Race time predictors are used constantly in running, but the formula behind them is rarely explained. You enter a recent 5K result and get a marathon estimate, or input a half marathon time and get a 10K projection. The output appears confident. Understanding the formula that drives it -- and why it sometimes misses by 15 or 20 minutes -- makes you a better interpreter of the prediction rather than a passive consumer.
Where the Formula Comes From
Peter Riegel published an empirical relationship between race time and distance in 1977 in the journal American Scientist. He analyzed world records across distances ranging from sprints to ultramarathons and fit a power law to the relationship between distance and performance time.
The result is:
T2 = T1 x (D2 / D1)^1.06
Where: - T1 is your known race time at distance D1 - D2 is the target distance - T2 is the predicted time at D2 - 1.06 is the fatigue exponent
The 1.06 exponent encodes a specific empirical claim about how human performance degrades with distance. If the exponent were exactly 1.0, the relationship would be perfectly linear: twice the distance, exactly twice the time. An exponent above 1.0 means degradation is steeper than linear -- each additional unit of distance demands proportionally more time than the previous one.
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A Concrete Example: 5K to Marathon
If you run a 5K in 25:00, what marathon time does Riegel's formula predict?
- T1 = 1500 seconds (25 minutes)
- D1 = 5 km
- D2 = 42.195 km
- D2/D1 = 8.439
Calculate the exponent: 8.439^1.06 = approximately 9.41
Multiply: 1500 x 9.41 = approximately 14,115 seconds = 3:55:15
So Riegel's formula predicts a 3:55 marathon from a 25:00 5K. Whether that matches your actual fitness depends on factors the formula was not designed to capture.
For a faster runner -- a 20:00 5K (1200 seconds): 1200 x 9.41 = approximately 11,292 seconds = 3:08:12
The Runner's World race predictor uses a version of this formula, as do most online race prediction calculators. The math is the same; what varies is whether they apply the formula directly or add adjustment factors.
Why the Exponent Is 1.06
The fatigue exponent of 1.06 is not arbitrary. It reflects the empirical finding that performance degrades slightly faster than linearly with distance across the range of competitive running distances.
VO2 max, the maximum rate at which the body can consume oxygen during exercise, is a key determinant of aerobic performance. But VO2 max alone does not determine race time. As distance increases, the fraction of VO2 max a runner can sustain decreases, fuel systems shift from primarily glycogen to more fat oxidation, and neuromuscular fatigue accumulates. The combined effect is that scaling from a short distance to a long one requires proportionally more time than a purely linear model would suggest.
Riegel's exponent captures the average of these effects across a large sample of world-class performances. It is a good fit for middle distances (5K through half marathon) and a reasonable approximation for the marathon.
How to Calculate Your Target Pace Using the Prediction
Once you have a predicted finishing time from the formula, the next step is converting it into a per-mile or per-kilometer target pace.
For the 3:55:15 marathon example: - Distance: 26.2188 miles - Time: 3:55:15 = 235.25 minutes - Pace: 235.25 / 26.2188 = approximately 8:59 per mile
You can also work backward: if you want to run a sub-4:00 marathon (240 minutes at 9:09 per mile), the formula tells you what 5K or 10K time indicates you are ready.
Sub-4:00 marathon target: T2 = 14,400 seconds T1 = T2 / (D2/D1)^1.06 = 14,400 / (42.195/5)^1.06 = 14,400 / 9.41 = approximately 1,530 seconds = 25:30
So Riegel's formula says you need a 5K around 25:30 or faster to have the physiological profile for a sub-4:00 marathon. The Pace & Race Time Calculator handles this arithmetic for any combination of distances -- try it free and enter your most recent race time to see predicted finish times across multiple distances at once.
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Where the Formula Works Best
Riegel's formula is most accurate when the two distances being compared are relatively close together and when the input race is run at full effort under good conditions.
5K to 10K: Highly accurate. The fatigue dynamics between these distances are similar enough that the 1.06 exponent fits well. If you ran a hard, well-paced 5K, the predicted 10K time is usually within 20-30 seconds of actual performance.
