# Riegel Race Time Prediction Formula and Calculator

Runners can estimate their time to finish a race based on the results of a previous race and one of several prediction formulas. One of the easiest equations to apply is the Riegel model. Riegel's projected running time formula is independent of the units of measurement, so no conversion is necessary. The equation is

T₂ = T₁(D₂/D₁)^{1.06}

where T₁ is the previous time, D₁ is the distance previously run, D₂ is the new distance to be run, and T₂ is the projected time for the new race. Distances can be in any unit so long as they are the same unit.

Since the exponent 1.06 is greater than 1, a runner's average velocity is expected to decrease with longer distances, thus increasing the time by a larger factor.

Put another way, when the distance doubles, the time to run increases by a factor of about 2.0849. When the distance is halved, time decreases by a factor of 0.4796.

### Example Prediction Using the Riegel Formula

Last week, Tom ran 3.5 miles in 51 minutes and 30 seconds (51.5 minutes). The week before, he ran 2.5 miles in 34 minutes and 45 seconds (34.75 minutes). He wants to predict his time to run a 5-mile race next week.Using the Riegel formula on the first set of race results gives us

T₂ = 51.5(5/3.5)

^{1.06}= 75.163 minutes, or 1:15:9.77

Using the Riegel formula on the second set of race results gives us

T₂ = 34.75(5/2.5)

^{1.06}= 72.451 minutes, or 1:12:27.08

Averaging the two projections gives us (75.163 + 72.451)/2 = 73.807 minutes, or 1:13:48.42. Notice that this is close the the predictions found with the Cameron and VO2 Max methods.

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