Race Time Predictor (Riegel Formula)
Enter a distance you have already run and the time you posted, then instantly project finish times for any other distance — 5K, 10K, half marathon, full marathon and beyond — using Peter Riegel's 1981 empirical formula. A full reference table from 1 km to 50 km is included alongside the target prediction.
Enter a valid finish time as h:mm:ss or m:ss.
Predicted finish time
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Predicted pace
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Predicted speed
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Predictions across common race distances
| Distance | Predicted time | Pace |
|---|
For reference only. The Riegel model assumes consistent training and pacing; accuracy degrades for very short or ultra-long extrapolations.
Formula
T₂ = T₁ × (D₂ ÷ D₁)^k, default k = 1.06
- · Source: Peter S. Riegel, "Athletic Records and Human Endurance", American Scientist 69(3), 1981, pp. 285–290.
- · The exponent k = 1.06 was derived by Riegel from world-record data across running, swimming and cycling.
- · Well-trained runners typically show real-world k between 1.05 and 1.08; novices and endurance-weak runners trend higher (1.10–1.15).
- · Most accurate between distances of similar order (5K → 10K → half → marathon). Extrapolations under 1 km or over 50 km lose accuracy.
- · Assumes consistent training state, fuelling, weather and course profile; does not model bonking, cramps or "the wall".
- · Half marathon = 21.0975 km, marathon = 42.195 km (World Athletics official distances).
Frequently asked
How accurate is the Riegel formula?
For trained runners projecting 5K → half marathon, real-world error is usually within ±2–5%. Projecting 5K → marathon tends to over-predict speed because the 1.06 exponent under-counts long-distance fatigue. Empirical studies (e.g. Vickers & Vertosick 2016) suggest amateurs use k ≈ 1.07–1.08, with marathon predictions sometimes needing k as high as 1.15.
Why does a 5K time predict an unrealistically fast marathon?
Marathon performance depends on more than aerobic capacity — muscle damage, glycogen depletion and fuelling all matter. The Riegel single-exponent model captures "speed decay" but does not model the "wall" most amateurs hit at 30–35 km. Predict from a closer distance (e.g. a recent half marathon) for a much tighter estimate.
Can I tune the exponent k myself?
Yes. The tool defaults to k = 1.06 but you can move it between 0.5 and 1.5. k < 1.00 implies perfect or improving endurance (rare); k > 1.10 typically reflects novice fatigue or long-distance falloff. The best practice is to back-solve k from your own past races, then forward-predict your next goal.
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