Predict Your Race Time with the Riegel Formula
If you can run 5 km in 25 minutes, you cannot simply multiply by eight to predict a 40 km effort: you slow down as the distance grows. Race predictors correct for that fatigue, and the best-known version is the Riegel formula, which needs only a distance and a time from a recent hard effort.
Below is the formula, a full worked example from a 25:00 5K, a table of predictions, and an honest look at when the numbers mislead. A prediction describes what your current fitness could deliver on the right day, with the right training, not a guarantee.
The formula and the fatigue exponent
T2 = T1 × (D2 ÷ D1) ^ 1.06T1 and D1 are your known time and distance; T2 and D2 are the prediction and target distance.
If the exponent were exactly 1, time would grow in step with distance and your pace would never change. The 1.06 makes time grow slightly faster than distance, so doubling the distance multiplies the time by 2^1.06 ≈ 2.085 rather than 2. That extra 4% or so is the allowance for fatigue, and it compounds as the gap between the distances widens.
On a scientific calculator, use the x^y or y^x key. In a spreadsheet, the same calculation is =T1*(D2/D1)^1.06 with the time in seconds.
Worked example: from a 25:00 5K
Convert 25:00 to seconds: T1 = 1,500 s, and D1 = 5 km. For a 10K, the distance ratio is 10 ÷ 5 = 2, so T2 = 1,500 × 2^1.06 = 1,500 × 2.0849 ≈ 3,127 s, which is 52:07.
Repeating the calculation for the other standard distances, and comparing with naive proportional scaling:
| Target | Riegel prediction | Pace per km | Naive scaling |
|---|---|---|---|
| 10K | 52:07 | 5:13 | 50:00 |
| Half marathon | 1:55:00 | 5:27 | 1:45:29 |
| Marathon | 3:59:47 | 5:41 | 3:30:59 |
The difference is large. Naive scaling would put the marathon at 3:30:59, nearly half an hour faster than the Riegel estimate, and it would have you starting at a pace you could not hold.
The formula also works from other starting points. A 50:00 10K predicts a half marathon of 3,000 × (21.0975 ÷ 10)^1.06 ≈ 6,619 s, which is 1:50:19 or about 5:14 per km.
Working backwards from a goal
Because the formula is a simple power law, you can rearrange it to ask what shorter-race fitness a goal requires. Divide the goal time by the distance ratio raised to 1.06, instead of multiplying.
T1 = T2 ÷ (D2 ÷ D1) ^ 1.06
Worked example: to run a half marathon in 1:45:00 (6,300 s), the ratio of 21.0975 km to 5 km is 4.2195, and 4.2195^1.06 ≈ 4.600. So T1 = 6,300 ÷ 4.600 ≈ 1,370 s, which is a 5K of about 22:50. If your current 5K is slower than that, the goal needs improved fitness first, and that is useful to know weeks before race day rather than at the start line.
Why predictions miss
The formula is an average fitted to many runners. Whether it fits you depends on several things:
- Training for the target distance. A good 5K says little about whether you have done the long runs a marathon demands. Predictions for the marathon are often optimistic for runners with modest weekly mileage.
- Quality of the input. Use a race or an honest all-out time trial from the last few weeks, not an easy training run or a result from a year ago.
- Distance gap. Predicting a 10K from a 5K is far safer than predicting a marathon from a 5K. Staying within a factor of about two to four in distance gives more reliable numbers.
- Conditions. Heat, hills and wind can add minutes that no formula includes.
- Your running profile. Some runners are naturally stronger at short, fast races, others at long, steady ones, and the formula treats everyone the same.
A sensible habit is to compare predictions from two recent results, such as a 5K and a 10K. If they agree within a minute or two over a half marathon, you can trust the figure more. If they differ a lot, one of the results was probably not a true best effort.
Turning a prediction into a pacing plan
Suppose you set a marathon target of 4:00:00. That is 14,400 seconds over 42.195 km, or 341.3 seconds per km (5:41 per km). Multiply by each checkpoint to build a split table:
| Checkpoint | Target time |
|---|---|
| 5 km | 28:26 |
| 10 km | 56:53 |
| 20 km | 1:53:45 |
| Half marathon | 2:00:00 |
| 30 km | 2:50:38 |
| 40 km | 3:47:31 |
| Finish | 4:00:00 |
Many runners aim for an even pace or a slightly faster second half (a negative split), because starting too quickly is a common cause of a late slowdown. Whatever the plan, check the first few kilometres against your table and settle into the pace rather than chasing a fast start.
The pace calculator converts between pace, distance and finish time, and the time calculator helps when you need to add or subtract split times.
This is general information for recreational runners, not medical or coaching advice. If you are new to endurance running, build distance gradually, and see a doctor before starting if you have any health concerns.
- Pace Calculator: Choose what you want to find, fill in the other two values and read the answer. Pace comes out per mile and per kilometre, and speed in two units.
- Time Calculator: Use the clock calculator to see what time it will be after adding or removing hours, minutes and seconds, or the date and time calculator to move a whole timestamp forwards or backwards.
This article is general information, not professional advice. See our Disclaimer and Editorial Policy.
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