How it works
T₂ = T₁ · (D₂/D₁)^1.06 (Riegel; + Cameron and VDOT)
Riegel scales your time by the distance ratio raised to the power 1.06 — the exponent capturing how pace decays as races lengthen for adult runners. Cameron reaches the same question through a velocity-fade function fitted to world-best performances from 800 m up to the marathon. VDOT works in physiological currency instead: it computes the oxygen-cost score your race implies, then looks up the time at the target distance that carries the same score. The headline number is the average of the three, and the gap between the quickest and slowest model doubles as an honesty meter — the models drift apart the further your target sits from the race you fed in.
Sources
- Riegel endurance model Riegel, P. S. (1981). “Athletic Records and Human Endurance.” American Scientist 69(3), 285–290. Exponent 1.06 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
What makes a race result good input for prediction?
Three things: it was genuinely all-out, it is recent enough to reflect current fitness, and its distance sits reasonably near the target. A month-old 10K predicts a half marathon well; a 5K from last fall predicts this spring’s marathon mostly by luck.
What does the range around the prediction mean?
It is the gap between the most optimistic and most pessimistic of the three models. A tight range means Riegel, Cameron, and VDOT nearly agree — typical when target and input distances are close. A wide range is the calculator telling you to hold the number loosely.
Can I predict a 5K from my marathon?
The math runs downward as happily as upward. Physiology cooperates less: marathon training builds endurance more than raw speed, so shorter-distance forecasts often flatter runners who have skipped fast work. Treat a downward prediction as a ceiling to test in a workout before trusting it.
Why is a marathon forecast the least reliable?
Because 26.2 punishes what no formula sees — fueling discipline, long-run volume, heat, and pacing errors that compound after mile 20. Predicting it from a 10K means extrapolating across a four-fold distance jump. A dedicated marathon predictor plus a real buildup says more than any single scaled number.
Do the models assume even pacing?
Effectively yes — all three were fitted to performances run at steady, well-distributed effort, so the forecast presumes you will not blow up at halfway. A badly positive-split input race also skews things, reading your fitness as lower than it actually is.
Where does VDOT fit into this?
VDOT is Daniels and Gilbert’s fitness score — an effective VO₂max inferred from race performance. Here it casts the physiological vote alongside two curve-fit models. To see the score itself and the training paces it implies, run your result through the VDOT calculator.
Three models sharing one input still produce a forecast, not a promise — course profile, weather, taper, and execution routinely push real finishes outside the predicted range. Check ambitious targets against your training before betting a race on them. General planning information, not coaching or medical advice.