What formula is used?

Riegel's endurance model (1977): T2 = T1 × (D2/D1)^1.06. The 1.06 exponent captures the non-linear fatigue increase with longer distances — you slow down proportionally more as distance increases.

How accurate are these predictions?

Within ±5% for well-trained runners predicting to distances within 3× their baseline. Accuracy drops for first-time marathoners extrapolating from a 5K, or for athletes who are significantly stronger at one distance.

Why does my predicted marathon time seem too slow?

Riegel's formula assumes consistent aerobic fitness across all distances. If you are undertrained for the marathon (short long runs, not enough weekly volume), your actual time will be slower than predicted. The formula models potential, not current race readiness.

Can I use a training run instead of a race?

You can, but add 5–8% to your training time to account for the difference between race effort and a typical training effort. Race results give the most accurate predictions because they represent maximum aerobic output.

Is the tool free and private?

Yes. All calculations are client-side. No data leaves your browser.

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.

Formula

T2 = T1 x (D2 / D1)^1.06

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

Coefficients

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

Data sources

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.

Assumptions

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.

Approximation range

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.

Limitations

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.

Reproducibility

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.

Change log

2026-04-24: methodology page first published.

Running Pace Calculator — Calculate pace per km and mile and project race finish times from one run.
VO2 Max Estimator — Estimate aerobic capacity with the Cooper 12-minute run or Rockport 1-mile walk field tests.
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.

Worked example

Computed by the same engine bundle served at /engines/race-time-predictor.js. Re-runnable: the values below are the literal output of compute(engineInput).

Input

tool: race_time_predictor
known_distance_km: 10
known_time_minutes: 50

Output

predictions: [{"label":"5K","distanceKm":5,"timeMinutes":23.98160298313161,"paceMinPerKm":4.796320596626321,"paceMinPerMile":7.718929774256991,"difficultyDelta":0.9592641193252642},{"label":"10K","distanceKm":10,"timeMinutes":50,"paceMinPerKm":5,"paceMinPerMile":8.04672,"difficultyDelta":1},{"label":"Half Marathon","distanceKm":21.0975,"timeMinutes":110.32015405342617,"paceMinPerKm":5.229062877280539,"paceMinPerMile":8.415360967174172,"difficultyDelta":1.0458125754561078},{"label":"Marathon","distanceKm":42.195,"timeMinutes":230.0099666628293,"paceMinPerKm":5.451119010850321,"paceMinPerMile":8.772725673397899,"difficultyDelta":1.090223802170064}]
baselinePaceMinPerKm: 5
baselinePaceMinPerMile: 8.04672

FAQ

What formula is used?: Riegel's endurance model (1977): T2 = T1 × (D2/D1)^1.06. The 1.06 exponent captures the non-linear fatigue increase with longer distances — you slow down proportionally more as distance increases.
How accurate are these predictions?: Within ±5% for well-trained runners predicting to distances within 3× their baseline. Accuracy drops for first-time marathoners extrapolating from a 5K, or for athletes who are significantly stronger at one distance.
Why does my predicted marathon time seem too slow?: Riegel's formula assumes consistent aerobic fitness across all distances. If you are undertrained for the marathon (short long runs, not enough weekly volume), your actual time will be slower than predicted. The formula models potential, not current race readiness.
Can I use a training run instead of a race?: You can, but add 5–8% to your training time to account for the difference between race effort and a typical training effort. Race results give the most accurate predictions because they represent maximum aerobic output.
Is the tool free and private?: Yes. All calculations are client-side. No data leaves your browser.