Tool

Race time predictor: Riegel, VDOT and Cameron, side by side

See this on your own runs →

How this works

Three published models, run on the same input, printed side by side.

Riegel (1981). The simplest and the most quoted: T₂ = T₁ × (D₂ ÷ D₁)^1.06. Riegel derived the 1.06 exponent from race records across distances. Many calculators quietly substitute 1.07 or 1.08 for the marathon because 1.06 is known to be optimistic there. We print 1.06 and tell you what 1.07 gives, which is the honest version of the same adjustment.

VDOT (Daniels and Gilbert, 1979). Turns your race into an oxygen-cost number, then inverts it for the target. Two equations do the work. The cost of running at speed v, in metres per minute, is VO₂ = −4.60 + 0.182258·v + 0.000104·v². The share of your maximum you can hold for t minutes is 0.8 + 0.1894393·e^(−0.012778·t) + 0.2989558·e^(−0.1932605·t). VDOT is the first divided by the second. The target time is then solved for.

Cameron (1998). Uses a distance factor a(d) = 13.49681 − 0.048865·d + 2.438936 ÷ d^0.7905, with d in miles, and scales between distances by the ratio of those factors. It tends to sit between the other two at marathon distance.

Why we print three numbers instead of one

Because they disagree, and the disagreement is information.

Run an 18:00 5K through them and Riegel at 1.06 returns a 2:52:38 marathon, while the same race at exponent 1.07 returns 2:56:22. That is nearly four minutes of difference from a single decimal place in one model, before you compare models at all. A tool that shows you one of those numbers to the second is not more accurate than one that shows you both. It is just quieter about what it does not know.

Keogh and colleagues (2019) reviewed the published equations. Formulas built from shorter races over-predict the marathon for club runners. The error grows the further you stretch it.

Vickers and Vertosick (2016) worked with 2,497 club runners. They found that adding weekly mileage improved the prediction. No formula on this page has that input.

The rule this leads to

Predict from the closest race you have actually run, and read why your watch and your app disagree before you trust either. A marathon predicted from a recent half is worth taking seriously. A marathon predicted from a 5K is a statement about your speed, not your endurance, and should be treated as an upper bound rather than a target.

If the models disagree by more than about 2% of the target time, do not pick one. Pace the first half at the slow end of the range and decide at halfway, where you will have better information than any formula has.

What this will not do

It will not account for heat, hills, wind, the course, your fuelling, or whether you have run further than 25 km in training. Those are the things that actually decide a marathon, and no prediction equation contains any of them.