean a 40 minute 10K, a 1:24 half, a 2:48 marathon. Anyone who has run a marathon is laughing right now, because it does not work like that. You slow down as the distance grows.

The 1.06 captures that slowdown. It is slightly more than 1, which means every time you go further, your pace fades a little. Plug in the numbers and that same 20 minute 5K predicts a 41:40 10K and a 3:05 marathon, not a 2:48. That extra five percent is the difference between a formula that flatters you and one that has actually watched people race.

Where it works well

The formula is at its best when you are not stretching too far from your known race. Predicting a 10K from a 5K, or a half from a 10K, is usually within a percent or two for a trained runner. I have lost count of the number of times I plugged in a recent 10K and the half marathon prediction landed within a minute of what I actually ran a month later.

Where it falls apart

Two places.

First, the marathon. Predicting 26.2 miles from a 5K assumes you have the endurance to back up your speed, and most people do not, at least not without specific long training. The formula does not know whether your longest run this year was 10 miles or 20. If your engine is fast but your fuel tank is small, the real marathon will be slower and uglier than the number suggests.

Second, very short stuff. Predicting your mile from a marathon is almost meaningless, because mile speed depends on things the formula has never heard of, like leg turnover and how much you redline.

A fair way to use it

Use a recent race, pick a target distance that is not wildly far from it, and treat the result as a goal to train toward rather than a guarantee. If you want to push the prediction further out, earn it with long runs first, then trust the number.

That is the whole trick. One formula, one magic number, and a healthy respect for the marathon.