Race Time Predictor
If you have run a recent race, the Riegel formula can predict what you are capable of at a different distance. Developed by Peter Riegel and published in American Scientist in 1981, the formula is T2 = T1 x (D2 / D1) raised to the power 1.06. The exponent 1.06 captures the natural fatigue effect: runners slow down as distance increases, and this factor was fitted to real-world athletic performances. Enter your recent result (5K, 10K, half marathon, or marathon), the time you ran, and your target race distance. The calculator returns a predicted finish time plus your required pace per kilometre and per mile. The formula is most reliable when comparing distances within two to three times of each other. Always factor in course elevation, weather, and your specific training when setting race-day goals.
Predicted finish time: --
How the Riegel formula works
The Riegel formula uses a power-law relationship between race time and distance. The exponent of 1.06 was empirically derived from thousands of athletic performance records.
T2 = T1 x (D2 / D1) ^ 1.06
Where:
T1 = known race time (seconds)
D1 = known race distance (metres)
D2 = target race distance (metres)
T2 = predicted finish time (seconds)
Worked example
Recent 5K time: 25:00 (1,500 seconds). Predicting marathon (42,195 m):
- D2 / D1 = 42,195 / 5,000 = 8.439
- (D2/D1)^1.06 = 8.439^1.06 = 9.337
- T2 = 1,500 x 9.337 = 14,006 seconds = 3:53:26
- Pace per km = 14,006 / 42.195 = 331.9 sec/km = 5:32/km
Equivalent performance table
| 5K | 10K | Half Marathon | Marathon |
|---|---|---|---|
| 18:00 | 37:20 | 1:19:42 | 2:46:09 |
| 20:00 | 41:28 | 1:28:32 | 3:04:39 |
| 25:00 | 51:50 | 1:50:41 | 3:50:50 |
| 30:00 | 1:02:12 | 2:12:49 | 4:37:00 |
| 35:00 | 1:12:34 | 2:34:58 | 5:23:11 |
| 40:00 | 1:22:57 | 2:57:06 | 6:09:22 |
Predictions are approximate and assume consistent fitness across all distances. Calculated using the Riegel formula with exponent 1.06.
Limitations and how to use predictions wisely
The Riegel formula assumes a reasonably fit runner racing honestly at both distances. It does not account for:
- Course elevation gain or loss
- Weather conditions (heat, wind, humidity)
- Training load differences between distances
- Pacing errors or inexperience at the new distance
- Health, nutrition, and race-day logistics
For best results, use a race within the past six to eight weeks that you ran at full effort. If you have run multiple recent races, the one closest in distance to your target will give the most reliable prediction.
Race time predictor: frequently asked questions
What is the Riegel formula?
The Riegel formula, published by Peter Riegel in American Scientist (1981), predicts a runner's finish time for a new distance based on a known time at another distance. The formula is: T2 = T1 x (D2 / D1) ^ 1.06. T1 is the known time, D1 is the known distance, D2 is the target distance, and 1.06 is an empirically derived fatigue exponent that accounts for how performance degrades over longer distances.
Why is the exponent 1.06 and not 1.0?
An exponent of 1.0 would imply that pace stays perfectly constant regardless of distance, which does not happen in practice. Riegel found that athletes slow down as distance increases, and an exponent of approximately 1.06 best fits observed athletic performance data across a wide range of distances. This means a runner who runs 5K in 20:00 would be predicted to run a 10K slightly slower than 40:00.
How accurate is the race time predictor?
The Riegel formula is most accurate when the known and target distances are within two to three times of each other (for example, 5K to 10K, or 10K to half marathon). Predictions become less reliable when predicting across very different distances (for example, from 5K to marathon), or when training load, course profile, and race conditions differ significantly. Use the prediction as a guide for pacing strategy, not a guaranteed finish time.
Does the formula work for walking or ultra-distances?
The Riegel formula was calibrated against competitive running performances. It is less reliable for very slow paces (walking), very short distances (under 3K), or ultra-marathon distances beyond 100 miles where physiology, sleep deprivation, and nutrition strategy dominate. For standard road race distances (5K to marathon), accuracy is generally within 2 to 5 percent for well-trained runners.
How do I use predicted pace in training?
The predicted finish time gives you a target average pace per kilometre and per mile. Use pace-per-km and pace-per-mile outputs to set your GPS watch target pace and to design training workouts. For example, lactate threshold intervals are typically run at slightly faster than marathon pace, and easy long runs are run at 60 to 75 percent of marathon pace.
Official sources
- Riegel, P.S. (1981). Athletic records and human endurance. American Scientist, 69(3), 285-290.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology. General information only.