What is the Riegel formula?

The Riegel formula predicts a race time at one distance from your time at another. It is T2 = T1 x (D2 / D1) raised to the power 1.06. This 1.06 exponent captures how runners naturally slow down as distance increases. Peter Riegel published it in 1977, and it remains the most trusted race time predictor.

How accurate is a race time predictor?

Riegel predictions are about 5% accurate for distances from 800m to the marathon. That is roughly a 10 minute window on a 3:30 marathon. The predictor is most accurate when your target distance is close to your input race and when your training matches the event. Think of these predictions as well informed estimates rather than guarantees.

Why is my predicted marathon time so optimistic?

The formula assumes you have trained equally well for both distances. A fast 5K predicts a marathon you could run only if you have the endurance to back it up. If your weekly mileage is on the lower side, your real marathon will likely be slower than the prediction. For a realistic marathon target, use a longer input race like a half marathon.

Should I use VDOT or Riegel to predict my times?

Both tools give great insights. Riegel simply scales your time by a distance ratio, making it quick and transparent. VDOT models your oxygen cost and endurance, while also providing your training paces. They usually agree within a minute or two for nearby distances. Use VDOT to find your training zones, and use Riegel for a quick race prediction.

Can I predict a short race from a long one?

Yes. The formula works both ways, so your marathon time can predict your 5K and 10K. These shorter predictions tend to be very reliable because endurance is rarely the limiting factor for a short race. Predicting a marathon from a 5K is the scenario you should treat with more caution.

What Riegel exponent should I use?

The default 1.06 fits most road racing perfectly. You might want to raise it toward 1.10 for ultra distances or if you know your endurance lags behind your speed. You can lower it slightly if you are a proven high mileage distance specialist. For the vast majority of runners, leaving it at 1.06 gives the best results.

Training & Physiology

Race Time Predictor

Enter a recent race result to instantly predict your finish times from 1K to the full marathon. See exactly how your current speed translates to other distances so you can set a realistic goal for your next race.

Distance

Race time

mm:ss or h:mm:ss

Riegel exponent

Defaults to 1.06. Nudge toward 1.10 for ultras, or if your endurance lags your speed.

Using your custom exponent.

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Predicted marathon

3:50:01

23:59

10K

50:00

Half

1:50:19

30K

2:40:13

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Riegel predictions are about 5% accurate from 800 m to the marathon. They assume even training across distances, so a marathon predicted from a short race tends to run optimistic.

Predicted finish times

What your race predicts across the distance ladder, from 1K to the marathon. Your input race is highlighted.

Predicted finish times
Distance	Predicted time	Pace
1K	4:21	4:21 /km
3K	13:57	4:39 /km
5K	23:59	4:48 /km
10K Your race	50:00	5:00 /km
15K	1:16:51	5:07 /km
Half	1:50:19	5:14 /km
30K	2:40:13	5:20 /km
Marathon	3:50:01	5:27 /km
Your race		/

Compare with VDOT-based predictions for this race

A single race result tells you a lot about your potential across every other distance. This race time predictor takes your recent finish time and projects it up and down the distance ladder. It helps you set a realistic goal for your next race or simply sanity check the target you already have in mind.

Pick your race distance below and enter your time. The predictor updates instantly and highlights your input race, showing you the exact pace required for each predicted distance. By default, the calculator uses kilometers, but you can switch to miles at any time.

How the prediction works

T₂ = T₁ × (D₂ / D₁)^1.06

The Riegel formula scales your known time (T₁ over distance D₁) to a target distance (D₂) using a specific exponent. If runners held the exact same pace no matter the distance, the exponent would be 1.0. In the real world, pace naturally fades as distance grows. An exponent of 1.06 perfectly captures this typical fatigue curve for road racing. It means each doubling of distance costs slightly more than double the time.

How to read the ladder

The ladder outlines your predicted time at every common race distance, from a fast 1K up to the full marathon. The row matching your input race is highlighted so you know exactly where you are starting from.

Keep in mind that the further a target distance sits from your input race, the more your specific training will dictate the result. Short predictions based on a longer race are very reliable. If you can run a 1:50 half marathon, the 23:59 5K prediction is well within your grasp. On the flip side, a marathon projected from a 5K is an optimistic scenario assuming months of proper endurance work.

