How the prediction works
T2 = T1 × (D2 ÷ D1)^1.06
T1 and D1 are your race time and distance; D2 is the distance you want to predict. Peter Riegel published the formula in 1981 after finding that world records across running, swimming and cycling followed this power law, with an exponent close to 1.06 for running.1 The exponent above 1 captures how pace slows as distance grows.
Worked example
A 25:00 5K:
| Distance | Predicted time |
|---|---|
| 1 mile | 7:31 |
| 5K | 25:00 |
| 10K | 52:07 |
| 15K | 1:20:07 |
| Half marathon | 1:55:00 |
| Marathon | 3:59:47 |
The 10K: 25:00 × (10 ÷ 5)^1.06 = 25:00 × 2.085 = 52:07.
Where predictions go wrong
In a survey of 2,303 recreational runners, Vickers and Vertosick found the Riegel formula well calibrated for races up to the half marathon, but its marathon predictions were at least 10 minutes too fast for half of the runners. A model that also used typical weekly mileage predicted better.2 In practice:
- Predictions between neighbouring distances (5K to 10K, 10K to half) are the most reliable.
- Marathon predictions from short races assume marathon-specific training. Without it, adding 5 to 10% is a sensible rule of thumb.
- Heat, hills, wind and altitude slow everyone; the prediction assumes a flat course in good conditions.
Training paces from your race
Your plan uses Jack Daniels' VDOT method: the race time gives an effective VO2max, and each training intensity is a percentage of it.3
VO2 (ml/kg/min) = −4.60 + 0.182258 v + 0.000104 v² (v in metres per minute) Fraction of VO2max sustainable for t minutes = 0.8 + 0.1894393 e^(−0.012778 t) + 0.2989558 e^(−0.1932605 t) VDOT = VO2 ÷ fraction
Easy runs sit around 62 to 70% of VDOT, threshold runs 85 to 88% and intervals 95 to 98%. The calculator solves the first equation for each speed. For a quick check of pace and splits at any distance, use the running pace calculator, and fuel your training with the TDEE calculator.