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Race Time Predictor (Riegel's Formula)

Predict your finish time at a new race distance from a recent result at another distance, using Peter Riegel's T2 = T1 × (D2/D1)^1.06 endurance formula.

Predicted finish time
3:38:55
Predicted pace (min:sec / km)
5:11 /km

How it works

Peter Riegel's race-prediction formula (published in American Scientist, 1977) estimates a runner's time at a new distance from one known result: T2 = T1 × (D2/D1)^b. If pace held perfectly steady at any distance, b would be 1 and the predicted time would simply scale with distance — Riegel's finding was that endurance performance instead degrades with distance at an empirical exponent of about 1.06 across a wide range of runners, so a longer target race predicts a disproportionately slower pace than a flat extrapolation would.

The fatigue exponent is left adjustable (default 1.06) rather than fixed, since how much an individual runner slows down over added distance genuinely varies — treat 1.06 as a well-supported starting point, not a universal constant. Because the formula only uses the ratio of the two distances, the unit they're entered in (km or miles) cancels out identically; the toggle just relabels and rescales both distance fields together.

FAQ

Why isn't the predicted pace just my known pace held constant?

Because real endurance performance slows down over longer distances faster than a flat-pace extrapolation suggests — fatigue, fueling, and pacing strategy all compound over a longer effort. Riegel's exponent of 1.06 captures that observed slowdown; setting the fatigue exponent to exactly 1 in this calculator reproduces the flat, no-slowdown extrapolation for comparison.

Is this prediction reliable for very different distances, like a 5K predicting an ultramarathon?

Riegel's formula is best supported for distances within a similar training domain (5K up through marathon), where a consistent exponent has been empirically observed. Extrapolating far beyond that — to multi-hour ultradistance events — stretches the formula outside the range it was validated on, since fueling and pacing dynamics change qualitatively at that scale.

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