Race Time Predictor: Riegel's Formula, Chart and Marathon Times
To predict a race time at a new distance, take a time you have run and scale it with Riegel’s formula: T2 = T1 x (D2 / D1)^1.06. A 25:00 5K predicts a 52:07 10K, a 1:55:00 half marathon and a 3:59:47 marathon. The prediction assumes you are trained for the longer race - it describes what your current fitness supports, not what you will run without the mileage.
The race time predictor formula
- T1 is the time you have run, D1 its distance.
- D2 is the distance you want to predict.
- T2 is the predicted time.
- 1.06 is the exponent - the whole reason the answer is not simple multiplication.
If the exponent were 1.0, time would scale exactly with distance and you would hold your 5K pace for a marathon. The 0.06 above 1 is the slowdown. Doubling the distance multiplies the time by 2.085, not 2, so each doubling costs about 4.2% on pace.
The same formula written for pace instead of time is often easier to think with:
- pace2 = pace1 x (D2 / D1)^0.06
The worked example: a 25:00 5K
The marathon is 8.439 times as long as a 5K. Linear scaling would multiply the time by 8.439. Riegel multiplies it by 8.439 raised to the 1.06, which is 9.591.
- Linear: 25:00 x 8.439 = 3:30:59
- Riegel: 25:00 x 9.591 = 3:59:47
That is a gap of about 29 minutes. In pace terms, the 5:00 per kilometer you hold over 5K becomes 5:41 per kilometer over the marathon - 13.7% slower. Even the 10K is not double: linear says 50:00, Riegel says 52:07.
Race time predictor chart: from your 5K
Find your current 5K on the left. Each row is what the formula predicts at the longer distances, with the pace per kilometer you would hold.
| 5K time | 10K | Half marathon | Marathon | 5K pace /km | Marathon pace /km |
|---|---|---|---|---|---|
| 18:00 | 37:32 | 1:22:48 | 2:52:38 | 3:36 | 4:05 |
| 20:00 | 41:42 | 1:32:00 | 3:11:49 | 4:00 | 4:33 |
| 22:00 | 45:52 | 1:41:12 | 3:31:00 | 4:24 | 5:00 |
| 24:00 | 50:02 | 1:50:24 | 3:50:11 | 4:48 | 5:27 |
| 25:00 | 52:07 | 1:55:00 | 3:59:47 | 5:00 | 5:41 |
| 26:00 | 54:12 | 1:59:36 | 4:09:22 | 5:12 | 5:55 |
| 28:00 | 58:23 | 2:08:48 | 4:28:33 | 5:36 | 6:22 |
| 30:00 | 1:02:33 | 2:18:00 | 4:47:44 | 6:00 | 6:49 |
| 32:00 | 1:06:43 | 2:27:12 | 5:06:55 | 6:24 | 7:16 |
| 35:00 | 1:12:58 | 2:41:00 | 5:35:41 | 7:00 | 7:57 |
Predicting a marathon from a half
The formula works from any distance to any other, and the half is the closest standard race to the marathon - exactly 2 times shorter, against the 5K’s 8.439. A shorter jump means the exponent has less distance to act over, so a small error in it moves the answer less.
An illustrative 1:50:00 half marathon:
- Doubled: 3:40:00
- Riegel: 1:50:00 x 2.085 = 3:49:21
The formula adds 9.3 minutes on top of doubling. If you have run a recent half, it is the better starting point for a marathon prediction than a 5K - because the 5K-to-marathon jump is longer, not because of any accuracy figure we can cite.
Pace chart: what each pace adds up to
Holding an even pace is plain arithmetic, no exponent involved. The min/mile column is the min/km column times 1.609344 (the exact definition of a mile in kilometers), and the race columns are pace times distance.
| Min/km | Min/mile | km/h | mph | 10K | Half | Marathon |
|---|---|---|---|---|---|---|
| 4:00 | 6:26 | 15.00 | 9.32 | 40:00 | 1:24:23 | 2:48:47 |
| 4:30 | 7:15 | 13.33 | 8.28 | 45:00 | 1:34:56 | 3:09:53 |
| 5:00 | 8:03 | 12.00 | 7.46 | 50:00 | 1:45:29 | 3:30:59 |
| 5:30 | 8:51 | 10.91 | 6.78 | 55:00 | 1:56:02 | 3:52:04 |
| 6:00 | 9:39 | 10.00 | 6.21 | 1:00:00 | 2:06:35 | 4:13:10 |
| 6:30 | 10:28 | 9.23 | 5.74 | 1:05:00 | 2:17:08 | 4:34:16 |
| 7:00 | 11:16 | 8.57 | 5.33 | 1:10:00 | 2:27:41 | 4:55:22 |
| 7:30 | 12:04 | 8.00 | 4.97 | 1:15:00 | 2:38:14 | 5:16:28 |
| 8:00 | 12:52 | 7.50 | 4.66 | 1:20:00 | 2:48:47 | 5:37:34 |
Use the two charts together: read your predicted marathon off the first chart, then find the even pace that produces it in the second.
What the 1.06 is, and what it is not
The exponent comes from Peter Riegel, a research engineer, who fitted a straight line to world-record times plotted against distance on log-log axes. He set it out in “Athletic Records and Human Endurance,” American Scientist, vol. 69, no. 3 (1981), pp. 285-290. It is an empirical fit - a description of how record times have scaled with distance - not a law of physiology, and it was fitted to record performances, not to you.
That matters because the prediction is sensitive to it. Holding the 25:00 5K fixed and nudging the exponent:
- at 1.04, the marathon prediction is 3:49:46
- at 1.06, it is 3:59:47
- at 1.08, it is 4:10:14
A change of 0.02 either side spreads the marathon prediction across about 20 minutes. The formula uses one exponent for every runner; it cannot know how your own times scale. If you have raced two distances recently, you can solve for your own exponent: log(T2 / T1) / log(D2 / D1).
Three honest limits:
- It assumes equivalent training for the longer race. A 5K run off 20 miles a week does not make you ready for a marathon. The prediction is the race your speed would support with the endurance work done.
- It gets less reliable as the jump gets longer. The marathon adds problems a 5K never tests - fueling, pacing discipline over hours, heat. We do not have a sourced error figure for this, so we are not quoting one.
- It knows nothing about the course or the day. Hills, heat, wind and altitude are outside the formula.
Treat the marathon column as a starting estimate to test in training, not a goal pace to commit to on race morning.
How these were calculated
Every time on this page was computed twice: by the generator script behind the poster below, which applies T1 x (D2/D1)^1.06, and by an independent implementation that works through logarithms and rounds to whole seconds once. The page only builds if they agree on every cell. The check also confirms that each prediction inverts - predicting the marathon from a 5K and then the 5K back from that marathon returns the original time - and that the formula’s marathon is slower than linear scaling for all 10 seed times. Times are rounded to the nearest second. Distances are 5 km, 10 km, 21.0975 km and 42.195 km. The 25:00 5K and 1:50:00 half are illustrative inputs. This is a planning estimate, not coaching or medical advice.
If you want the prediction chart and the pace conversions on the wall where you plan your training, the poster prints both tables at 11 x 17: