What this calculator does
Use a recent race to predict your finish time at a different distance. Maybe you want to know what your 10K time suggests for a half marathon. Or what pace is realistic for your first marathon. A simple, popular rule for this is the Riegel formula. It stretches a known time to a new distance and allows for the fact that you slow down as races get longer.
Enter a recent race distance and time, and choose the distance you want to predict. The calculator applies the Riegel formula for you. It also fills a table of predicted times and paces for standard races from 1,500 m to the marathon. You can change the exponent, the number that sets how much you slow down. Raise it for a more cautious guess if you tend to fade over long distances.
Where it's used
Why this math matters outside the classroom:
- Riegel formula. A 25:00 5K predicts a 10K time of 25 × 2^1.06 minutes, which is about 52:07.
- Power functions. Students see a power function with a non-integer exponent, since doubling the distance multiplies the time by 2^1.06 rather than 2.
- Setting a goal. Runners pick a realistic goal time for an upcoming half marathon from a recent 10K result.
- Pace groups. Runners use a predicted finish time to choose which pace group to start with on race day.
- Comparing efforts. Coaches compare results from different race distances by converting each one to a predicted 10K time.
How to use it
- Enter the distance of a recent race or timed run, in kilometers or miles.
- Enter your finish time in hours, minutes and seconds.
- Enter the distance you want a prediction for.
- Leave the exponent at 1.06 to start. Then read your predicted time, pace and the race table.
What the inputs mean
- Recent race distance
- Use a recent race where you gave it everything, on a course measured accurately. Results from 5K to the half marathon usually give the most useful predictions.
- Distance to predict
- The distance you want to predict. The marathon is 42.195 km (about 26.22 miles).
- Fatigue exponent
- 1.06 is the standard value. Values around 1.07 to 1.10 give slower, more cautious long-distance predictions. These may suit runners who have done less endurance training. An exponent of 1 means you never slow down at all.
Formula and method
T2 = T1 × (D2 ÷ D1)^k k = 1.06 by default pace = T2 ÷ D2
T1 and D1 are the time and distance you already know. D2 is the distance you want to predict, and T2 is the predicted time. The letter k is the exponent, the number that sets how much you slow down. Because k is a little above 1, doubling the distance slightly more than doubles your time.
Distances in miles are changed to kilometers using exactly 1 mile = 1.609344 km. That means you can mix units freely.
Times are worked out in seconds, then rounded to the nearest second.
Worked example
A runner finished a 10K in 50:00 and wants a marathon prediction.
- Known time: 50 minutes = 3,000 s.
- How many times longer the new race is: 42.195 ÷ 10 = 4.2195.
- Raise that to the exponent: 4.2195^1.06 = 4.600199.
- Predicted time: 3,000 × 4.600199 = 13,800.6 s = 3:50:01.
Result: The predicted marathon time is about 3:50:01. That's a pace of about 5:27 per km (8:46 per mile). The same 10K suggests a half marathon of about 1:50:19.
Understanding the result
A prediction is the time you could run if you train for the new distance. It isn't a time you'll get automatically. Marathon predictions in particular assume you've done the long runs and weekly mileage a marathon needs.
Predictions are most trustworthy between nearby distances, such as a 10K to a half marathon. Stretching all the way from a mile to a marathon makes any error much bigger.
Are your real long-race results always slower than predicted? Then raise the exponent until the formula matches your past races.
Assumptions and limitations
- Your known result was an all-out effort.
- Both races are on similar ground, in similar weather, and you've trained for each.
- Your slowdown follows the formula's curve (a power law) with the exponent you chose.
- It doesn't account for heat, hills, wind or how you pace yourself on race day.
- The formula is generally seen as less reliable for races shorter than a few minutes or longer than about four hours.
- It doesn't allow for people who are naturally better at speed or better at endurance.
Frequently asked questions
How accurate is the Riegel formula?
It gives reasonable estimates for many trained runners between 5K and the half marathon. For the marathon, it's often a little too hopeful. That's especially true for runners who don't run many miles each week.
What exponent should I use?
Start with 1.06. If your past long races came out slower than the formula predicted, try 1.07 to 1.10. A lower value suits runners who hold their pace unusually well.
Can I predict a shorter race from a longer one?
Yes. The same formula works in both directions. A shorter target just gives you a faster pace.
Why is the predicted pace slower for longer races?
Tiredness builds up over time, so nobody can hold their 5K pace for a whole marathon. An exponent above 1 builds that slowdown into the prediction.
How this calculator is checked
Method: Riegel endurance formula T2 = T1 × (D2/D1)^1.06 with a user-editable exponent; exact mile definition; standard race distances. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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