The Riegel formula explained: predict your race time

Many online race time predictors run on the same short formula. It was published by Peter Riegel, first in Runner's World in 1977 and then in a longer paper in American Scientist in 1981.

T2 = T1 × (D2 ÷ D1)^1.06

T1 is the time of a race you've run. D1 is its distance. D2 is the distance you want to predict, and T2 is the predicted time.

What the 1.06 means

If you ran at the same pace no matter the distance, the exponent would be 1. Double the distance, double the time.

Real runners slow down as races get longer. The exponent captures that. With 1.06, doubling the distance multiplies your time by 2^1.06 = 2.085. So the predicted pace for a race twice as long is about 4% slower.

Riegel called this number the fatigue factor. In his 1981 paper, he fitted world records and found exponents around 1.08 for running: 1.077 for men and 1.083 for women. The rounded 1.06 is the version most widely quoted and used by calculators today. It is a bit more optimistic.

A worked example, step by step

You ran a 5K in 25:00. What does the formula say about a 10K?

1. T1 = 25:00 = 1,500 seconds. D1 = 5,000 m. D2 = 10,000 m.
2. D2 ÷ D1 = 2.
3. 2^1.06 = 2.0849.
4. 1,500 × 2.0849 = 3,127 seconds.
5. 3,127 s = 52:07, or 8:23 per mile.

The distances must be in the same unit, but which unit doesn't matter. Only the ratio counts.

From one 5K to every race

Here is what the formula predicts from a 25:00 and a 30:00 5K. Values come from the Pace Notes predictor with exponent 1.06 and the exact race distances (half marathon 21,097.5 m, marathon 42,195 m).

Race	From 25:00 5K	Pace /mi	From 30:00 5K	Pace /mi
Mile	7:31	7:31	9:01	9:01
10K	52:07	8:23	1:02:33	10:04
Half marathon	1:55:00	8:46	2:18:00	10:32
Marathon	3:59:47	9:09	4:47:44	10:58

The 10K numbers are believable for most runners. The marathon numbers are where you should start to doubt.

Where the formula breaks down

It assumes you're equally trained for both races. A 25:00 5K runner who has never run longer than 8 miles will not run a 3:59 marathon. The 5K says little about how well you've built endurance for 26.2 miles. The farther the jump, the more the prediction depends on training you may not have done.

It was built on a time range. Riegel described the relationship for efforts lasting about 3.5 to 230 minutes. A 4:47:44 marathon is outside that window. The Pace Notes predictor flags rows like this.

It was fitted on elite performances. Riegel worked from world records, set by athletes who train specifically for each distance. Your own fade over a long race depends on how your training compares, and 1.06 is gentler than the 1.08 he found in the records.

Course and weather aren't in it. A hilly half or a humid marathon will be slower than the formula says.

Making it more conservative

The simplest fix is to raise the exponent. For the same 25:00 5K:

Exponent	Predicted marathon
1.06	3:59:47
1.07	4:04:57
1.08	4:10:14

The second fix is better: predict from a closer distance. A half marathon is the best guide to a marathon. From a 2:00:00 half, the formula predicts 4:10:12 with 1.06, and 4:13:41 with 1.08. That's a much narrower spread than a 5K would give.

A rough rule for using the predictor:

• Predicting up to twice the distance: trust it, adjusted for course and weather.
• Two to four times the distance: use it as a target only if your long runs match the new race.
• More than four times: treat it as a ceiling, not a plan.

Use it in reverse

The formula also works backward. If your goal is a 4:00:00 marathon, the 1.06 version says you should be able to run a half in about 1:55:07 first (4:00:00 ÷ 2.0849). If your recent half is much slower than that, the goal is probably a stretch.

Try it

The race time predictor takes any recent race and predicts the mile, 5K, 10K, half and marathon, with warnings when the prediction stretches too far. You can change the exponent. Then turn the predicted time into a race plan with the marathon pace chart or the split calculator.