Race Time Predictor (Riegel formula)

Understanding the race time predictor — concept and principle

A race time predictor takes one recent race result and estimates what you could run over other distances, from 5 km to the marathon. Runners use it to set realistic goal times, choose a starting pace for a first half marathon or marathon, and check whether training has improved their endurance relative to their speed.

How it is calculated

The calculator uses Peter Riegel's endurance formula:

T₂ = T₁ × (D₂ ÷ D₁)^1.06

• T₁ is your known time (hours, minutes and seconds turned into minutes).
• D₁ is the distance of that race; D₂ is the distance you want to predict.
• 1.06 is the fatigue exponent. Results are shown to the nearest second.

The principle

If you could hold the same speed forever, doubling the distance would simply double the time (an exponent of 1). In reality speed falls as races get longer, because you must run at a lower share of your aerobic capacity and depend more on fuel stores. Riegel studied world records across running, swimming, cycling and walking and found that time grows with distance raised to a power slightly above 1. For running, an exponent of about 1.06 fits records from roughly 3.5 minutes to 4 hours. Each doubling of distance therefore costs about 4% in average speed (2^1.06 ≈ 2.085).

Worked example

Known result: 5 km in 25:00 (T₁ = 25 min).

1. 10 km: 25 × (10000 ÷ 5000)^1.06 = 25 × 2.0849 = 52.12 min → 52:07.
2. Half marathon: 25 × 4.2195^1.06 = 25 × 4.6002 = 115.00 min → 1:55:00.
3. Marathon: 25 × 8.439^1.06 = 25 × 9.5911 = 239.78 min → 3:59:47.
4. The 5 km line simply returns your own time, 25:00.

How to read the result

Predictions are best when the two distances are close and when you have trained specifically for the longer one. Many recreational runners run slower in the marathon than Riegel predicts from a 5 km, because limited weekly mileage, fuelling and pacing problems weigh more heavily over 42 km. Treat a marathon forecast from a short race as an upper bound and plan an opening pace slightly slower; use a recent half marathon for a better marathon estimate.

Common mistakes

• Predicting a marathon from a 1 km or 1 mile time; the further you extrapolate, the larger the error.
• Using a result from a hilly, hot or short-measured course.
• Expecting a marathon time without long runs in training.
• Using a race result from many months ago.

Frequently asked questions

Why 1.06 and not another exponent?

It is Riegel's best fit to world-class records. Some coaches use 1.07 or higher for less-trained runners over the marathon, which gives slower predictions.

Does it work for ultramarathons?

Riegel's fit covered efforts up to about four hours, so predictions beyond the marathon become unreliable.

Can I predict a shorter race from a longer one?

Yes, the formula works in both directions, but a runner with mainly endurance training may not be as fast over 5 km as predicted.

Sources: Riegel PS. Athletic records and human endurance. American Scientist 1981;69(3):285–290.