How Accurate Is the Riegel Formula?

Short answer: accurate up to the half marathon, unreliable at the marathon, and always fast when it is wrong. That asymmetry matters more than the size of the error, because a prediction that is too fast is the one that wrecks a race. Run the numbers, then read what the error looks like:

Where the formula comes from

Pete Riegel published a time-versus-distance equation fitted to record performances across endurance events — people at peak fitness, with near-perfect pacing, equally prepared for every distance on the curve. The exponent that came out, around 1.06, encodes how much sustainable speed decays as an event lengthens.

That origin is the whole story. Applied to a runner who is equally trained for two nearby distances, the assumption holds. Applied to a runner whose 5K is sharp and whose longest run is 90 minutes, it quietly assumes an endurance base that does not exist. Riegel himself did not publish one constant: he reported roughly 1.08 for elite runners and 1.05 to 1.06 for recreational men aged 40 to 70.

The measured error, distance by distance

In 2016 Vickers and Vertosick surveyed 2,303 recreational endurance runners and tested the formula against what they actually ran. They fitted a regression with the intercept at zero and checked whether the coefficient on the Riegel prediction equalled 1, which is what perfect calibration looks like:

Distance predicted	Calibration test	Verdict
10K	p = 0.9	well calibrated
Half marathon	p = 0.3	well calibrated
Marathon	p < 0.0001	miscalibrated, predictions too fast

For the marathon, the distribution of residuals is worth reading in full — negative means the prediction was faster than reality:

Percentile of runners	Riegel error
5th	−36:17
25th	−19:47
50th	−10:09
75th	−2:48
95th	+5:12

Half of all runners came in ten minutes or more behind the prediction. Only the fastest quarter of the field beat it at all.

Why tweaking the exponent does not fix it

The obvious repair is a bigger fatigue factor. It barely helps. The same team reran everything with 1.08 instead of 1.07 and still overestimated marathon speed for about 75% of runners, with mean squared errors far above the alternatives. What actually closed the gap was adding one piece of information the formula has no slot for — typical weekly mileage. That single variable took the marathon mean squared error from 380.7 down to 227.6, and using two prior races instead of one took it to 208.3.

Read those three numbers with their sample attached. All of them were computed on the same validation subsample of 156 runners — the ones in the held-out third of the data who had run a marathon plus two other races at different, non-marathon distances — not on the 2,303 who filled in the survey. It is a like-for-like comparison between the three methods, on a small group.

The pattern repeats further out. A 2024 study benchmarking prediction methods over 60 races, mostly ultras, scored the plain Riegel formula at 80% accuracy against 90.4% for a model trained on runners’ complete logs.

Three situations where you should discount the output

1. Big jumps between the two distances. Predicting a marathon from a 5K crosses a factor of 8.4. Predicting a 10K from a 5K crosses a factor of 2, and that is where the formula is at its best.
2. Uneven specific training. The equation cannot tell that you race 10Ks every month and have never run past 25 km.
3. Race-day variables. Heat, elevation profile, fueling and pacing decide the last quarter of a long race and appear nowhere in the arithmetic.

Using it well

Predict one step up, not three. Re-predict from your newest result rather than your fastest one. And when the target is the marathon, treat the number as a floor and add time — see the marathon prediction page for how much. The race time predictor is the general-purpose version of the same math.