Race Time Predictor

How the Riegel race time predictor works

In 1977 Pete Riegel, an engineer and course measurer, published a single equation that still underpins almost every race time predictor online: T2 = T1 x (D2 / D1)^1.06. T1 is the time you actually ran, D1 is the distance you ran it over, D2 is the distance you want to predict, and T2 is the answer. The exponent 1.06 is the whole story in one number: it says that every time the distance doubles, your pace slows by about four percent.

That is why the formula beats the naive approach. If you simply held 5K pace for a marathon you would be predicting a time no human has ever run relative to their 5K. Riegel bakes in the fade.

Worked example: a 25:30 5K predicting a half marathon

Start by converting everything to one system. The 5K time is 25 minutes 30 seconds, which is 1,530 seconds. A half marathon is 21.0975 km, so the distance ratio is 21.0975 / 5 = 4.2195. Raise that to the power 1.06: 4.2195^1.06 = 4.601. Multiply: 1,530 x 4.601 = 7,039 seconds, or 1:57:18.

The pace that implies is 7,039 / 21.0975 = 333.6 seconds per kilometre — 5:34/km, which is 8:57 per mile. The even-pace splits work out at 27:48 for 5 km, 55:36 for 10 km, 1:23:24 for 15 km and 1:51:12 for 20 km, with 1:57:18 at the line. Those numbers are what you write on your wrist the night before.

Tuning the exponent to your training

1.06 is an average across thousands of runners, not a law of physics. Runners with high weekly mileage fade less; runners who race off speedwork alone fade more. Same 25:30 5K, same half marathon target:

Nearly seven minutes separates the optimistic and pessimistic ends. If you have run both a 5K and a half recently, you can back out your own personal exponent and see which column you actually live in.

The marathon caveat

The same 25:30 5K predicts a 4:04:34 marathon. Treat that with suspicion. The prediction assumes you can hold roughly 5:47/km for over four hours, which is a question about glycogen, fat oxidation, thermoregulation and how many 30 km long runs you have done — none of which appear anywhere in the formula.

There is a mathematical detail worth knowing here. Riegel is a power law, so it is transitive: predicting a half from your 5K and then a marathon from that half gives the same 4:04:36 you would get by going straight from the 5K. The formula cannot correct itself, so a bad extrapolation stays bad no matter how many steps you take. The correction has to come from physiology, not arithmetic.

What physiology says is blunt. The wall — hitting the point where muscle glycogen runs out, usually somewhere past 30 km — is not a pacing failure the formula can see. Runners whose longest run is 16 km typically finish 5 to 15 minutes behind their Riegel marathon prediction. Runners with three months of 30 km long runs and a couple of 60 to 80 km weeks land close to it, and the well-trained sometimes beat it. This is why the tool warns you when the target is more than four times your race distance.

A better input beats a better formula

If you want an honest marathon number, race a half marathon six to eight weeks out. A 1:45:00 half predicts a 3:38:55 marathon, and because the jump is only 2x, that prediction sits inside the range where Riegel is reliable. A 50:00 10K predicts a 3:50:01 marathon — usable, but the 4.2x jump already puts you in warning territory. The rule of thumb: the closer your input distance is to your target, the more the prediction is measurement and the less it is hope.

Turning the prediction into a race plan

The split table assumes even pacing, and that is deliberate. Analysis of large marathon fields keeps finding the same thing: the runners who slow the least in the final 10 km are the ones who started closest to their average pace. Going out 10 seconds per kilometre fast for the first 10 km banks 100 seconds and usually costs three to five times that after 30 km.

The refinement most experienced runners use is a slight negative split: run the first half one to two percent slower than target, then use whatever is left to squeeze the second half. On a 4-hour marathon that means about 2:01 through halfway rather than 2:00 — a difference small enough to feel patient and large enough to matter at 35 km. Add 10 to 20 seconds per kilometre on hilly courses and expect to lose two to four percent overall in heat above 20°C, which no predictor accounts for.

What this predictor is not

It is not a training plan, and it does not know your age, your recovery, the course profile, the wind or whether you slept. It takes one honest data point — a race you actually ran, hard, recently — and projects it. Use it to set a target range rather than a single number: take the 1.04 and 1.08 rows as your realistic floor and ceiling, aim for the middle, and let the first 5 km of race day tell you which one you are on.