Key Takeaways
- The Riegel formula (T2 = T1 × (D2/D1)^k) is the most widely used race prediction model, validated across distances from 1,500 m to ultramarathons.[1]
- The exponent (k) varies by experience: beginners slow down more per unit distance (k ≈ 1.08) than advanced runners (k ≈ 1.04).[2]
- Predictions are most accurate when the input race is at least half the target distance — a 10K predicts a marathon better than a 5K.[3]
How the Prediction Works
The Riegel (1977) formula models the relationship between race distance and finish time:
T2 = T1 × (D2 ÷ D1)^k
T1 = known time, D1 = known distance, D2 = target distance, k = fatigue exponent
The fatigue exponent captures the non-linear slowdown as distance increases. This calculator adjusts k by experience level, as less-trained runners experience greater pace decay at longer distances.[1]
For pacing strategy during races, use the Running Pace Calculator. To estimate calorie needs for race day, see the Running Calorie Calculator.
Accuracy Considerations
The Riegel formula tends to be optimistic for beginners at the marathon distance. First-time marathoners should add a 3–5% buffer to the prediction to account for pacing inexperience and the physiological "wall."[2]
Predictions are based on the assumption that training is proportional to race distance. Runners who train specifically for the target distance will outperform the prediction, while those who don't may fall short.
For VO₂max-based assessment, check the VO₂ Max Calculator.
Limitations and Important Notes
- Race conditions (heat, wind, course elevation) substantially affect finish times but are not modeled.
- Predictions assume a recent, all-out effort at the input distance. Training runs do not reflect race potential.
- For distances beyond the marathon, the formula becomes progressively less reliable due to additional factors like nutrition and sleep.
- This tool is for informational and journaling purposes only. It does not constitute personalized advice.
Frequently Asked Questions
Sources & References
- Modeling of marathon runner performance. Various. PMC (2020)
- Athletic Records and Human Endurance. Riegel PS. Am Scientist (1981)
- Race time prediction models in running. Various. PMC (2025)
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This tool is for informational and journaling purposes only.
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