Riegel formula:
predict a 10K, half or marathon from one result

What the Riegel formula does and does not claim

Predicting a race time is a question of how pace fades as the distance grows. Running twice as far takes more than twice the time because you cannot hold the same speed. Engineer and runner Pete Riegel described that fade with a single exponent of about 1.06, and the resulting equation is still the most widely used quick race predictor.

The formula takes one number you trust, a recent race at a known distance, and projects it to another distance. It does not look at your weekly mileage, long runs, hills or the weather. It assumes you are equally well prepared for both distances, which is the part to be honest about.

That assumption is why it is accurate for a runner who has trained for the target event and optimistic for someone who has not. A fast 5K from a runner doing 20 km a week does not quietly become a marathon time.

The formula and the exponent

An exponent of exactly 1 would mean you hold the same pace forever. With 1.06, doubling the distance multiplies time by 2^1.06 ≈ 2.085, so average pace slows by about 4.2% for each doubling. Fitter endurance athletes tend to fade a little less and beginners a little more.

Common distances worth keeping in mind are 5 km, 10 km, 21.0975 km for the half marathon and 42.195 km for the marathon. A mile is 1.609344 km, which matters only if your reference race was in miles and the target is in kilometres.

Worked example: from a 10K of 50:00

Note the pace slide. The 10K pace was 5:00 per km. The half is 14 seconds per km slower and the marathon 27 seconds per km slower. That is the exponent doing its job.

Run the formula in the other direction too. If your target is a 3:45 marathon, solve for T1 by dividing by the distance ratio: it points to a 10K of about 48:55. Seeing the implied 10K is a good reality check on whether the goal fits your present fitness.

What a few reference times predict

Treat the marathon column with the most caution. Rows that rely on a 5K reference stretch the formula across a factor of more than eight in distance, and the marathon is also the event where fuelling, pacing and training volume matter most.

Where the estimate breaks down

• Reference too short. A one-mile or 800 m time rewards speed that doesn't predict endurance. Use a race of at least 5 km.
• Target too long. The exponent is a poorer fit for the marathon than for the half, and ultramarathons are not covered by it at all.
• Different conditions. A flat, cool race and a hilly, hot one are not comparable; adjust or choose a cleaner reference.
• Training mismatch. If long runs top out at 12 km, a marathon prediction assumes endurance you have not built.
• A single day's result. A race run while ill or tired will pull every prediction too slow.

This is a fitness estimate, not medical advice. If you are new to running or return after illness, build mileage gradually and check with a doctor before racing long distances.

Turning the prediction into a pacing plan

Divide the predicted time by the distance to get an average pace, then start the first quarter of the race a touch slower than that. Even splits are efficient, but they are hard to hold for runners who set off too fast, and the 1.06 exponent already contains an assumption of sensible pacing.

A practical routine is to run a test 5K or 10K every six to eight weeks, recalculate and compare. If predictions rise faster than your longer-run performances, you may be building speed faster than stamina, a useful signal to add more steady running.

Working backwards from a goal time

Most runners start with the finish time they want and need to know what to run now. Rearranging the formula gives the equivalent time at the distance you can actually race today: T1 = T2 ÷ (D2 ÷ D1)^1.06.

A goal of 1:45:00 for the half marathon means a 5K or 10K that is itself consistent with it. Divide 105 minutes by 2.10975^1.06 = 2.2064 and you get 47.6 minutes for the 10K, about 4:46 per km. If you can run 10 km in 50:00 today, the half marathon goal needs roughly two and a half minutes off your 10K.

The prediction chain is internally consistent, which is a handy check. From the 50:00 10K the formula gives 1:50:19 for the half. Doubling that distance applies the same ratio again: 110.32 min × 2^1.06 = 230.0 min, the same 3:50:01 reached directly from the 10K.

Flat even running at the 10K pace of 5:00 per km would imply a marathon of 3:30:58, nearly twenty minutes quicker than the formula predicts. That gap is the cost of fatigue the exponent builds in, and the reason a marathon plan that simply extends your 10K pace usually ends in a late-race slowdown.

Why some predictors use a different exponent

The 1.06 value is an average fitted to many athletes. Some online predictors use a larger exponent for the marathon to be conservative about runners with modest training volume. For the 50:00 10K, an exponent of 1.08 would put the marathon at about 3:56:44 instead of 3:50:01, a difference of nearly seven minutes.

Neither value is wrong. The right choice depends on how much weekly mileage you can show. Higher volume and long runs argue for the standard 1.06; low volume argues for a more cautious estimate.