The formula
Peter Riegel published it in 1977. Time does not scale linearly with distance: doubling the distance costs more than double the time, because holding a pace gets harder the longer you hold it. The exponent is exactly that penalty.
T₂ = T₁ × (D₂ ÷ D₁) ^ 1.06
The 1.06 is not a law of physiology. Riegel fitted it to race results, and it describes a trained runner moving between neighbouring distances. It is at its best going from 5K to 10K, and at its worst going from 5K to a marathon.
A worked example
You ran 5K in 25:00 and want a half marathon estimate. The ratio of distances is 21.0975 ÷ 5 = 4.2195 — the same ratio in miles, 13.1 ÷ 3.1, gives the same answer, because a ratio has no units. Raised to the power 1.06 that is 4.6002. Multiply by 1500 seconds and the prediction is 6900 seconds — 1:55:00.
Why the marathon comes out as a range
The formula knows your speed. It does not know your endurance, and the marathon is decided by endurance. Analyses of large sets of recreational results consistently find that extrapolating from short races gives marathon predictions that are too fast, and that the gap widens as weekly volume falls. So any long extrapolation is shown here as a band, the marathon above all: the fast end uses Riegel’s 1.06, the slow end a conservative 1.10. From a 25:00 5K the band runs 3:59:47 to 4:21:08 — twenty-one minutes wide. From a 45:00 10K it narrows to 3:27:01 through 3:39:17, because you are extrapolating half as far. The shorter the leap, the more the formula actually knows.
Equivalent times from a 5K result
Riegel’s prediction at 1.06, with the conservative marathon column beside it. Read the marathon as the interval between the two columns, not as either number on its own.
| 5 km | 10 km | Half | Marathon | Marathon · conservative |
|---|---|---|---|---|
| 16:00 | 33:22 | 1:13:36 | 2:33:27 | 2:47:07 |
| 18:00 | 37:32 | 1:22:48 | 2:52:38 | 3:08:01 |
| 20:00 | 41:42 | 1:32:00 | 3:11:49 | 3:28:54 |
| 22:00 | 45:52 | 1:41:12 | 3:31:00 | 3:49:48 |
| 24:00 | 50:02 | 1:50:24 | 3:50:11 | 4:10:41 |
| 26:00 | 54:12 | 1:59:36 | 4:09:22 | 4:31:35 |
| 28:00 | 58:23 | 2:08:48 | 4:28:33 | 4:52:28 |
| 30:00 | 1:02:33 | 2:18:00 | 4:47:44 | 5:13:22 |
| 32:00 | 1:06:43 | 2:27:12 | 5:06:55 | 5:34:15 |
Every cell is computed with the same function the calculator above uses, so the table and the widget cannot drift apart.
What the formula cannot know
Weekly volume, above all: a 25:00 5K off 30 km a week — about 20 miles — and off 80 km a week, around 50 miles, predict the same marathon, and they should not. Then heat and humidity, which cost minutes over the marathon and seconds over 5K. Then the course — elevation, surface, how crowded the first mile is. Then fuelling, which only becomes a variable after roughly ninety minutes and can end a race the formula said you were fit for. None of that appears in a ratio of distances.
How to use it well
Predict from the closest distance you have raced recently, not from your best-ever result at any distance: a 10K from last month beats a 5K personal best from two years ago. Treat the output as the ceiling of a good day rather than a plan — setting out at predicted marathon pace off a 5K time is the classic way to walk the last six miles. And re-run the prediction after every race. The formula is much better at describing where you are than at promising where you will be.
Frequently asked questions
How accurate is a race time predictor?
For neighbouring distances it is quite good: predicting a 10K from a 5K typically lands within a percent or two for a trained runner. For a marathon from a short race it is unreliable in a specific direction — too fast — and the error grows as weekly volume falls. Treat the marathon output as an upper bound rather than a forecast.
What is Riegel’s formula?
T₂ = T₁ × (D₂ ÷ D₁) ^ 1.06, published by Peter Riegel in 1977. Your predicted time equals your known time multiplied by the ratio of the two distances raised to the power 1.06. It is the most widely used race equivalence formula, and almost every predictor you find online is running it under some other name.
Why is the exponent 1.06?
It is an empirical fit, not a derived constant. Riegel obtained it from race results across a range of distances. It encodes the observation that pace decays slowly but steadily as a race lengthens. Different populations fit different exponents: elite runners sit slightly below 1.06, and recreational runners extrapolating to a marathon sit above it.
Can I predict my marathon from a 5K?
You can, but it will be the weakest prediction the formula makes. A half marathon result predicts a marathon far better, and a 10K better than a 5K. If a 5K is all you have, use the conservative end of the range and sanity-check it against your weekly mileage.
How does this compare with a VDOT or VO₂max calculator?
VDOT-style tables convert a race result into a fitness score and then read equivalent times off that score. Over neighbouring distances they produce numbers close to Riegel’s, because both are fitted to the same kind of race data. Neither one knows your training volume, so neither fixes the marathon problem.
How recent does the race result need to be?
Within six to eight weeks for the prediction to mean much. Fitness moves quickly in both directions, and a result from last season describes a runner who no longer exists.