Predict your marathon time from a half marathon
A 1:55 half says 3:59:46 with Riegel. Checked on 2,303 recreational runners, half of them finished at least 10 minutes slower than that.
Updated
Run a 1:55 half and Riegel’s formula says you’re a 3:59:46 marathoner. Sub-4, on paper. Cameron’s formula says 4:04:23.
When Vickers and Vertosick checked Riegel against 2,303 recreational runners, half of them finished at least 10 minutes slower than predicted.
Where the formulas break
Riegel held up fine from the 5K to the half in that study. It broke at the marathon, and the fix that worked was adding weekly mileage to the model.
A formula extends a curve from one race to another. It doesn’t know if you run 20 miles a week or 50, and the marathon does.
A 10K mostly tests your VO2max and your threshold. A marathon also tests glycogen, your legs after mile 20 and how patient you were in the first 10K. Smyth looked at more than a million marathon results, mostly recreational runners, and found a late-race pace collapse (the wall) in 28% of men and 17% of women.
Riegel, Cameron and Daniels-Gilbert
Riegel is a power law: T2 = T1 × (D2 ÷ D1)1.06. Peter Riegel fitted it on world records for efforts from about 3.5 to 230 minutes. 230 minutes is 3:50, so a four-hour marathon is already off the end of the data.
Cameron fits a different curve on best times from 400 m to 50 miles, with a slowdown that changes with distance. In the table below it comes out 4 to 5½ minutes slower than Riegel.
Estimated VO2max (Daniels-Gilbert) goes through oxygen cost. Your half gives a VO2max, and that VO2max gives a time at any distance. It lands a little faster than Riegel, by 43 seconds to 4 minutes here.
| Half marathon | Riegel | Cameron | Daniels-Gilbert |
|---|---|---|---|
| 1:40:00 | 3:28:30 | 3:32:30 | 3:27:47 |
| 1:55:00 | 3:59:46 | 4:04:23 | 3:57:48 |
| 2:15:00 | 4:41:28 | 4:46:53 | 4:37:25 |
The slower you are, the wider the spread, and the further past Riegel’s 230 minutes you’re asking it to reach.
Which race to plug in
A recent all-out half on a flat course, 4 to 8 weeks before race day. A 10K works too. A 5K measures speed more than endurance, so the marathon it predicts is almost always optimistic: a 25:00 5K gives 3:59:47 with Riegel, the same as the 1:55 half, but only the half marathoner has held a hard pace for close to two hours.
Turning it into a goal pace
Take the slower of Riegel and Cameron. For a first marathon, or if you run fewer than four days a week, add 10 minutes. That’s the gap half the runners in the Vickers study gave back.
For the 1:55 half, that’s 4:04:23 from Cameron, or 9:19 per mile. Add the 10 minutes and you get 4:14:23, which is 9:42 per mile (6:02 per km).
Hold that pace to mile 20 even if it feels easy at mile 8. If you still have legs at 20, speed up then. A small negative split costs a lot less than walking from mile 22.
Check it on a long run
Three to five weeks out, put 10 to 12 miles at goal pace into a long run. Compare your heart rate over the first half of that block with the second. If it climbs more than 5% at the same pace, the pace is too fast. Drop back to the slowest of the three predictions.
The race time predictor shows Riegel and Cameron side by side, the VO2max calculator gives the Daniels-Gilbert time, and the pace calculator turns your goal into mile splits.
Sources
- Riegel formula: Riegel, Am Sci 1981;69(3):285–290. The 1.06 exponent comes from a 1977 Runner’s World article.
- Cameron model: model description, archived.
- Riegel’s accuracy on 2,303 recreational runners: Vickers and Vertosick, BMC Sports Sci Med Rehabil 2016;8:26.
- Late-race pace collapse: Smyth, PLoS One 2021;16(5):e0251513.
- Estimated VO2max: Daniels and Gilbert, Oxygen Power, 1979.
- The 5% decoupling threshold: Friel, Efficiency Factor and Decoupling, TrainingPeaks. Bands above 5% are coaching convention, with no published cutoff.