# Tesla Battery Longevity

As a Tesla owner, you have probably done the simple math of dividing the current Rated range of your car by the battery percentage to compute the maximum range and noticed that it is different than the nominal rated range when you first purchased the car.

# How Is Rated Range Computed?

Rated Range is the range that the car is expected to provide in nominal conditions set by a government agency (e.g., EPA). This range is a function of battery capacity. Battery capacity is the amount of energy that a battery can store.

To measure the stored energy in a battery accurately, you can continuously measure the current and voltage of the battery as you drain it to zero and then compute the following integral.

Obviously, this is not practical or useful for displaying the battery capacity in the car because while it gives an accurate measure of stored energy, it only provides answer after the battery is fully drained.

But, if you can live with some inaccuracy for computing the Rated Range or State of Charge (SoC), there is an easier way to compute them:
You can create a table that maps the SoC to battery voltage while battery is discharged and use this table and the battery voltage to lookup the SoC or Rated Range of the car. The following figure shows an example of such a graph (this example graph is not for Tesla battery).

Once you know the SoC, you can map it to the Rated Range using another table lookup. This method is not precise because the mapping between voltage and SoC is not exactly static and it can change based on temperature and several other factors. But, this method is simple and practical and can estimate the SoC (and Rated Range) instantaneously.

You might have noticed that the slope of the graph is very small for the large range of SoC. This is why this method cannot be very accurate: the battery voltage changes minimally when the SoC ranges between 80% and 20%.

# My Tesla’s Max Rated Range Is Not What It Used To Be. Should I Be Worried?

As the developer of Stats app for Tesla, I get this question frequently. For example, here is the Battery Health graph for our Model 3 LR AWD (my wife’s, actually). Each dot represents the maximum Rated Range at the corresponding odometer value (in miles).

As you can see, the Rated Range has degraded somewhat as the odometer value is increased. This should not be alarming as all batteries degrade with usage. The degradation is typically more pronounced at the beginning and then it will level off. Here is another graph (from @SteelSully on Twitter) from a car with significantly more mileage. As you can see, there is virtually no degradation from 65k to 85k miles:

To demonstrate that the battery degradation levels off with odometer value, I have plotted the average value of full Rated Range vs. odometer value in the following two graphs (for RWD and AWD Model 3 cars). The average is taken over enough number of cars to make the average statistically meaningful.

If you are a data geek (as I am) and want a more detailed view of the data, you would like the following “violin graph” which shows the distribution of the Rated Range for different odometer values (for both single and dual motor Model 3 cars).

1. Find your odometer value on the horizontal axis
2. The range that has the biggest “bump” corresponds to the rated range that most other owners get.

If you find the above graph too confusing, you can use the BatteryCompare app (which I have developed) to compare your max Rated Range against other Model 3 cars with the same mileage.

You may also be interested in this excellent video by Matt which explores the same topic.