Pace and Race Time Prediction
One division gives you pace. One exponent turns a time you have run into a time at a distance you have not. Here is both, worked, and where the second stops being honest.
Last updated: 1 July 2026
Pace is one division
Pace = time ÷ distance
25 minutes for 5 km is 1500 seconds ÷ 5 = 300 seconds per kilometre, which is 5:00 per km.
For miles, multiply by the number of kilometres in a mile:
300 × 1.609344 = 482.8 seconds, which is 8:03 per mile.
Or as a treadmill speed, 3600 ÷ 300 = 12.0 km/h.
That is the whole of it. The interesting question is the other one.
Predicting a time at a distance you have not run
The obvious approach is to hold your pace. Run 5 km at 5:00 per km, so a marathon is 42.195 × 5:00, which is 3 hours 31. Nobody does this. Pace falls as distance rises, for everybody, and the fall is regular enough to put a number on.
Predicted time = raced time × (target distance ÷ raced distance) ^ 1.06
The exponent is the whole formula. At 1.0 it would be flat pace. At 1.06, doubling the distance costs about 8.5 percent more than double the time.
From that same 25 minute 5 km, to 10 km:
1500 × (10 ÷ 5) ^ 1.06 = 1500 × 2.0849 = 3127 seconds, which is 52:07.
What a 25 minute 5 km predicts
| Distance | Predicted time |
|---|---|
| 1 km | 4:32 |
| 1 mile | 7:31 |
| 5 km | 25:00 |
| 10 km | 52:07 |
| Half marathon | 1:55:00 |
| Marathon | 3:59:47 |
Work it out: the [pace calculator](/tools/pace) does both steps for any run, and marks the predictions that are reaching.
Where this stops being honest
Riegel fitted the exponent across race results, and it holds well when the two distances are close. It flatters badly when they are not.
The rule of thumb is a factor of four. Predicting 10 km from 5 km is reliable. Predicting a marathon from a 5 km is a factor of eight, and the 3:59:47 above should be read as the time you would run if endurance were the only thing that mattered and you had trained for the distance. If you have never run beyond 10 km, you will not run that marathon time, and the gap is not a fitness problem. It is that a marathon punishes things a 5 km never tests: fuelling, pacing discipline, and how your legs behave in the third hour.
Used the other way round it is far more trustworthy. A half marathon time predicts a marathon within a factor of two, which is inside where the formula works.
Common questions
Why 1.06 and not something else?
It is a fitted average across a lot of race results. Individuals vary: a runner with a strong endurance base beats their prediction at long distances, and a fast runner with no mileage misses it.
Does it work for other sports?
The same shape applies to swimming, cycling and rowing, but the exponent differs. The number here is the running one.
Should I use it to set a race target?
As a ceiling, not a plan. Predict from the closest distance you have actually raced, and take the number down rather than up if the target is much longer than anything you have trained for.
Sources
Riegel, Athletic Records and Human Endurance (American Scientist, 1981) - https://www.jstor.org/stable/27850427
NHS couch to 5k - https://www.nhs.uk/live-well/exercise/get-running-with-couch-to-5k/
NHS exercise guidelines - https://www.nhs.uk/live-well/exercise/exercise-guidelines/