The logic behind race time prediction
A race time predictor estimates the finish time a runner could achieve at one distance based on a performance at another distance. The underlying observation, formalized by engineer Peter Riegel in a 1981 American Scientist article, is that average sustainable speed declines predictably as race distance increases: plotting record times against distance on logarithmic axes yields a nearly straight line with a slope of about 1.06 across a wide range of running distances and durations, from roughly 3.5 minutes to 230 minutes.
The exponent 1.06 means that doubling the race distance multiplies the predicted time by about 2.085 rather than exactly 2 -- the extra 4-5% reflects the slower sustainable pace required at the longer distance. This 'fatigue factor' is what distinguishes the Riegel formula from a simple linear scaling of pace.
The Riegel formula
The formula scales a known time T1 at distance D1 to a predicted time T2 at distance D2 using a power law with exponent 1.06: T2 = T1 x (D2 / D1)^1.06.
Worked example: a runner completes a 5K in 22:00 (1,320 seconds). For the marathon (42.195 km), the distance ratio is 42.195 / 5 = 8.439, and 8.439^1.06 is approximately 9.591, giving a predicted marathon time of 1,320 x 9.591 = 12,660 seconds, or approximately 3:31:00. The same 5K result predicts a half marathon (21.0975 km) of approximately 1:41:12, using a distance ratio of 4.2195 and a factor of approximately 4.600, and a 10K of approximately 45:52, using a distance ratio of 2 and a factor of approximately 2.085.
The formula is symmetric: it can also predict a shorter distance from a longer one. A downward prediction, such as marathon time to 5K, carries the mirror-image caveat -- it assumes the top-end speed that shorter racing requires, which high-mileage marathon training does not always preserve.
Why smaller distance jumps are more reliable
Predictions spanning a small distance gap, such as 10K to half marathon, are generally more reliable than predictions spanning a large gap, such as 5K to marathon. This is because the Riegel exponent is a single average value fitted across all running distances, while the true relationship between speed and endurance demand varies by individual and by how well-matched the runner's training is to the target distance. The closer the input and target distances are, the less that individual variation has room to compound.
Honest limitations: the training assumption
The Riegel formula assumes the runner is equally trained and prepared for both distances. In practice, a fast 5K result mainly reflects speed and does not guarantee the aerobic endurance base a marathon requires. Research on recreational runners by Vickers and Vertosick (2016), published in BMC Sports Science, Medicine and Rehabilitation, found that the standard Riegel exponent tends to underestimate marathon finish times for typical non-elite runners, often by a meaningful margin, with predictions improving when weekly training volume is accounted for alongside the shorter-race result.
Because of this, many coaches treat a Riegel marathon prediction from a short race as an optimistic, best-case scenario rather than an expected outcome. Course profile, weather, altitude and race-day pacing execution can each shift an actual marathon result by minutes beyond what any formula captures.
Using a prediction responsibly
A prediction is most useful as a planning reference rather than a fixed target. Predictions generated from a recent, maximal-effort race are more meaningful than those from an old personal best, since they reflect current fitness. Runners preparing for a longer target distance than their input race, particularly a marathon predicted from a 5K or 10K, benefit from treating the predicted time as an upper bound on ambition and building in pacing margin rather than committing to it as a guaranteed finish time.
الأسئلة الشائعة
How accurate is the Riegel formula for predicting marathon time?
Riegel's 1.06 exponent fits record-level performances well across a range of distances, but a 2016 study of recreational runners by Vickers and Vertosick found it tends to underestimate real marathon times for typical non-elite runners, with the shortfall growing when weekly training volume is low. Predictions from a half marathon result are generally closer to actual outcomes than predictions from a 5K or 10K.
What marathon time does a 22-minute 5K predict?
Using the Riegel formula, T2 = 1,320 seconds x (42.195 / 5)^1.06, which works out to approximately 12,660 seconds, or about 3:31:00. This assumes the runner has marathon-appropriate endurance training; for many recreational runners the realistic time is slower, which is why coaches often treat Riegel marathon projections from short races as a best-case scenario.
Why is the Riegel exponent 1.06?
Peter Riegel plotted record times against distance on logarithmic axes and found running performances fall on a nearly straight line with a slope of about 1.06 for durations between roughly 3.5 and 230 minutes. The exponent captures the empirical rate at which sustainable pace declines as distance increases; an exponent of exactly 1.0 would imply pace never slows with distance, which is not what the data show.
Which race distance gives the most reliable marathon prediction?
A half marathon result generally gives the most reliable marathon prediction, because it is close enough in distance that the pace-endurance relationship transfers reasonably well, while a 5K result mostly measures speed. The Vickers and Vertosick analysis of recreational runners found predictions improve as the input race distance gets closer to the target distance.
Can a race time predictor work in reverse, from marathon to 5K?
Mathematically yes -- the Riegel formula scales in both directions. The reverse prediction carries a mirror-image caveat: it assumes the top-end speed that a 5K demands, which high-mileage marathon training does not always preserve, so a marathon-to-5K prediction can be optimistic in the same way a 5K-to-marathon prediction can be.
المراجع
- Riegel PS. Athletic records and human endurance. American Scientist 1981; 69(3): 285-290.
- Vickers AJ, Vertosick EA. An empirical study of race times in recreational endurance runners. BMC Sports Science, Medicine and Rehabilitation 2016; 8: 26.
- Tucker R, Lambert MI, Noakes TD. An analysis of pacing strategies during men's world-record performances in track athletics. International Journal of Sports Physiology and Performance 2006; 1(3): 233-245.
- World Athletics. Competition and technical rules -- certified road-race distances (half marathon 21.0975 km, marathon 42.195 km).
- American College of Sports Medicine. ACSM's Guidelines for Exercise Testing and Prescription, 11th edition. Wolters Kluwer, 2021.