How it works
T_marathon = T_race · (42.195 km / D_race)^1.06 (Riegel; + Cameron, VDOT)
The three models attack the extrapolation differently. Riegel raises the distance ratio to the power 1.06, an exponent he fitted for adult runners — double the distance and the time more than doubles. Cameron instead applies a velocity-fade function calibrated on world-best performances, which behaves well anywhere from 5K up to the marathon. VDOT converts your race into Daniels and Gilbert’s pseudo-VO₂max score, then reads off the marathon time that carries the same score. The headline number is simply the average of the three, and the quoted range runs from the most optimistic model to the most cautious one. Watch how far your input distance sits from 26.2 miles: a half marathon keeps the models honest, while stretching a 5K result across the full distance widens the spread quickly.
Sources
- Riegel endurance model Riegel, P. S. (1981). “Athletic Records and Human Endurance.” American Scientist 69(3), 285–290. The exponent 1.06 is Riegel’s value for adult runners.
- Cameron model David F. Cameron, race-time prediction model (1998), fitted to world-best times across 800 m–marathon.
- Daniels & Gilbert VDOT Jack Daniels & Jimmy Gilbert, “Oxygen Power: Performance Tables for Distance Runners” (1979); Jack Daniels, “Daniels’ Running Formula” (Human Kinetics).
FAQ
Which race result should I feed the marathon time predictor?
The most recent race where you genuinely emptied the tank, ideally a half marathon — the distance field defaults to 13.1 miles for a reason. A 10K or 15K works too. Training runs and comfortable races undersell your fitness and drag the prediction slower than you deserve.
Why do I get three times plus a range instead of one answer?
Because the models genuinely disagree, and hiding that would mislead you. Riegel, Cameron, and VDOT each encode different assumptions about endurance fade. When the three land within a minute or two of each other, the consensus is solid; when they fan out, treat the whole exercise as a rough bracket.
How should I read the consensus number?
As the fitness you have demonstrated, not the marathon you are owed. The models see one race result; they cannot see whether your long runs, fueling practice, and pacing discipline can carry that fitness through the last 10 km, which is where most first marathons come apart.
Can I use a 5K to predict a marathon?
You can enter one, and the math will oblige — but a 5K measures speed far more than marathon endurance, so the models are extrapolating across more than an eightfold jump in distance. Expect a wide range, read the result as a ceiling, and re-run the prediction after your next 10-miler or half.
Does the prediction work in miles and kilometers?
Yes. The distance field toggles between mi and km and offers presets for the 10K (6.2 mi), 10 miles, and the half marathon. Everything is converted internally before the models run, so a 21.1 km entry and a 13.1 mi entry produce the same marathon projection.
What do I do with the predicted time?
Turn it into a plan. Take the consensus — or something slightly more conservative — and split the goal into race-day paces, or structure a controlled faster second half so the prediction survives contact with the final 10 km.
A marathon prediction is an extrapolation from one race through published formulas — Riegel, Cameron, and Daniels & Gilbert — and it assumes the endurance training to match. Weather, course profile, fueling, and pacing move real finish times by minutes. Plan with it, but do not treat it as a promise, coaching, or medical advice.