How this works
Pete Riegel's 1981 formula T₂ = T₁ × (D₂ / D₁)^1.06 is the most widely used race-time predictor among runners. It scales a known race time to a different distance using a fatigue exponent of 1.06 — meaning longer races run slightly slower per kilometre than shorter ones, reflecting the physiological reality that you can't hold 5K pace over a marathon. The formula was empirically derived from running results and is uncannily accurate for predictions within ±2× the original distance.
Where it works well: predicting half-marathon time from a 10K, or marathon time from a half-marathon. Where it gets shakier: predicting marathon time from a 5K (the 8.4× distance ratio is too far) or predicting ultramarathon times. For ultra distances (50K+), use a higher exponent (1.10–1.15) since fatigue scaling becomes nonlinear, or use specialised tools like Daniels' VDOT tables. The Riegel result also assumes you've trained for the target distance — predicting marathon time from a sprint test will overestimate your finish time even if the math is mechanically correct.
For practical use: pick your most recent race or hard time trial as the input, and accept the prediction as a "fitness ceiling" rather than a guaranteed time. Race-day variables (weather, sleep, fuelling, course profile, pacing strategy) can shift your actual finish by 5–10% from the prediction. Use the predicted time to set realistic goal paces, not as a definitive number.
The formula
The exponent 1.06 was empirically determined and works for most middle-distance running. Lower exponents (e.g. 1.03) over-predict slowdown for ultra distances; higher exponents (1.10+) better match real ultra results. The formula assumes the runner has trained appropriately for the target distance.
Example calculation
- Known: 25:00 for 5K. Target: 10K time.
- T₂ = 25:00 × (10/5)^1.06 = 25:00 × 2.085 ≈ 52:08.
- Half marathon prediction from same 5K: 25:00 × (21.1/5)^1.06 ≈ 1:55:25. Marathon: 25:00 × (42.2/5)^1.06 ≈ 4:00:09.
Frequently asked questions
How accurate is the Riegel prediction?
Within 2–3% for trained runners predicting within ±2× the original distance, when the target distance has been specifically trained for. The error grows with distance ratio: 5K to 10K is very accurate, 5K to marathon is ±10–15% off (because it assumes endurance you may not have built). Real-world race results also depend on weather, course, sleep, fuelling, and pacing — all of which can shift your time by 5–10% from any prediction.
Should I use Riegel or another formula?
Riegel is the simplest and most-cited; it works fine for the vast majority of recreational running. Daniels' VDOT tables (used by Jack Daniels in "Daniels' Running Formula") are slightly more sophisticated and incorporate VO2 max-based equivalents — they give similar predictions but with training-pace tables baked in, so they're more useful if you're doing structured Daniels-style training. For ultra distances, neither standard model works perfectly; consult ultra-specific calculators or coaching.