10K to half marathon: Good accuracy. Most trained runners who complete a hard 10K see half marathon predictions within 1-2 minutes.
5K or 10K to marathon: Reasonable approximation but with wider error margins. The formula assumes world-class aerobic efficiency and optimal pacing. Recreational runners with less marathon-specific training -- particularly long run volume and fueling adaptation -- typically run 5-15 minutes slower than the formula predicts.
Sprint distances to marathon: Not reliable. The formula was derived primarily from world records at middle and long distances. Applying it across a very wide distance range introduces compounding error.
Where the Formula Breaks Down
Riegel's formula has three structural limitations that matter for recreational runners.
It assumes proportional aerobic development: The formula was calibrated on world records, where elite athletes have developed every physiological system to its maximum. A recreational runner may have excellent 5K speed but inadequate long run base for the marathon, meaning their 5K-predicted marathon time is genuinely unachievable with their current training.
It does not account for fueling: Marathon performance depends on carbohydrate fueling during the race in a way that 5K and 10K performance does not. A runner who has not practiced fueling in training, or who cannot tolerate gels at race pace, will typically run 10-20 minutes slower than the formula predicts at the marathon distance.
It ignores course difficulty: The formula assumes flat, fast conditions. A hilly marathon will produce slower times than a flat one, but the formula cannot account for elevation gain.
It does not capture training volume: Two runners with identical 5K times but very different weekly mileage will have very different marathon capabilities. The formula sees only the recent race result, not the training that produces sustainable long-distance performance.
Adjusting the Prediction for Real-World Conditions
Most experienced coaches and runners apply an adjustment factor to the raw Riegel prediction when it is being used for marathon planning:
- Less than 40 miles per week of training: add 10-20 minutes to the predicted time
- 40-55 miles per week with consistent long runs: use the raw prediction as a starting point
- 55+ miles per week with marathon-specific training: the prediction may be close or even slightly conservative
The World Athletics data that Riegel used to develop the formula reflects maximal human performance. Most recreational runners are performing at some fraction of their theoretical maximum, which means the formula will tend to predict times slightly faster than what training volume and specificity will actually support.
Photo by Using the Formula in Training
The most practical use of Riegel's formula is not predicting a single race finish time but tracking fitness trends across training cycles.
If you run a time trial 5K in March and another in June, the formula tells you exactly how much your predicted marathon time changed and in what direction. Recording these time trials alongside race results in Strava or any structured training log makes the trend visible across an entire training cycle, connecting predicted times to actual race outcomes and identifying whether fitness gains are translating as expected. Progress that shows up in a 5K time trial will show up as a proportional improvement in the marathon prediction -- assuming training volume and specificity are maintained.
Race prediction tools also help with setting realistic intermediate goals. If your 10K time predicts a 1:58 half marathon, targeting a 1:52 in your next race is likely too aggressive. Riegel's formula anchors goal-setting in recent measured performance rather than aspiration.
A Calculator Built for This
Doing the exponent arithmetic by hand is tedious. The Pace & Race Time Calculator on EvvyTools implements the Riegel formula directly: input any recent race time and distance, and it returns predicted finishing times for 5K, 10K, half marathon, and marathon distances, along with the corresponding target paces.
Try it free using your most recent race result. The output gives you a set of pace targets grounded in your current fitness rather than abstract goals, which makes it more useful for structuring training blocks and race-day pacing plans.
For more articles on running pacing strategy and performance tools, visit the EvvyTools blog and explore the full training and fitness calculator library.
Reading the Prediction Correctly
Riegel's formula gives you a physiologically grounded estimate of your performance ceiling under ideal conditions. The practical question is not whether the formula is exactly right -- it rarely is -- but whether you are above or below it.
If you consistently run marathons faster than the formula predicts from your 5K time, you have strong marathon-specific fitness: excellent long run base, good fueling, and efficient pacing. If you consistently underperform the prediction, the gap identifies where to focus training: more long run volume, better fueling practice, or improved pacing discipline.
The formula is a benchmark. Used as one, it is a reliable and useful tool. Used as a guarantee, it will mislead. Most good tools are like that.
