Key Takeaways
- The Riegel formula uses an exponent of 1.06 to account for fatigue at longer distances
- Predictions are most accurate for distances within 2-4x of your known race
- Marathon predictions from 5K times may be 2-5% optimistic
- Training, course profile, and weather significantly affect actual times
- Use predictions as guidelines, not absolute targets
What Is the Riegel Formula?
The Riegel formula is a mathematical equation developed by researcher Peter Riegel in 1977 to predict race times across different distances. It accounts for the natural slowdown that occurs as race distance increases due to physiological fatigue.
Unlike simple pace multiplication, the Riegel formula recognizes that you cannot maintain 5K pace for a marathon. The formula includes a fatigue factor (exponent of 1.06) that adjusts predictions to reflect this reality.
T2 = T1 x (D2 / D1)1.06
How to Use This Calculator
- Select your known distance - Choose the race distance you have recently completed
- Enter your time - Input your finish time in hours, minutes, and seconds
- Choose your target distance - Select the distance you want to predict
- Click Predict Time - View your predicted finish time and pace
Pro Tip: Use Recent Race Results
For best accuracy, use a race time from the past 4-8 weeks when you were properly tapered and racing at full effort. Training run times will typically underestimate your race potential.
Standard Race Distances
| Race Name | Distance (km) | Distance (miles) | Beginner Time |
|---|---|---|---|
| 5K | 5.0 km | 3.1 miles | 30-40 min |
| 10K | 10.0 km | 6.2 miles | 60-80 min |
| Half Marathon | 21.0975 km | 13.1 miles | 2:15-3:00 |
| Marathon | 42.195 km | 26.2 miles | 4:30-6:00 |
Accuracy Considerations
The Riegel formula provides excellent estimates, but several factors affect real-world accuracy:
- Training specificity - Marathon-specific training improves marathon predictions
- Course difficulty - Hills, terrain, and altitude affect times
- Weather conditions - Heat and humidity can add 5-10% to times
- Experience level - New runners may see larger variations
- Individual physiology - Some runners are better at speed vs. endurance
Distance Prediction Accuracy
Predictions are typically most accurate when the distances are within 2-4x of each other:
- 5K to 10K: Very accurate (typically within 1-2%)
- 10K to Half Marathon: Good accuracy (within 2-3%)
- Half to Full Marathon: Moderate accuracy (within 3-5%)
- 5K to Marathon: Less reliable (can be 5-10% off)
Frequently Asked Questions
The 1.06 exponent was derived from analyzing thousands of race results. It represents the average rate of fatigue across the running population. Some researchers suggest values between 1.05-1.08 may be more appropriate for specific populations or distances.
The Riegel formula becomes less accurate for ultramarathons (50K+) because factors like nutrition, sleep deprivation, and mental fatigue become more significant. For ultras, specialized calculators using different models are recommended.
Always use race times when possible. Race conditions (taper, adrenaline, competition) typically result in 3-5% faster times than training runs. If using training times, expect your actual race performance to be faster than predicted.
A general rule is to add 12-15 seconds per mile for every 100 feet of elevation gain. If your base race was on a hilly course but your target is flat (or vice versa), adjust your input time accordingly before predicting.
Beginners often show larger improvements than predicted because they have more room for growth. The formula works best for experienced runners whose fitness has stabilized. New runners should view predictions as starting points rather than targets.