Quick answer: a 25:00 5K predicts about 52:07 for the 10K, 1:55:00 for the half marathon and 3:59:47 for the marathon with Riegel's formula. The Daniels and Gilbert VO2 model gives 51:53, 1:55:04 and 3:57:55 from the same race.
How to use the predictor
Pick a race you ran recently and all-out, type your time, and choose the race you want to predict. The headline uses the method you select; the table underneath shows all three columns for the mile, 5K, 10K, 15K, 10 miles, half and marathon, so you can see how far apart they are. A short, hard race from the last month or two is the best input. A training run is not.
Method 1: Riegel
Peter Riegel published his endurance formula in American Scientist in 1981: T2 = T1 x (D2 / D1)^1.06, where 1.06 is the popular exponent. Worked by hand for a 25:00 5K to the marathon: 42.195 / 5 = 8.439; 8.439^1.06 = 9.591; 1,500 seconds x 9.591 = 14,387 seconds, or 3:59:47. The cautious option raises the exponent to 1.08, which stretches longer predictions (4:10:14 for the same marathon).
Method 2: Daniels and Gilbert
Jack Daniels and Jimmy Gilbert (1979) fitted two curves: the oxygen cost of running at a given speed, and the share of VO2 max a runner can hold for a given time. Your race gives a single fitness number, VDOT (38.3 for a 25:00 5K), and the model finds the time at which that VDOT balances over the new distance. The table below lists race times for a range of VDOT values, calculated from the published equations.
| VDOT | Mile | 5K | 10K | Half | Marathon |
|---|---|---|---|---|---|
| 30 | 9:10 | 30:41 | 1:03:49 | 2:21:17 | 4:49:49 |
| 32 | 8:40 | 29:05 | 1:00:27 | 2:13:55 | 4:35:17 |
| 34 | 8:13 | 27:38 | 57:25 | 2:07:17 | 4:22:11 |
| 36 | 7:49 | 26:21 | 54:42 | 2:01:18 | 4:10:19 |
| 38 | 7:27 | 25:10 | 52:15 | 1:55:51 | 3:59:30 |
| 40 | 7:07 | 24:06 | 50:01 | 1:50:54 | 3:49:37 |
| 42 | 6:49 | 23:08 | 47:58 | 1:46:22 | 3:40:33 |
| 44 | 6:32 | 22:14 | 46:06 | 1:42:12 | 3:32:12 |
| 46 | 6:17 | 21:24 | 44:23 | 1:38:21 | 3:24:29 |
| 48 | 6:03 | 20:38 | 42:48 | 1:34:48 | 3:17:19 |
| 50 | 5:50 | 19:56 | 41:20 | 1:31:31 | 3:10:40 |
| 52 | 5:38 | 19:17 | 39:58 | 1:28:28 | 3:04:28 |
| 54 | 5:27 | 18:40 | 38:42 | 1:25:37 | 2:58:40 |
| 56 | 5:16 | 18:05 | 37:31 | 1:22:58 | 2:53:15 |
| 58 | 5:06 | 17:33 | 36:24 | 1:20:28 | 2:48:09 |
| 60 | 4:57 | 17:03 | 35:22 | 1:18:09 | 2:43:22 |
| 62 | 4:49 | 16:34 | 34:23 | 1:15:57 | 2:38:52 |
| 64 | 4:41 | 16:07 | 33:28 | 1:13:54 | 2:34:37 |
| 66 | 4:33 | 15:42 | 32:36 | 1:11:57 | 2:30:37 |
| 68 | 4:26 | 15:18 | 31:47 | 1:10:07 | 2:26:49 |
| 70 | 4:19 | 14:56 | 31:01 | 1:08:23 | 2:23:13 |
| 72 | 4:13 | 14:34 | 30:17 | 1:06:44 | 2:19:48 |
| 74 | 4:07 | 14:14 | 29:35 | 1:05:10 | 2:16:33 |
| 76 | 4:01 | 13:54 | 28:56 | 1:03:42 | 2:13:28 |
| 78 | 3:56 | 13:36 | 28:18 | 1:02:17 | 2:10:31 |
| 80 | 3:51 | 13:18 | 27:42 | 1:00:57 | 2:07:43 |
Limits
Both methods assume you have trained for the target distance. A fast 5K with low weekly mileage often turns into an optimistic marathon prediction, because endurance, fuelling and pacing matter more over 26.2 miles. Heat, hills and a poor night's sleep are not in any formula either.
Turn the prediction into a plan: get training paces from the same race, see every split on the marathon pace chart, or try the half marathon time predictor. To compare results across ages, try the age grading calculator. All formulas used here are listed on the methodology page.
Sources: Riegel PS (1981), Athletic records and human endurance, American Scientist 69(3):285-290; Daniels J, Gilbert J (1979), Oxygen Power: Performance Tables for Distance Runners (equations as quoted by L. Simpson). Rules checked . Found a problem? Tell us.
Questions
How accurate is the Riegel formula?
It is a good first estimate when you have trained for the longer race. It tends to be optimistic for the marathon if your weekly mileage is low, which is why the cautious 1.08 option is offered.
What marathon time does a 25 minute 5K predict?
About 3:59:47 with Riegel (exponent 1.06), 3:57:55 with the Daniels and Gilbert model and 4:10:14 with the cautious 1.08 exponent.
What is VDOT?
A single fitness score from the Daniels and Gilbert equations: the oxygen cost of your race speed divided by the share of VO2 max you can hold for that race duration. A 50:00 10K gives a VDOT of 40.0.
Which race should I use to predict a marathon?
A recent half marathon is usually the best guide because it is closest in length. A 10K is next best; a mile or 5K is the least reliable.