Key Takeaways
- This page uses two equations from a 2016 study of recreational runners[1][2]. With one recent race, it needs your time and your weekly mileage. With two races, it also looks at how much you slow down between them.
- A half marathon in 1:45:00 at 40 miles a week gives 3:49:16. Riegel's formula with an exponent of 1.06 gives 3:38:55[3], so at moderate mileage the mileage model is the more cautious of the two. At 80 miles a week the same race gives 3:31:33.
- In the paper's validation runners, Riegel predicted marathon times that were at least 10 minutes too fast for about half of them. The new models did that for about a quarter[1].
- Age, sex, course and weather are not in the equations. Treat the answer as the middle of a range, and read the range shown under your result.
How the Marathon Time Predictor Works
Choose a recent race from 5K to a half marathon, enter your finish time, then add your typical weekly mileage. In the study, that meant the miles you run in a normal training week in the build-up to your longest race[1].
If you have a second race of a different length, add it. The page then uses the paper's two-race model, which looks at how much you slow down between the two distances.
If a race was clearly harder or easier than usual, you can say so. The survey asked runners to rate each course on wind, hills and temperature, and the paper adjusts those times to an average course[1][2].
The Prediction Formulas
Both models are from the paper's Additional file 1[2]. Distances are in metres, times in seconds, and v is velocity in metres per second.
| Model | Equation |
|---|---|
| Model 1: one race | v = 0.16018617 + 0.83076202 × vRiegel + 0.06423826 × (miles per week ÷ 10), where vRiegel is the marathon velocity from Riegel's formula with exponent 1.07. Marathon time = 42,195 ÷ v. |
| Model 2: two races | kbetween = ln(T2 ÷ T1) ÷ ln(D2 ÷ D1). kmarathon = 1.4510756 − 0.23797948 × kbetween − 0.01410023 × (miles per week ÷ 10). Marathon time = T2 × (42,195 ÷ D2)^kmarathon. |
| Difficult or fast race | Adjusted time = D ÷ (D ÷ T + adjustment). The adjustment depends on the distance and is listed in the next table. |
The two marathon prediction models from Vickers and Vertosick (2016).
The paper has no worked example, so each equation here is checked against a separate hand calculation. A half marathon in 1:45:00 at 40 miles a week gives 3:49:16 from Model 1.
For two races, a 10K in 50:00 and a half marathon in 1:50:00 at 40 miles a week give a slowing exponent of 1.056, a marathon exponent of 1.143 and a time of 4:02:59.
| Race | Difficult (added to velocity) | Fast (subtracted from velocity) |
|---|---|---|
| 5K | +0.1129 | -0.0238 |
| 5 miles | +0.1090 | -0.1550 |
| 10K | +0.0246 | -0.0781 |
| 10 miles | +0.1031 | -0.1358 |
| Half marathon | +0.0336 | -0.0978 |
Velocity adjustment in metres per second for a race the runner called difficult or fast, from the paper's Additional file 1.
A 10K in 50:00 on a difficult course counts as 49:38 on an average one, and the marathon prediction at 40 miles a week moves from 4:00:46 to 3:59:15. The paper left races rated very difficult or very fast out of its data, so only difficult and fast are offered.
Marathon Time Predictor Chart: Half Marathon, 10K and 5K
Each time is Model 1 for one race on an average course. Find your race time in the first column and read across to your weekly mileage. For a second race, a difficult course or a mileage between columns, use the calculator.
Half marathon to marathon
| Half marathon | 20 mi/week | 30 mi/week | 40 mi/week | 50 mi/week | 60 mi/week |
|---|---|---|---|---|---|
| 1:30:00 | 3:28:01 | 3:24:08 | 3:20:24 | 3:16:48 | 3:13:20 |
| 1:40:00 | 3:48:58 | 3:44:16 | 3:39:46 | 3:35:27 | 3:31:17 |
| 1:45:00 | 3:59:17 | 3:54:10 | 3:49:16 | 3:44:34 | 3:40:03 |
| 1:50:00 | 4:09:31 | 4:03:57 | 3:58:38 | 3:53:33 | 3:48:40 |
| 2:00:00 | 4:29:41 | 4:23:12 | 4:17:01 | 4:11:08 | 4:05:30 |
| 2:10:00 | 4:49:29 | 4:42:02 | 4:34:57 | 4:28:13 | 4:21:48 |
Predicted marathon time from a half marathon time and weekly mileage, Model 1.
10K to marathon
| 10K | 20 mi/week | 30 mi/week | 40 mi/week | 50 mi/week | 60 mi/week |
|---|---|---|---|---|---|
| 40:00 | 3:25:44 | 3:21:56 | 3:18:17 | 3:14:45 | 3:11:21 |
| 45:00 | 3:49:02 | 3:44:20 | 3:39:50 | 3:35:30 | 3:31:21 |
| 50:00 | 4:11:51 | 4:06:11 | 4:00:46 | 3:55:35 | 3:50:37 |
| 55:00 | 4:34:12 | 4:27:30 | 4:21:07 | 4:15:02 | 4:09:14 |
| 1:00:00 | 4:56:06 | 4:48:18 | 4:40:54 | 4:33:52 | 4:27:11 |
| 1:05:00 | 5:17:33 | 5:08:36 | 5:00:08 | 4:52:08 | 4:44:32 |
Predicted marathon time from a 10K time and weekly mileage, Model 1.
