The formula
pace = time ÷ distance · Riegel projection: T₂ = T₁ × (D₂ ÷ D₁)^1.06
Where it comes from
Pace is a simple division. The interesting part is the projection: Riegel's formula estimates a time at another distance by raising the ratio of distances to the power 1.06, an exponent fitted against thousands of real results. The excess over 1 captures the fact that nobody holds their 5 km pace for a marathon.
How to work it out by hand
- Convert the total time to seconds
- Divide by the kilometres to get seconds per kilometre
- Convert that to minutes and seconds
- To project, multiply the time by the ratio of distances raised to 1.06
What is worth knowing
The projection holds up when the target distance is not far from the one you have run and the training backs it: 10 km to a half marathon works well; 5 km to a marathon is optimistic, because past two hours the limit stops being cardiovascular and becomes glycogen and muscular wear. Treat it as a theoretical ceiling, not a forecast.