Riegel vs. VDOT

You might be wondering how this compares to our VDOT calculator. Both tools answer the same question but use different approaches. Comparing them gives you a clearer picture of your fitness.

The race time predictor uses the Riegel formula to scale your time by a simple distance ratio. It is fast, fully transparent, and only needs a single race result. The VDOT calculator models the actual oxygen cost of running to estimate your maximum sustainable effort, then reads predicted times and training paces from the Daniels tables.

When the two calculators agree, you can be very confident in your target. When they disagree, the gap usually points to your endurance base. For a runner with raw speed but low weekly mileage, both methods will overpredict the marathon. You can easily open your race in the VDOT calculator using the link under the ladder to compare both methods side by side.

Honest accuracy

The Riegel formula is about 5% accurate across the standard racing range. We prefer to share this upfront rather than pretending the numbers are perfectly precise. Two main factors will shift a prediction off target: choosing a target distance that is completely different from your input race, and lacking the specific training required for that event.

This predictor shows you what your current speed allows on an ideal day. Your actual race time will always depend on the weather, the course profile, your pacing strategy, and how well you fuel.

Test your prediction in Tokyo

The absolute best way to check a prediction is to get out there and race. Tokyo offers incredible opportunities to test your fitness year round. You can join the many 30K tune up races along the Arakawa River during winter, target the Tokyo Marathon in spring, or hop into local park races any weekend. Running a 30K before a goal marathon is a very popular tradition here, and your predicted time gives you the exact pace to aim for.

Training alongside others makes hitting those target paces feel much easier. You can browse our club directory to find runners near your level, or sign up for our free weekly email to discover upcoming races where you can put your new prediction to the test.

Keep running in Tokyo

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How to use this tool

Enter your race

Pick the distance of a recent hard race and type in your finish time. A result close to your target distance will give you the most reliable prediction.
Read the ladder

Review your predicted times from 1K to the marathon, along with the pace required for each. Your input race is highlighted so you can see how everything scales.
Adjust for your event

Use a longer input race for a marathon goal. You can also open the VDOT calculator to compare another method and get your exact training paces.

Riegel vs. VDOT for a 50:00 10K

From this 10K result, the two methods land within a minute of each other. They will drift apart if your endurance does not match your speed, and both methods can predict optimistic marathons from a short race. Cross check them and trust the longer input race.

Two methods predicting the same race from the same result
Target	Riegel	VDOT (Daniels)
Half marathon	1:50:19	1:50:52
Marathon	3:50:01	3:49:34

Sources

FAQ

What is the Riegel formula?: The Riegel formula predicts a race time at one distance from your time at another. It is T2 = T1 x (D2 / D1) raised to the power 1.06. This 1.06 exponent captures how runners naturally slow down as distance increases. Peter Riegel published it in 1977, and it remains the most trusted race time predictor.
How accurate is a race time predictor?: Riegel predictions are about 5% accurate for distances from 800m to the marathon. That is roughly a 10 minute window on a 3:30 marathon. The predictor is most accurate when your target distance is close to your input race and when your training matches the event. Think of these predictions as well informed estimates rather than guarantees.
Why is my predicted marathon time so optimistic?: The formula assumes you have trained equally well for both distances. A fast 5K predicts a marathon you could run only if you have the endurance to back it up. If your weekly mileage is on the lower side, your real marathon will likely be slower than the prediction. For a realistic marathon target, use a longer input race like a half marathon.
Should I use VDOT or Riegel to predict my times?: Both tools give great insights. Riegel simply scales your time by a distance ratio, making it quick and transparent. VDOT models your oxygen cost and endurance, while also providing your training paces. They usually agree within a minute or two for nearby distances. Use VDOT to find your training zones, and use Riegel for a quick race prediction.
Can I predict a short race from a long one?: Yes. The formula works both ways, so your marathon time can predict your 5K and 10K. These shorter predictions tend to be very reliable because endurance is rarely the limiting factor for a short race. Predicting a marathon from a 5K is the scenario you should treat with more caution.
What Riegel exponent should I use?: The default 1.06 fits most road racing perfectly. You might want to raise it toward 1.10 for ultra distances or if you know your endurance lags behind your speed. You can lower it slightly if you are a proven high mileage distance specialist. For the vast majority of runners, leaving it at 1.06 gives the best results.