If you have a recent 5K time, you can predict — within a few minutes — what you should be capable of running for a 10K, half marathon, and marathon. The math is the Riegel formula, a simple power equation that has been the gold standard for race-time prediction since Pete Riegel published it in 1977. It's roughly 95% accurate up to the half-marathon distance and 80–90% accurate at the marathon, with a clear and well-understood failure mode.
The Riegel formula
T₂ = T₁ × (D₂ ÷ D₁)1.06
- T₁ = your known race time
- D₁ = the distance of that race
- D₂ = the distance you want to predict
- 1.06 = the Riegel exponent (a "fatigue factor")
Worked examples
From a 25:00 5K (D₁ = 5, T₁ = 25 minutes):
- 10K: 25 × (10/5)^1.06 = 52:11
- Half marathon: 25 × (21.1/5)^1.06 = 1:55:42
- Marathon: 25 × (42.2/5)^1.06 = 4:01:02
From a 22:00 5K:
- 10K: 45:55
- Half marathon: 1:41:50
- Marathon: 3:32:18
Why the marathon prediction overestimates
The Riegel formula assumes you've trained equally well for the longer distance. In practice, a 22:00 5K runner who's only ever run 30 mi/week will not run 3:32 — they'll likely run 3:50–4:10. The marathon depends heavily on aerobic endurance built through long runs and high weekly mileage. If you've never run more than 13 miles, your marathon time will be 15–25 minutes slower than Riegel predicts. The fix:
- Underprepared (peak weekly < 30 mi): add 10%–15% to the Riegel marathon estimate
- Adequately prepared (peak weekly 40–50 mi, 3+ runs over 16 mi): Riegel is roughly correct
- Well-prepared (peak weekly 60+ mi, multiple long runs): Riegel may slightly overestimate; competitive runners often beat it
The exponent matters
Some predictors use 1.05 or 1.07 instead of 1.06. The differences are small but consistent — 1.05 is more optimistic for longer distances, 1.07 more conservative. For most amateur runners on a marathon prediction, 1.06 is the right anchor and 1.07 is a useful sanity check.
Better predictions from longer races
Predicting a marathon from a 5K stretches the formula across an order of magnitude. Predicting from a half marathon is more reliable because:
- The aerobic systems used in a half are closer to those used in a marathon
- Your half-marathon time already reflects how well you handle 13+ miles
- The Riegel exponent is empirically more accurate at distances within 4× of each other
From a 1:45 half: predicted marathon = 1:45 × (42.2/21.1)^1.06 ≈ 3:38. This is usually within 5 minutes of what a properly trained runner will achieve.
Using race-time prediction in training
- Set realistic goals. If your 5K predicts a 4:00 marathon, don't enter trying to break 3:30.
- Find weak distances. If your 5K predicts a 25:00 10K but you ran 28:00, you have a specific endurance gap.
- Plan a tune-up race. 2–4 weeks before a marathon, run a half marathon and use Riegel forward — that's your most reliable predictor.
Try the predictor
Our race time predictor applies the Riegel formula across all common race distances — enter any one race result and see your projected times for everything from a mile to a marathon.