In 1977 an American engineer and runner named Pete Riegel published a simple relationship in a running magazine: race times scale with distance raised to the power 1.06. Nearly fifty years later, that formula — or a close descendant — sits inside almost every race-time predictor on the internet, including ours. Understanding it means understanding both why your 10K can say something real about your marathon, and why it sometimes lies with complete confidence.
A footnote before the worship begins: Riegel himself refined the idea in later work, adjusting the exponent for different athlete populations and durations. The 1.06 that conquered the world is the popular simplification of a careful engineer’s more nuanced tables — which makes its accuracy across fifty years of abuse more impressive, not less.
The formula, in plain language
Riegel’s formula is T₂ = T₁ × (D₂ ÷ D₁)^1.06. Take a known time over one distance, multiply by the distance ratio raised to 1.06, and out comes the predicted time at the new distance. If the exponent were exactly 1, doubling the distance would double the time. The extra 0.06 is the quantified fingerprint of fatigue: over a doubled distance you do not just run twice as far, you run progressively slower doing it. That six percent of exponent, compounded, is worth about thirteen minutes between a doubled 10K time and a predicted half marathon.
Key takeaways
- T2 = T1 × (D2 ÷ D1)^1.06
- The 0.06 above 1 is the fatigue tax
- It predicts best between neighbouring distances
Why an engineer’s curve fit survived
Riegel fitted his exponent to real performances across thousands of runners, and later analyses on much larger datasets keep landing near the same value for trained endurance athletes — typically 1.05–1.08 depending on the population. It survives because it captures something true about physiology without needing to know anything about you: no weight, no age, no heart rate. One honest race performance implies a whole curve of performances, because the slowdown pattern of humans over distance is remarkably consistent when training is equal.
That last clause — when training is equal — is where the formula’s authority ends, and it is written into this site’s predictor page for a reason.
Where it misleads
Three failure modes repeat. First, the short-to-long leap: predicting a marathon from a 5K assumes marathon-specific endurance the 5K cannot see, and the prediction comes out optimistic for almost everyone who has not done the long training. Second, the contaminated input: a downhill, wind-assisted or tactical race is not a clean performance, and the formula amplifies whatever it is fed. Third, the specialist: sprinters and ultra runners sit at the edges of the population the exponent was fitted on, and their personal exponents genuinely differ.
The exponent is personal
Fit the formula to your own race history and you get your personal exponent. Runners with several recent results across distances can solve for the exponent that connects their own 10K and half marathon: if your times stretch more than 1.06 predicts, your endurance outruns your speed (exponent lower) — or your shorter racing is soft. If they stretch less, speed is your gift and endurance your homework. Coaches use exactly this diagnostic: the exponent is a fingerprint of what kind of runner you currently are, and training is partly the project of moving it.
This reframes prediction entirely. The formula is not only a fortune-teller for the next race; it is a measurement of the present athlete, and the prediction improves as the athlete becomes more balanced across distances.
Race equivalence and its limits in the real world
Predictors assume comparable courses and conditions, and the real world rarely complies. A hilly 10K and a pancake half marathon are not the paired performances the formula wants; a windy point-to-point marathon can be minutes ‘faster’ than fitness, as Boston qualifiers on tailwind years discover when the standard tightens. Honest use means auditing the inputs: same season, honest effort, fair courses, ordinary weather. If one input was freakish, its predictions will be freakish in the same direction, amplified by distance.
Our pace calculator prints all four standard predictions side by side for this reason: a curve that looks orderly invites trust; a single number invites worship. Judge the family, not the individual figure.
What the formula cannot see: the day itself
Even a perfectly-fed Riegel prediction describes the athlete, not the event. Race-day variables sit entirely outside its view: heat alone can cost 2–4% at marathon distance for every few degrees above the low teens Celsius, hills and wind take their own percentages, and a course measured long or crowded with runners adds distance that no stopwatch apologises for. Experienced racers therefore hold two numbers — the Riegel fitness number and the day number, adjusted downward for the forecast, the course profile and the size of the field. The finishing time is the second number executed well.
This is not a defect to be patched with more mathematics; it is a reminder that prediction and planning are different activities. The formula finishes the sentence ‘my fitness is worth…’. The race plan — splits, fuelling, the split calculator’s curves — finishes ‘…and today I will collect it like this.’ Confusing the two is how fit runners produce inexplicable results.
Keeping the prediction honest across a season
A prediction is a snapshot of a moving athlete, and its shelf life is one training block. Re-run the pace calculator after every significant race and treat the newest curve as the current one; the older predictions become a diary of what your fitness used to promise, which is its own quiet motivation. Athletes who re-anchor regularly are rarely surprised by their results — and being unsurprised on race day, it turns out, is most of what experience means.
Using it like a coach
Coaches treat the prediction as a ceiling and a conversation. If it promises a 3:30 marathon, the training plan gets built around proving the inputs — a half marathon near the predicted 1:44 — before the goal is believed. Use it the same way: predict, verify at the neighbouring distance, then extend. The pace calculator on this site shows all four standard distances at once precisely so the curve can be judged as a curve, not worshipped as a point.
Common mistakes
- Predicting a first marathon from a parkrun personal best
- Feeding it a training run and believing the marathon it returns
- Ignoring course and weather differences between the source race and the target
Questions this raises
Elite endurance runners cluster closer to 1.05 and sometimes below, reflecting exceptional fatigue resistance. Recreational runners often sit nearer 1.07–1.09. Our predictor uses the standard 1.06 and labels itself a ceiling.
Yes — the formula runs both ways, and a marathon predicting a 5K is often its most accurate direction, since endurance is proven and speed is the open question.
Put a number on it.
Pete Riegel's 1977 insight still powers nearly every race predictor. How it works, where it shines, and the three situations where it quietly fails.
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