Methodology: Race Time Predictor

Scope

Projects finish times across 5K, 10K, half marathon, and marathon distances from a single known race result using Riegel's formula.

Useful as a sanity check for race-day pacing; not a substitute for distance-specific training.

T2 = T1 x (D2 / D1)^1.06

predicted_time = known_time * (target_distance / known_distance) ** 1.06

Parameter	Value	Note
Fatigue exponent	`1.06`	Empirically fit by Riegel on endurance event records.

Riegel PS. Athletic records and human endurance. Am Sci. 1981;69(3):285-290. — Originally published in Runner's World before the American Scientist piece; the 1.06 exponent is from Riegel's regression on world-record data.
Vickers AJ, Vertosick EA. An empirical study of race times in recreational endurance runners. BMC Sports Sci Med Rehabil. 2016;8:26. — Modern validation of Riegel-style extrapolation on ~2,300 non-elite runners.
World Athletics — Road running measurement and record statistics. — Certified distance definitions used throughout the tool.

Athlete is adequately trained for the target distance; untrained marathoners should expect slower than Riegel predicts.
Race conditions (temperature, wind, elevation) are comparable to the reference race.

Within 5K–half-marathon range, typical prediction error for trained runners is 1–3%.

Marathon prediction from a 5K is systematically optimistic for under-trained runners and typically off by 5–15 minutes.

The 1.06 exponent reflects a generic population; elite endurance athletes are better modeled by 1.05, novice marathoners by 1.08+.
Course profile, weather, and fueling strategy are not inputs — the formula sees only time and distance.
Below 1,500 m or above marathon the formula extrapolates and should not be trusted.

Known 5K = 25:00 (1500 s). Predicted marathon (42.195 km): T2 = 1500 * (42.195 / 5) ^ 1.06 = 1500 * 9.77 = 14,650 s ≈ 4:04:10.

Running Pace Calculator — Calculate pace per km and mile and project race finish times from one run.
VO2 Max Estimator — Estimate aerobic capacity with Cooper run, Rockport walk, or no-exercise questionnaire methods.
Walking Calorie Calculator — Estimate calories burned from walking using speed, duration, body weight, and incline.
Calories Burned Calculator — Estimate exercise calorie burn from body weight, duration, MET intensity, and incline.