Race-day prediction in two formulas
The Riegel formula (T₂ = T₁ × (D₂/D₁)^1.06) is the gold standard for predicting race times across distances — it accounts for the fact that pace slows as distance grows because of accumulated fatigue.
The exponent 1.06 fits most road runners well, but elites can hold pace closer to 1.04 while newer runners often fade closer to 1.08. Calibrate the exponent against your own 5K → half marathon ratio if you have data.
Live projection is simpler: assume you finish at your current average pace, or override with a target pace for the remaining distance. Combine with a GPS watch to get a real-time finish clock prediction at every mile.