Endurance is your ability to hold a given effort for a certain amount of time. The more endurance you have, the longer you can sustain the same intensity. In running, you can actually quantify a runner’s endurance with the Endurance Index (EI). Let’s look at how to calculate your endurance index.
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Running performance: vVO2max and the endurance index
Running performance depends on many factors, especially how long the effort lasts. At the extremes, the qualities needed for sprinting are nothing like those required for ultra trail.
For middle and long distances, lasting from 6 minutes up to around 4 to 5 hours, you can predict performance using only two parameters: vVO2max and the endurance index.
Beyond 5 hours of effort, other variables come into play and the formula is no longer applicable.
The endurance index is not necessarily a perfect reflection of your overall level. You could have the same endurance index as Eliud Kipchoge, but you still would not run as fast, because his vVO2max is almost certainly much higher than yours ;).
The endurance index according to Peronnet and Thibault
Back in the 1980s, researchers François Peronnet and Guy Thibault found a relationship for races from 3000m to the marathon.
To make their model easier to use, they shared a simplified equation that lets runners quantify endurance with just two inputs: your vVO2max and a race result, ideally one lasting more than an hour.
The formula: Endurance Index = (% of vVO2max sustained during the race – 100) / ln (race time in minutes / 6)
As a rule of thumb, an athlete with very strong endurance has an endurance index around -5, and an athlete around -10 has low endurance.
This approach can feel a bit confusing for runners because the endurance index is always negative. Basically, you are calculating the slope of a line, and that slope is always negative. The flatter the slope is, meaning the closer the value is to 0, the more endurance you have.
Note: in Peronnet and Thibault's original publication, the 6-minute limit for vVO2max was set at 7 minutes. That is why you will sometimes see the formula written with a 7 instead of a 6.
Long-distance endurance with the MIT/CNRS model
In this article, I explain in detail the performance prediction model for middle and long distance, developed with Thorsten Emig and Matthew Mulligan at MIT and CNRS. We defined long-distance endurance (roughly 6 minutes to 4 to 5 hours) in a way that is easier to read and interpret.
Long-distance endurance represents how long a runner can hold 90% of their vVO2max. In other words, a fast but sustainable pace for several tens of minutes.
Long-distance endurance = time you can run at 90% of your vVO2max / time you can run at vVO2max (fixed at 6 min)
The math is fairly complex, because you first have to determine how long you can hold 90% of your vVO2max, which you do not know in advance. You can estimate it using at least two race results.
This endurance scale can be read like this:
3: Low endurance.
5: Average endurance.
7: Good endurance.
8: Excellent endurance.
10: Exceptional endurance.
You can read it like a score out of 10, which makes it much more intuitive.
If your endurance is 10, you can run 1 hour (60 minutes) at 90% of your vVO2max, which is exceptional. If your endurance is 3, you can run only 18 minutes at 90% of your vVO2max. Average (5 out of 10) is around 30 minutes at 90% of your vVO2max.
What does low endurance (between 3 and 5) mean? It means that, proportionally, your 10K or half marathon performances are much better than your marathon performance. This can happen if you had a rough patch in your best marathon, or if you had to walk for a few kilometers.
On the other hand, an excellent endurance index can indicate that you ran a great marathon relative to your best shorter-distance references. This often happens when you have improved a lot for the marathon but have not raced a new 10K recently. If you run a 10K soon, you are almost guaranteed to beat your personal best on the distance ;)
Calculate your long-distance endurance index
We created a simulator so you can calculate your long-distance endurance, you will find it on this page. You'll also get performance predictions from 5K to marathon.
Note that this endurance index and long-distance endurance are only valid for running, and cannot be directly transferred to cycling, swimming, or other endurance sports.
How to improve your endurance index
To improve your endurance index, there is no magic trick, you have to train. Ideally with varied workouts and a range of training paces, easy endurance runs, threshold, intervals, and more.
If you want to level up, I invite you to download RunMotion Coach, which builds your personalized training plan and directly includes the right training paces. It uses your race results to estimate your vVO2max and your endurance index.