5K to marathon
| 5K | 20 mi/week | 30 mi/week | 40 mi/week | 50 mi/week | 60 mi/week |
|---|---|---|---|---|---|
| 20:00 | 3:35:03 | 3:30:55 | 3:26:56 | 3:23:05 | 3:19:23 |
| 22:30 | 3:59:18 | 3:54:11 | 3:49:16 | 3:44:34 | 3:40:03 |
| 25:00 | 4:23:01 | 4:16:51 | 4:10:57 | 4:05:20 | 3:59:57 |
| 27:30 | 4:46:14 | 4:38:56 | 4:32:00 | 4:25:24 | 4:19:08 |
| 30:00 | 5:08:57 | 5:00:28 | 4:52:26 | 4:44:50 | 4:37:37 |
| 32:30 | 5:31:12 | 5:21:28 | 5:12:18 | 5:03:38 | 4:55:26 |
Predicted marathon time from a 5K time and weekly mileage, Model 1.
Weekly mileage moves the answer. The 1:45:00 half marathon gives 3:54:10 at 30 miles a week and 3:44:34 at 50, a gap of 9:36. The study's marathon runners reported a median of 40 miles a week, with half of them between 30 and 50[1].
A 5K is a long way from a marathon
Riegel's Formula vs the Mileage Model
Riegel's formula scales a time by the distance ratio raised to an exponent[3]. The paper notes that the Runner's World online calculator used 1.06 when it was written. The authors chose 1.07 as an average and checked 1.06 and 1.08 in sensitivity analyses[1].
They found Riegel well calibrated up to the half marathon, but too fast for the marathon. For the 1:45:00 half marathon, Riegel at 1.07 gives 3:40:26. The mileage model gives 3:49:16 at 40 miles a week.
What the mileage model adds is training volume, which Riegel ignores. To compare Riegel across every distance, or to get VDOT and training paces, use the running performance calculator.
How Accurate Is the Prediction?
The paper tested the models on 156 validation runners who had reported a marathon and two other races[1]. Mean squared error was 227.6 for Model 1, 208.3 for Model 2 and 380.7 for Riegel, in minutes squared.
That is a root mean squared error of about 15.1, 14.4 and 19.5 minutes. The table below shows the spread of predicted minus observed time.
| Centile | Model 1 | Model 2 | Riegel (1.07) |
|---|---|---|---|
| 5th | −23:53 | −21:38 | −36:17 |
| 25th | −9:55 | −7:31 | −19:47 |
| 50th | −1:47 | 0:23 | −10:09 |
| 75th | 6:28 | 7:20 | −2:48 |
| 95th | 15:23 | 21:05 | 5:12 |
Predicted minus observed marathon time in minutes and seconds, by centile, from Table 4 of Vickers and Vertosick (2016). A negative value means the prediction was too fast.
The middle half of Model 1 errors runs from 9:55 too fast to 6:28 too slow. After a result, this page adds those minutes to your prediction to show a range of finish times.
The paper reports the errors in minutes. Applying the same number of minutes to every runner is a simplification made by this page, and whether it holds for much slower or faster finishers is not known.
What the Predictor Cannot Know
- Age, sex and body mass are not in the prediction equations[2]. The paper found that they relate to race velocity, but its two prediction models use only race times and weekly mileage.
- The marathon course, the weather and your pacing on the day are not included. A hot or hilly marathon will run slower than the number shown.
- Long runs, injuries and how many weeks you have trained are not included. Weekly mileage is one average, so it cannot tell a steady 40 miles from a single big week.
- The data come from an internet survey of 2,303 recreational runners in 2014, with a median age of 35[1]. Only 21 of the marathon runners were over 60 and 3 were over 70, so the authors say predictions for older runners are less certain.
- Mileage enters the equations as a straight line, so a very low or very high figure goes beyond what the study can support. At 80 miles a week, the 1:45:00 half marathon gives 3:31:33. The page adds a note below 15 or above 80 miles a week, and when two races are less than 1.5 times apart in distance. Those cut-offs are mine, not published limits.
Once you have a goal time, the marathon pace calculator turns it into pace and splits. A mile is 1,609.344 m exactly[6], the marathon is 42.195 km[4] and the half marathon is 21.0975 km[5]. The 3:49:16 example works out to 8:45 per mile.
Frequently Asked Questions
Sources & References
- An empirical study of race times in recreational endurance runners. Vickers AJ, Vertosick EA. BMC Sports Science, Medicine and Rehabilitation 8:26 (2016)
- Additional file 1: Formulae for Prediction Models (supplement to Vickers and Vertosick 2016, Word document). Vickers AJ, Vertosick EA. BMC Sports Science, Medicine and Rehabilitation 8:26 (2016)
- Athletic records and human endurance. Riegel PS. American Scientist 69(3):285-290 (1981)
- Marathon. World Athletics. World Athletics, Disciplines: Road Running
- Half Marathon. World Athletics. World Athletics, Disciplines: Road Running
- NIST Guide to the SI, Appendix B.8: Factors for Units Listed Alphabetically. National Institute of Standards and Technology. NIST Special Publication 811
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Disclaimer: This tool applies published prediction equations to the race times and weekly mileage you enter. The equations come from a survey of recreational runners and cannot see your course, weather, long runs, age or health. Treat the result as an estimate, not a promise, and check with a coach or doctor before a first marathon or a big jump in training.