Race time predictor

How does the race time predictor work?

It uses Peter Riegel’s formula T₂ = T₁ × (D₂ ÷ D₁)^1.06: time grows a little faster than distance, because pace slows as races get longer.

Example

A 10K in 50:00 predicts a half marathon in about 1:50:19 and a marathon in about 3:50:01.

Where does 1.06 come from?

It is the exponent Riegel published for endurance events. His 1981 analysis of world records found slightly different exponents for different groups, so 1.06 is a typical value, not a law.

How accurate is it?

It is an estimate from a single result and assumes you are as well trained for the new distance as for the one you ran. Use a recent, all-out race and treat the prediction as a guide.

Can I predict a shorter race?

Yes — the formula works both ways. A 3:50:01 marathon predicts a 10K in about 50 minutes.

What does a 25:00 5K predict for longer races?

A 25:00 5K predicts a 10K in 52:07, a half marathon in 1:55:00 and a marathon in 3:59:47.

Pace per mile and per kilometer

Race distances are metric, so the same time reads as two paces. The 25:00 5K above is 5:00 per kilometer, which is 8:03 per mile (1 mile = 1,609.344 meters). The predicted marathon, 3:59:47, is 5:41 per kilometer or 9:09 per mile. The half marathon is 21,097.5 meters and the marathon 42,195 meters (26.2 miles, about 26.219 in decimals); entering rounded distances such as 13.1 or 26.2 miles moves the prediction by a few seconds.

Estimating your own exponent from two races

The 1.06 is an average, and you can test it against your own results. Solving the formula for the exponent gives k = ln(T₂ ÷ T₁) ÷ ln(D₂ ÷ D₁). If you ran a 25:00 5K and a 52:30 10K, k = ln(2.10) ÷ ln(2) = 1.070. Using that exponent, the marathon prediction from the 10K becomes 4:05:09, compared with 4:01:31 from the standard 1.06. An exponent above 1.06 means your pace fades faster than average as the distance grows; below it, slower. Two races close together in distance say little about the fade over a marathon, so the estimate is most useful when the second distance is at most about twice the first.

The arithmetic

The formula multiplies your time by the distance ratio raised to the power 1.06. For a 25:00 5K (1,500 seconds) and a 10K, the ratio is 2 and 2^1.06 = 2.085, so the 10K prediction is 1,500 × 2.085 = 3,127 seconds, or 52:07. Because the exponent is above 1, the predicted pace slows with distance: 8:03 per mile at 5K, 8:23 at 10K, 8:46 at the half marathon and 9:09 at the marathon.

What the exponent does

With an exponent of exactly 1 you would hold the same pace forever, and the marathon prediction from the same 5K would be 3:30:59. The extra 0.06 turns that into 3:59:47, about 29 minutes slower, which is the allowance for fatigue. Riegel published the exponent in American Scientist in 1981 from analyses of records, so it describes how performance falls off on average; individual runners fall off faster or slower depending on endurance training.

Common mistakes

Feeding in a training run or a race that was not an all-out effort gives a prediction that is too slow. Predicting a marathon from a 5K when your weekly mileage is low is the opposite problem: the formula has no way to know that your endurance training is lacking. Using a hilly or very hot race as the input mixes in conditions you will not repeat. Another trap is a distance typed in the wrong unit, such as miles in a kilometer box, which changes the ratio and the answer by a large factor. Finally, a prediction is not a pace plan; use the pace calculator for splits, and allow for the course and the weather on the day.

Sources: Riegel PS, “Athletic Records and Human Endurance”, American Scientist 69 (1981), 285–290, for T₂ = T₁ × (D₂ ÷ D₁)^1.06; standard race distances from World Athletics. Related: pace calculator, VDOT calculator, VO2 max calculator and target heart rate calculator.