Race Time Predictor
Riegel race-time prediction across distances — doubling the distance costs only 4.2% per km, and the exponent is a fitted number.
This assumes the training behind the longer race actually exists. The formula is fitted to people who race the distances it predicts, so it is at its most optimistic exactly where it is least tested — the marathon, for someone who has never run one. Treat a long prediction as a ceiling rather than a plan. Nothing is uploaded.
Distance is cheaper than it feels
Riegel's formula raises the distance ratio to a power a little above one, so doubling the distance costs a factor of 2.0849 rather than 2 — about 4.2% slower per kilometre, not the collapse most people picture. From a 20:00 5k it projects a 3:11:49 marathon.
| Race | Distance | Predicted | Pace per km |
|---|---|---|---|
| 1500 m | 1.5 km | 5:35 | 3:43 |
| 5 km | 5 km | 20:00 | 4:00 |
| 10 km | 10 km | 41:42 | 4:10 |
| Half marathon | 21.0975 km | 1:32:00 | 4:22 |
| Marathon | 42.195 km | 3:11:49 | 4:33 |
The marathon is 8.44 times the distance of the 5k and only 9.59 times the time, so across that whole jump the pace degrades by about 14%. That ratio is exactly the distance ratio raised to the exponent less one, which is the entire content of the formula written another way.
And it all rests on a fitted number
The 1.06 is an empirical fit over race results, not a law of anything. Set it to 1 and pace never degrades at all, which would predict a 2:48:47 marathon off that same 5k. Set it to 1.15 and the prediction moves to 3:52:25 — a spread of 1:03:38 from one number.
| Exponent | Doubling costs | Marathon from a 20:00 5k |
|---|---|---|
| 1 | 2.0000× | 2:48:47 |
| 1.02 | 2.0279× | 2:56:08 |
| 1.04 | 2.0562× | 3:03:49 |
| 1.06 — the usual value | 2.0849× | 3:11:49 |
| 1.08 | 2.1140× | 3:20:11 |
| 1.1 | 2.1435× | 3:28:54 |
| 1.15 | 2.2191× | 3:52:25 |
Two hundredths either way is worth about eight minutes over a marathon, which is more than most people's goal margin. That is not a reason to distrust the formula — it predicts a 10 km from a 5 km very well — but it is a reason to treat the long end as an estimate with a range rather than a time to print on a plan. The prediction is reversible and composes cleanly, so any inconsistency you find is in the exponent, not the arithmetic.
How to use
- Enter a distance you have actually raced and the time.
- Read the predicted times across the standard distances.
- Vary the exponent to see how much it is carrying.
- Treat long predictions as a ceiling, not a plan.
Frequently asked questions
How does race time prediction work?
Riegel raises the distance ratio to a power: the new time is the old time times the distance ratio to the 1.06. Because that exponent is only a little above one, longer races cost less time than most people expect.
What does doubling the distance cost?
A factor of 2 to the 1.06, which is 2.0849 — so about 4.2% slower per kilometre, not a collapse. A twenty-minute 5k projects to a 41:42 10k on that basis.
Does that really hold to the marathon?
The arithmetic does; the running often does not. A 20:00 5k projects a 3:11:49 marathon, which assumes the training behind a marathon actually exists. The formula is most optimistic exactly where it is least tested.
How much does the exponent matter?
A great deal at long distances. Two hundredths either way is worth about eight minutes over a marathon, which is more than most goal margins. That is why the exponent is an input here rather than baked in.
What would an exponent of 1 mean?
That pace never degrades with distance at all — a 20:00 5k would be a 2:48:47 marathon. Nobody runs like that, which is the evidence that the exponent has to be above one.
Is the formula reliable at all?
For nearby distances, yes, and predicting a 10 km from a 5 km is about as good as this kind of estimate gets. The uncertainty grows with the extrapolation, so the further the prediction, the wider the range it deserves.
Can I predict backwards?
Yes — the relationship is reversible and composes, so a marathon time predicts a 5k and going via the 10 km gives the same answer as going directly. Any inconsistency you find is in the exponent, not the arithmetic.
Does this send anything anywhere?
No. Every figure is computed in your browser, and nothing is uploaded or stored.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.