The Riegel Formula Explained
T₂ = T₁ × (D₂ / D₁)^1.06
Where: T₁ = your known race time (in seconds), D₁ = known race distance (km), D₂ = target distance (km), T₂ = predicted finish time (in seconds).
The exponent 1.06 is the key. A value of 1.00 would assume pace stays perfectly constant across distances — which is not physically possible. 1.06 captures the empirically observed slowdown that occurs as race distance increases.
Step-by-Step Example: 10K to Marathon
Known: 10K in 45:00 (2700 seconds). Target: Marathon (42.195km).
T₂ = 2700 × (42.195 / 10)^1.06
T₂ = 2700 × (4.2195)^1.06
T₂ = 2700 × 4.671
T₂ = 12612 seconds = 3:30:12
💡 Why 1.06 and not 1.0? Research by Riegel across thousands of race results found that athletes consistently slow down at a rate described by this exponent. The slowdown represents the cumulative metabolic cost of prolonged running.
Riegel Formula Reference Table
| Known Distance | Target Distance | Multiplier |
|---|---|---|
| 5K | 10K | 2.14× |
| 5K | Half Marathon | 4.97× |
| 5K | Marathon | 10.88× |
| 10K | Half Marathon | 2.32× |
| 10K | Marathon | 5.09× |
| Half Marathon | Marathon | 2.19× |
Limitations and Criticisms
The Riegel formula assumes a single universal fatigue coefficient (1.06) for all runners. In reality, this value varies between individuals. Highly trained ultramarathon runners may have a lower exponent (less slowdown), while recreational runners may have a higher one. Specialized models like the Cameron formula offer alternatives, but Riegel remains the most practical for everyday use.
Frequently Asked Questions
Who invented the Riegel formula?
Peter Riegel, an American engineer and recreational runner, published the formula in Runner's World magazine in 1977. It was based on an analysis of world record times across distances.
What does the 1.06 exponent mean?
It means that for every doubling of race distance, your finish time increases by 2^1.06 = 2.085× rather than 2.00×. This extra 4.25% represents the additional physiological cost of sustaining effort over longer distances.
Is there a more accurate formula than Riegel?
The Cameron formula uses a slightly different mathematical approach and some studies show marginally better accuracy for marathon prediction from 10K times. However, Riegel remains the most widely used due to its simplicity.