Running & Racing

Race Time Predictor & Equivalents

Predict your finish times across all distances from a known race result using Riegel’s endurance formula with an adjustable fatigue exponent, accompanied by a Daniels–Gilbert VDOT comparison.

Source: Riegel (1981, American Scientist 69(3)) • Daniels & Gilbert • Checked 24 Aug 2026

Recent Race Baseline

Example Baselines:
h
m
s
1.06
1.05 = high mileage/endurance runner • 1.06 = typical trained runner • 1.08 = low mileage
Predicted Times Est. VDOT: ~49.8
Predicted Marathon Time
3:11:49
4:33 /km • 7:19 /mile
Event Predicted Time Pace (/km)
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How Riegel's race time formula works

In 1981, engineer Peter Riegel published an empirical power-law model analyzing athletic records across distance running, swimming, and cycling. It remains the most accurate and widely used formula for distance equivalence in amateur athletics.

T2 = T1 × (D2 / D1) ^ fatigue_exponent
T1, D1
Your known recent race time and its exact distance in kilometres.
T2, D2
The predicted time and target distance.
1.06
Riegel’s standard fatigue exponent, representing the average rate of aerobic decay as distance increases.

Accuracy notes and governing-body limits

Limits of the Riegel Formula
  • Duration Window: Riegel is most reliable between approximately 3.5 minutes and 3 hours 45 minutes. It over-predicts beyond the marathon distance or below 1500m.
  • The Aerobic Base Assumption: Riegel assumes you have trained adequately for the target distance. Stepping from a 5K to a Marathon without sufficient weekly long runs will result in a slower time than the formula predicts.
  • Weather and Elevation: The formula assumes comparable course difficulty, temperature, and wind between both events.

Worked example: 5K in 20:00 to Marathon

Given: D1 = 5.0 km, T1 = 1,200 seconds (20:00), Target: D2 = 42.195 km (Marathon) with exponent 1.06:

  1. Calculate distance ratio: 42.195 / 5.0 = 8.439
  2. Raise to power 1.06: (8.439)^1.06 = 9.5911
  3. Multiply by base time: 1,200 × 9.5911 = 11,509 seconds
  4. Convert to hours, minutes, seconds: 11,509 s = 3 hours 11 minutes 49 seconds (3:11:49)
  5. Required pace: 4:33 per km (7:19 per mile)

That 3:11:49 assumes marathon-specific endurance. The same 5K time nudged to a 1.08 exponent — realistic for a low-mileage runner — predicts about 3:20, and the gap between the two is a fairer read on the uncertainty than either single number. For the full picture of when to trust this, see how accurate the Riegel predictor is.

Equivalent race times comparison table

Riegel equivalents at the standard 1.06 exponent, computed from each 5K reference time:

Level 5K Result 10K Equivalent Half Marathon Marathon Equivalent
Recreational30:001:02:332:18:004:47:44
Intermediate25:0052:071:55:003:59:47
Competitive20:0041:421:32:003:11:49
Advanced18:0037:321:22:482:52:38
Sub-Elite16:0033:221:13:362:33:27
Elite14:0029:111:04:242:14:17

These are mathematical equivalents, not promises: the marathon column in particular assumes the endurance base to match, which is exactly where Riegel most often over-predicts.

Related running calculators

Read

How accurate is the Riegel predictor?

Quantified accuracy by distance, where it breaks down, and VDOT and Yasso cross-checks.

Tool

Running Pace Calculator

Turn any predicted finish time into target splits in min/km and min/mile.

Frequently asked questions

What fatigue exponent should I use?

The standard default is 1.06. High-mileage runners (over ~70 km/45 mi weekly) with strong endurance often use 1.05; lower-mileage or speed-oriented runners fit 1.07–1.08, especially for the marathon. The slider lets you see the effect.

How does this compare to Jack Daniels' VDOT?

VDOT is based on an oxygen-cost curve fitted to trained runners; Riegel is a single power law. Above 5K they usually agree within 1–2%. The estimated VDOT shown here is a cross-check on the Riegel predictions.

Why does it over-predict my marathon?

It assumes you are as trained for the target distance as for your reference race. Predicting a marathon from a fast 5K or 10K without the endurance base gives a time you can't yet hold — the exponent's effect compounds over the large distance ratio.

How accurate is the predictor?

Between neighbouring distances, roughly 1–2% for a trained runner. Accuracy falls as the gap grows: a plausible exponent change moves a half prediction by a few minutes but a marathon by over ten — see the full accuracy breakdown.

Sources

  • Peter RiegelAthletic Records and Human Endurance (American Scientist, 1981, 69(3)), the power-law model and 1.06 exponent. Checked 24 Aug 2026.
  • VDOT running calculator — the Daniels & Gilbert oxygen-cost model used for the VDOT estimate. Checked 24 Aug 2026.
  • All predicted times were computed by ScoreIndexer from the Riegel formula; the VDOT estimate uses the Daniels & Gilbert oxygen-cost and %VO2max equations.