Race Time Predictor
Predict race times across distances from a known performance, using the Riegel formula.
Last updated · View algorithm, constants and default inputs (JSON)
About this calculator
Riegel predicted time equals the known time multiplied by the ratio of distances raised to the power 1.06. The exponent captures fatigue: the same effort cannot be held across a longer distance at the same pace.
Worked example
calculated with the default values below
Known distance 10 km · Known time — hours 0 h · Known time — minutes 45 min · Fatigue exponent 1.06 5 km 21:35 · 10 km 45:00 · Half marathon 1:39:17 · Marathon 3:27:01 · Note Predictions are most reliable between a 5 km and a half marathon — a marathon needs distance-specific training
General background references
Disclaimer
These calculators give general mathematical results. They suit study, planning and estimation — verify anything that feeds a graded submission, a published figure or a financial commitment.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
T(d) = T₀ × (d ÷ d₀)^p
- T₀
- Known time (min)
- d₀
- Known distance (km)
- d
- Target distance (km)
- p
- Fatigue exponent
- T
- Predicted time
Applied to d = 5, 10, 21.0975 (half marathon), 42.195 (marathon); shown as h:mm:ss. Default p = 1.06 (Riegel-style).
Frequently asked questions
Why does the fatigue exponent push longer races slower than pace suggests?
Riegel's model scales known time by the new distance divided by known distance raised to the exponent, so the 1.06 power bakes in fatigue. From a 45 minute 10 km, the default exponent predicts a marathon at about 3 hours 27 minutes, far slower than simply quadrupling pace would imply. Raising the exponent toward 1.25 assumes you tire faster and stretches the longer distances even more.