Race Time Predictor
Predict your time for another race distance from a recent result, with Riegel’s formula (adjustable exponent) and the Daniels–Gilbert VDOT equations side by side, plus a table from 1,500 m to the marathon.
How to Use
- Pick the distance of a recent race (or Custom, with its distance and unit) and enter your time as h:mm:ss or m:ss.
- Pick the distance you want to predict.
- Leave the Riegel exponent at 1.06, or raise it (say 1.08) if you tend to fade over longer races.
- Read the two predictions, your VDOT and the goal pace, then compare every distance in the table and on the pace chart.
- Check Show Work for each equation with your numbers, and use the Pace Calculator for splits at the goal pace.
Worked Example
Riegel, 5K to marathon. 20:00 is 1,200 s. The distance ratio is 42,195 ÷ 5,000 = 8.439, and 8.4391.06 = 9.5911. 1,200 × 9.5911 = 11,509 s = 3:11:49, a pace of 4:33 per km.
VDOT from the same 5K. Speed v = 5,000 ÷ 20 = 250 m/min. Oxygen cost: −4.60 + 0.182258 × 250 + 0.000104 × 250² = 47.46 ml/kg/min. Fraction of maximum for 20 minutes: 0.8 + 0.1894393 e−0.25556 + 0.2989558 e−3.86521 = 0.9530. VDOT = 47.46 ÷ 0.9530 = 49.8. Solving the same two equations for 42,195 m gives a marathon of 3:11:17.
The common mistake: doubling the half-marathon time. A 1:45:00 half does not make a 3:30:00 marathon. With Riegel’s exponent the factor for twice the distance is 21.06 = 2.0849, so the prediction is 6,300 × 2.0849 = 13,135 s = 3:38:55 — almost nine minutes slower than simple doubling.
Show Work
Formulas
Where the Two Methods Come From
Peter Riegel, an American research engineer, proposed a simple formula for comparing performances at different distances in Runner’s World in August 1977, and expanded it in “Athletic Records and Human Endurance” in American Scientist (May–June 1981, vol. 69, pp. 285–290). Looking at world records in running, swimming and walking for events lasting from about 3.5 to 230 minutes, he found that time grows as a power of distance; 1.06 is the exponent runners use.
Jack Daniels, an exercise physiologist and coach, and Jimmy Gilbert published Oxygen Power: Performance Tables for Distance Runners in 1979. They fitted one equation for the oxygen cost of running at a given speed and another for the fraction of VO₂max a runner can sustain for a given time; the ratio, which Daniels called VDOT, ties every race distance to a single number. Daniels’ later book Daniels’ Running Formula made VDOT tables widely used.
About This Tool
This predictor runs Riegel’s formula and the Daniels–Gilbert VDOT equations side by side for any race distance, including custom ones, and solves the VDOT equations exactly rather than looking times up in a table. You can change the Riegel exponent, see predictions for every standard distance from 1,500 m to the marathon with paces per km and per mile, and compare both models on a pace-by-distance chart.
Everything runs in your browser; nothing you enter is sent anywhere. For general information only — not medical advice. Talk to a doctor or other qualified professional about your own health.
Related tools: Pace Calculator, VO₂ Max Calculator, and Calorie Burn Estimator.
Frequently Asked Questions
What is the Riegel formula?
T₂ = T₁ × (D₂ ÷ D₁)^1.06, published by the engineer Peter Riegel. The exponent 1.06 means each doubling of distance costs a little more than double the time. A 1:45:00 half marathon predicts 6,300 s × 2.0849 = 3:38:55 for the marathon.
What is VDOT?
A performance-based measure of running fitness from Jack Daniels and Jimmy Gilbert’s 1979 tables. It is the oxygen cost of your race pace divided by the fraction of maximum you can hold for that long. A 20:00 5K is 250 m/min, an oxygen cost of 47.46 ml/kg/min held at 95.3 % of maximum, so VDOT = 49.8.
Why do Riegel and VDOT give different times?
They are different models fitted to different data. For a 20:00 5K they agree closely on the marathon (3:11:49 against 3:11:17), but from a 6:00 mile Riegel predicts a 19:57 5K while VDOT predicts 20:29.
What exponent should I use?
1.06 is the standard value. A higher exponent predicts more slowing: a 1:50:00 half becomes a 3:49:21 marathon at 1.06, 3:52:33 at 1.08 and 3:55:47 at 1.10. Runners with less endurance training often fit a higher value.
How accurate are race predictions?
They assume equal training for both distances, similar courses and conditions, and an even effort. Riegel fitted his formula to performances lasting about 3.5 to 230 minutes, and the published VDOT tables cover VDOTs from 30 to 85; the page warns you outside those ranges.
How do I use the Race Time Predictor?
Just type your numbers. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Is it free? Does it work without internet?
Yes to both. It is free with no sign-up, and once the page has loaded it keeps working even with no internet.
Where does my data go?
Nowhere — every calculation runs on your own device. Nothing you enter is uploaded, logged, or stored.
Common Use Cases
Setting a marathon goal
A 1:45:00 half marathon predicts 3:38:55 (Riegel) or 3:37:50 (VDOT 42.6) — a goal pace of about 5:11 per km.
Checking a half-marathon target
A 45:00 10K predicts 1:39:17 by Riegel and 1:39:44 by VDOT 45.3.
Speed from endurance
A 3:30:00 marathon is VDOT 44.6, which equals a 45:37 10K — useful for pitching 10K training.
Odd distances
7 km in 35:00 predicts 2:43:41 for a 30 km trail race by Riegel and 2:44:12 by VDOT 39.1.
Comparing two races
A 6:00 mile (VDOT 48.4) and a 20:00 5K (VDOT 49.8) show the 5K was the stronger run.
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