T2 = T1 × (D2 / D1)^1.06
Where T1 is your known time, D1 is the known distance, D2 is the target distance, and the exponent is sport-adjusted (1.06 running, 1.04 cycling, 1.02 swimming, 1.03 rowing).
Endurance time prediction uses mathematical models to estimate how long it will take you to complete a race distance based on your performance at another distance. The most widely used model is the Riegel formula, developed by researcher Peter Riegel in 1977 and published in Runner's World magazine. It has since become the gold standard for endurance performance prediction.
The underlying principle is that as race distance increases, your average pace slows in a predictable, exponential manner due to physiological factors like glycogen depletion, lactate accumulation, and muscular fatigue. By knowing your time at one distance, the formula can reliably project your performance at a longer or shorter distance, helping athletes set realistic goals and plan race strategies.
The Riegel formula uses a power-law relationship between distance and time. The exponent (typically 1.06 for running) represents the fatigue factor -- how much performance degrades as distance increases. A higher exponent means more performance loss over distance, while a lower one indicates better endurance relative to speed.
Different sports use slightly different exponents because of their biomechanical demands. Swimming uses 1.02 because water resistance increases exponentially with speed, making pace more consistent across distances. Cycling uses 1.04 due to aerodynamic drag effects. Rowing uses 1.03 as a hybrid between the fluid dynamics of water and the metabolic demands similar to running.
Endurance predictions are most accurate when your known time comes from a recent all-out effort and when the target distance is within a reasonable range of your known distance. Predicting a marathon time from a 5K works well, but predicting a 100-mile ultra from an 800m time would be far less reliable. The model assumes consistent training and similar conditions.
Best Practices
Use a recent race time (within 4-6 weeks) for best accuracy. Ensure your known time was from a maximal effort in similar conditions. Train specifically for your target distance rather than relying solely on predictions. Adjust expectations for hilly courses, extreme weather, or altitude changes.
The Riegel formula assumes that your training is proportional to the target distance and that race conditions are similar. It does not account for terrain, weather, nutrition strategy, or mental factors that significantly affect performance in longer events. Athletes who are naturally better at shorter or longer distances may find predictions less accurate for them.
For distances beyond the marathon or ultra-endurance events, the formula tends to underestimate completion times because additional factors like sleep deprivation, cumulative muscle damage, and prolonged nutrition needs become dominant. Always treat predictions as guidelines rather than guarantees, and use them alongside your training experience and coaching advice.