Running Pace Calculator & Riegel Race Time Predictor

Pace and Race Predictor

Enter a recent race. Results update as you type, in your browser.

1. Your race result

Race distance

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Unit

Hours

Minutes

Seconds

Riegel exponent

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Predicted race	Time	Pace /km	Pace /mile

2. Pace and speed converter

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Value

Enter a pace or a speed above

Distance at this pace	Finish time

How it works: pace = time / distance, speed = distance / time, 1 mile = 1.609344 km (the international mile, defined in 1959). Race distances follow World Athletics: marathon 42.195 km, half marathon 21.0975 km. Predictions use the Riegel formula T2 = T1 × (D2/D1)^1.06 (Peter Riegel, Runner's World, 1977; American Scientist, 1981). Riegel fitted it to performances of roughly 3.5 to 230 minutes, so results outside that range are flagged. An estimate, not a guarantee.

Bar chart of Riegel formula predictions from a 25:00 5K: 52:07 for 10K, 1:55:00 for the half marathon and 3:59:47 for the marathon, using T2 = T1 x (D2/D1)^1.06

A 25:00 5K (5:00 per km) projects to a 3:59:47 marathon, an average pace of 5:41 per km.

Pace vs Speed

Pace is time per unit of distance, such as 5:00 per kilometre. Speed is distance per unit of time, such as 12 km/h. They describe the same effort from two directions, and each is the reciprocal of the other: pace in minutes per km equals 60 divided by speed in km/h.

Runners prefer pace because races are fixed distances: finish time is pace multiplied by distance. Treadmills, cyclists and most physiology papers use speed instead, which is why converting between the two is a daily task.

Two details cause most errors. First, a mile is exactly 1.609344 km, so 5:00 per km is 8:03 per mile, not 8:00. Second, pace does not change in a straight line with speed. Going from 10 to 11 km/h cuts pace by about 33 seconds per km, while going from 15 to 16 km/h cuts it by only 15 seconds.

The Riegel Formula

In 1977 the engineer and marathon runner Peter Riegel published a simple race predictor in Runner's World: T2 = T1 × (D2/D1)^1.06. T1 is a known time at distance D1, and T2 is the predicted time at distance D2. In 1981 he expanded the idea in the paper "Athletic Records and Human Endurance" in American Scientist. There he fitted the same power law to world records in running, swimming, walking and other endurance sports.

The exponent carries the meaning. If it were exactly 1, you could hold the same pace at any distance. An exponent of 1.06 says that each time the distance doubles, average pace slows by about 4.2 percent, because 2^0.06 is about 1.042. That is why the infographic above shows the 25:00 5K runner slowing from 5:00 to 5:41 per km over the marathon.

Limits you should know

Duration range. Riegel applied the relation to efforts of roughly 3.5 to 230 minutes. Sprints and ultramarathons fall outside it.
Equal training. The formula assumes you are as prepared for the long race as for the short one. A fast 5K does not give you the endurance for 42 km.
Marathon optimism. Vickers and Vertosick (BMC Sports Science, Medicine and Rehabilitation, 2016) studied recreational runners and found that the Riegel formula tends to predict marathon times that are too fast, most of all for runners with low weekly mileage.
Conditions. Heat, hills, wind and crowded starts slow you down. The formula knows only distance and time.
One exponent for everyone. Endurance-type runners slow less than 1.06 suggests and speed-type runners slow more. If you have two recent races, you can solve for your own exponent and enter it in the tool.

How to Use Pace Predictions in Training

Start from a real result. Use a recent all-out race on a flat course in normal weather.
Predict from the nearest distance. A half marathon predicts a marathon better than a 5K does, because the error grows with the distance ratio.
Treat the number as a ceiling. For a first marathon, plan your pace a little slower than the prediction and run the second half faster if you feel good.
Turn the goal into session paces. Use the converter to set goal race pace for tempo runs and long-run segments, and to set the treadmill speed in km/h or mph.
Re-test. Run a new time trial after a training block and enter it again. If the predictions keep missing in the same direction, adjust the exponent.

Common Race Distances

Standard road race distances in kilometres and miles (1 mile = 1.609344 km).

Race	Kilometres	Miles
5K	5.0 km	3.107 mi
8K	8.0 km	4.971 mi
10K	10.0 km	6.214 mi
15K	15.0 km	9.321 mi
10 Mile	16.093 km	10.0 mi
Half Marathon	21.0975 km	13.109 mi
Marathon	42.195 km	26.219 mi
50K Ultra	50.0 km	31.069 mi

Pace and Prediction Questions

What is the difference between pace and speed?

Pace is time per distance, for example 5:00 per kilometre. Speed is distance per time, for example 12 km/h. Pace in minutes per km equals 60 divided by speed in km/h.

What is the Riegel formula?

T2 = T1 × (D2/D1)^1.06. Peter Riegel published it in Runner's World in 1977 and expanded the analysis in American Scientist in 1981.

How accurate is the Riegel marathon prediction?

It is a good first estimate when you have trained for the longer distance. For recreational runners with low weekly mileage, a 2016 study by Vickers and Vertosick found that it tends to predict marathon times that are too fast.

Which race should I use as the input?

Use a recent, all-out race on a flat course in normal weather, at a distance close to the target. A half marathon predicts a marathon better than a 5K does.

Running Pace Calculator and Race Time Predictor