The Riegel formula in one line
T₂ = T₁ × (D₂ / D₁)1.06. Pete Riegel published this in American Scientist in 1981, fitting a power-law to elite track and road records across the full 1500 m → marathon range. The 1.06 exponent reflects the slight pace-decay that comes from sustaining race pace longer; without that exponent (i.e. just dividing by distance), the predictor would be wildly optimistic.
When the formula works
Best use case: predicting an upcoming 10K from a recent 5K time, or upcoming half-marathon from a recent 10K. In these ranges Riegel matches actual race performances to within 2–3 %. Use it to set realistic pace targets — if your 5K pace is 5:00/km, your 10K race pace is roughly 5:18/km (not 5:00, which is a common over-pacing mistake that blows up the second half).
When it doesn’t work
Marathons, ultra-marathons, and predictions across very different terrain (track to trail, sea-level to altitude) are unreliable. The formula assumes comparable conditions and comparable training depth for both distances. If your weekly mileage is 30 km but the marathon prediction asks you to sustain race pace for 42 km, the prediction will be optimistic by 5–15 %. Plan accordingly.