How the Riegel Formula Predicts Your Race Times

The 1977 equation behind nearly every race predictor on the internet — including ours.

Nearly every race-time predictor you have ever used — on a website, in a training book, inside your GPS watch — traces back to a single short paper. In 1977, an engineer named Peter Riegel published a deceptively simple observation in American Scientist: across an enormous range of endurance events, the relationship between race distance and race time follows a consistent mathematical pattern.

The formula

T1 is your time at a known distance D1, and T2 is the predicted time at the new distance D2. The exponent — 1.06 — is where all the interesting physiology hides. If humans could hold the same pace forever, the exponent would be exactly 1 and doubling the distance would exactly double the time. It isn't, and it doesn't. The extra 0.06 encodes fatigue: every time the race gets longer, the sustainable pace gets a little slower.

Run the numbers and the effect is obvious. A runner who covers 5K in 25:00 holds 8:03 per mile. The formula predicts that same runner completes a 10K not in 50:00 but around 52:07 — roughly 8:23 per mile. The distance doubled; the time slightly more than doubled. That gap is the fatigue exponent doing its work.

Why it works — and where it breaks

Riegel's model works because endurance performance is governed by a fairly stable relationship between intensity and duration. The pace you can hold for 20 minutes sits at a predictable fraction of the pace you can hold for 60, which sits at a predictable fraction of the pace you can hold for three hours. The exponent captures that decay curve in one number.

But the model has honest limits, and pretending otherwise is how runners blow up at mile 20:

• It assumes you're trained for the target distance. A sharp 5K runner who has never run past 15 miles will not hit their Riegel marathon prediction. The formula predicts what equivalent fitness looks like, not what undertrained legs will do.
• Extrapolation range matters. Predicting a 10K from a 5K is reliable. Predicting a 100-miler from a 5K is astrology with extra steps.
• Terrain changes the exponent. The 1.06 value was derived largely from road racing. Fatigue accumulates faster on technical trails and in ultras, which is why our predictor offers adjusted exponents — 1.08 for trail and 1.10 for ultra distances — that produce more realistic long-race predictions.

The prediction is a starting point — a number to train toward, argue with, and eventually beat.

How to actually use it

Use a recent race — within the last two or three months — at a distance you ran hard. Tune-up races beat time trials, and time trials beat workout guesses. Then treat the output as a fitness ceiling for race-day planning: your opening miles should be at or slightly slower than predicted pace, never faster. If the predictor says 3:45 for your marathon and you open at 3:30 pace, the formula was never your problem.