Race Time Predictor
Predict your time at another distance from a recent race result, using Riegel's endurance formula, with equivalent paces and honest error bounds.
How to use this calculator
- 1Enter a recent race result — a genuine all-out effort, not a training run.
- 2Choose the distance you want to predict.
- 3Read the prediction, then check the equivalent-performance table for every other common distance.
How the calculation works
T₂ = T₁ × (D₂ ÷ D₁)^1.06- T₁, D₁
- Your known race time and its distance
- T₂, D₂
- The predicted time at the target distance
- 1.06
- Riegel's fatigue exponent, fitted to observed race results across many distances
The exponent carries the entire model. An exponent of 1 would mean identical pace at every distance; 1.06 means pace degrades slightly as distance doubles. Doubling the distance takes about 2^1.06 = 2.085 times as long, not twice.
Riegel derived the value empirically in 1977 from race results, and it has held up well for distances between roughly 1,500 m and 50 km when the two distances are not wildly different.
Some coaches prefer 1.07 or 1.08 for marathon predictions specifically, on the grounds that 1.06 is optimistic for runners without marathon-specific endurance. The difference is a few minutes over 42 km.
The formula is symmetric: predicting downwards from a marathon to a 5K uses exactly the same equation with the ratio inverted.
Worked example
A 20-minute 5K projected to the marathon
- 1.The distance ratio is 42.195 ÷ 5 = 8.439.
- 2.Raise it to the power 1.06: 8.439^1.06 = 9.59.
- 3.Multiply the known time: 20 minutes × 9.59 = 191.8 minutes.
- 4.That is 3 hours 11 minutes 49 seconds.
- 5.Pace goes from 4:00/km in the 5K to 4:33/km in the marathon — about 13.6% slower.
- 6.A ratio of 8.4 is a long extrapolation, and most runners without marathon-specific training will finish slower than this.
Result: 3:11:49 marathon
A half marathon projected to 10K
- 1.The ratio is 10 ÷ 21.0975 = 0.474 — predicting downwards this time.
- 2.0.474^1.06 = 0.45323.
- 3.95 minutes × 0.45323 = 43.06 minutes, or 43:03.
- 4.Pace improves from 4:30/km to 4:19/km over the shorter distance.
- 5.A ratio near 0.5 is well within the formula's reliable range, so this prediction is more trustworthy than the marathon one.
Result: 43:03 for 10K
Why the exponent is 1.06 and not 1
If runners held the same pace regardless of distance, predicting a race would be simple multiplication — a marathon would take exactly 8.44 times a 5K. Nobody does that, because sustainable pace falls as duration rises. The physiological ceiling shifts from oxygen delivery over minutes to substrate availability and thermoregulation over hours.
Riegel captured that decline with a single exponent above 1. At 1.06, doubling the distance takes 2^1.06 = 2.085 times as long — about a 4% pace penalty per doubling. It is a crude model of a complicated phenomenon, and its accuracy across a wide range of runners and distances is genuinely surprising for something with one free parameter.
The formula is symmetric, which is worth knowing. It predicts downwards from a marathon to a 5K exactly as readily as upwards, and downward predictions are generally more reliable because they demand less of the runner's endurance than they have already demonstrated.
Where it goes wrong, and it always goes wrong the same way
The formula assumes equal training for both distances, and that assumption is what breaks in practice. A runner with a sharp 5K and a longest run of 10 km is not going to hit their predicted marathon time — not because the arithmetic is wrong, but because the marathon asks a question their training has never answered.
The failure is systematically optimistic for long extrapolations. Beyond about 90 minutes of running, glycogen depletion, fluid loss and accumulated muscular damage become limiting in ways that do not feature at all in a 20-minute race. This is why some coaches use 1.07 or 1.08 when predicting marathons specifically, and why the honest advice is to treat a 5K-derived marathon prediction as a ceiling rather than a target.
Conditions are the other systematic gap. Heat, hills and altitude cost far more over a marathon than a 5K, because there is more time for the penalty to accumulate. A 20 °C day might cost a few seconds over 5 km and several minutes over 42.
What this assumes, and where it stops
Assumptions
- The known result is a genuine maximal race effort, not a training run or a paced group run.
- The runner is appropriately trained for both distances.
- Riegel's exponent of 1.06, which fits observed results between roughly 1,500 m and 50 km.
- Comparable conditions — flat course, temperate weather, sea level — for both races.
Limitations
- Systematically optimistic when predicting long races from short ones. A marathon predicted from a 5K assumes endurance the runner may not have built.
- Extrapolations beyond a distance ratio of about 4 stretch the formula past where it was fitted, and the calculator flags when that happens.
- Ignores course profile, temperature, humidity, wind and altitude, all of which cost more over longer distances.
- Says nothing about whether the target race is a sensible goal or how to train for it.
- Not applicable to ultramarathons beyond about 50 km, where terrain, nutrition and sleep dominate over aerobic capacity.
Common questions
How accurate is a marathon prediction from a 5K time?
Less accurate than it looks, and optimistic. Riegel assumes you are equally trained for both distances, which almost nobody is — a 5K takes twenty minutes while a marathon exposes glycogen depletion and muscular damage that never arise in a short race. Treat a 5K-derived marathon prediction as a best case that requires marathon-specific long runs to reach.
What is Riegel's formula?
T₂ = T₁ × (D₂ ÷ D₁)^1.06, published by Peter Riegel in 1977. The exponent above 1 encodes the fact that sustainable pace falls as distance rises — doubling the distance takes about 2.085 times as long, not twice as long.
Why do I run slower per mile in longer races?
Because the limiting factor changes. A short race is limited by how much oxygen you can deliver and use; over an hour or more, glycogen availability, fluid loss, core temperature and muscular fatigue take over. Riegel's exponent of 1.06 is an empirical summary of that shift — roughly a 4% pace penalty each time the distance doubles.
Should I use 1.06 or a higher exponent?
Use 1.06 for moderate extrapolations between similar distances. Some coaches prefer 1.07 or 1.08 specifically for marathon predictions, since 1.06 tends to flatter runners without marathon-specific endurance. The difference is a few minutes over 42 km — meaningful if you are pacing to it.
Sources
Formula and content last reviewed on .
Results are estimates for information only, not professional advice.
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