CalcVitalsRace Time Predictor — Riegel Formula
Race prediction uses Riegel's formula, which slows you down as distance grows: time scales with distance to the power 1.06, not linearly. A 10K in 50:00 predicts a marathon of about 3:50 (3:49:56 by the formula) — noticeably slower than naive pace multiplication, because fatigue is real.
How it works
Peter Riegel, a mechanical engineer and runner, published his formula in 1977 after fitting it to world-record progressions: finish time grows with distance raised to the power 1.06. That small exponent is the entire insight — double the distance and the time a bit more than doubles (×2.09), the extra being fatigue's tax. The formula has survived nearly fifty years of scrutiny because, for trained runners racing comparable efforts, it is usually right within a percent or two.
The assumption to respect is 'equally trained'. A prediction from a sharp 5K to a marathon presumes marathon-level endurance work that a 5K runner may not have done; the further the jump in distance, the more the prediction becomes a statement about your potential after appropriate training rather than your current readiness. Predictions in the other direction — marathon to 5K — flatter your speed for the mirror-image reason.
Use the numbers for goal-setting and pacing plans (the split planner turns the marathon figure into a race-day schedule), then let training races correct them. Every runner's personal exponent differs slightly; two or three results at different distances let you see whether you fade more or less than Riegel's average athlete.
The method
Riegel: T₂ = T₁ × (D₂ ÷ D₁)^1.06, distances in the same unit. Standard distances: 5 km, 10 km, half marathon 21.0975 km, marathon 42.195 km.
Frequently asked questions
How accurate is the Riegel prediction?
Within about 1–2% for runners trained for both distances, racing similar effort in similar conditions. Heat, hills, wind and under-training for the longer distance are the usual reasons real results land slower.
Why is my predicted marathon slower than my training suggests?
It may not be, if you are endurance-trained: Riegel describes the average trained runner. High-mileage athletes often beat their short-race predictions at the marathon, and speedsters fall short of theirs.
Can I predict from a treadmill or parkrun time?
Yes — any honest maximal effort over a known distance works. Soft surfaces, heat or a casual effort make the input unrepresentative, and the prediction inherits the error.