# Forums

## What is wrong with your "rated range" calculation

I've been thinking about the common occurrence of posts complaining about the "Rated Range" not being what it should be. I've have some very important observations that will help make this much more understandable.

1. The first scenario goes like this: I charged my car to 80%, toggled to miles and it says 250 miles. So I took 250 miles / .8 = 312.5 miles. But just the other day I saw 320 miles. So I lost 7.5 miles in one day.

The problem here is all about display resolution. The "power meter" shows you battery percentage in 1 % resolution and miles in 1 mile resolution. There are only 101 possible values for battery percentage. And somewhere around 325 different values for miles (for a LR RWD).

For any given percentage that you read on the power meter there is just about 3 different values possible for the miles display.

As an example, here is a collection of real world percentage and miles for my car observed during a charge:

37% 119 miles
38% 119 miles
38% 120 miles
38% 121 miles
38% 122 miles
39% 122 miles

In this case I actually got 4 different mileage numbers all while the percentage was 38%.

If I use the classic case of dividing range by battery percentage, I get the following:

37% 119 miles. 321.6
38% 119 miles. 313.2
38% 120 miles. 315.8
38% 121 miles. 318.4
38% 122 miles. 321.1
39% 122 miles. 312.8

I can calculate a "rated range" that varies by about 9 miles. That's about 3% of false degradation, just by looking at the display at different times.

As I got near the end of that charge, I saw the following:

54% 174. 322.2
55% 174. 316.4
55% 175. 318.2
55% 176 320.0
55% 177 321.8
56% 177. 316.1

Only about a 6 mile difference in "rated range". This makes sense, in that the variance of the "rated range" calculation decreases as we get close to 100%. By the time you get to about 100% we should be seeing a maximum of 3 miles of variance.

I use Teslafi and I noticed that the data collected by Teslafi has battery percentage in 1% resolution and mileage in .01 resolution. But this doesn't really help because there is still up to 3 or more miles of range that can be accounted for a single percentage number. Having percent battery capacity as a 1% resolution number is a major culprit to why Teslafi's battery health graph is so noisy.

If you use Teslafi, you can go to battery health and change the "Include charges equal to or greater than" number to 100% and you will most likely see that your data only varies by about 3 miles. And the sneaky thing is that Teslafi knows this because they actually give you the option to only include certain charges and they limit that number to at least a 50% charge. That's because the error gets bigger, due to simple math, as the SOC gets lower. If you included charges that stopped around 5-10% you would see huge swings in your "rated range". If you went down to 0% your "rated range" calculation would actually go to infinity.

Changing that percentage to different numbers will basically decrease the volatility of the end result when you limit to higher final percentages.

jallred | 12. Februar 2020

2. Even with the above explanation, I'm definitely seeing a bigger step down in "rated range" then you are showing, especially in the winter.

This is problem #2 and it is due to the fact that the number shown on the power meter is % charge of what is usable. On the power meter, you can't ever see the usable battery capacity. Teslafi knows about this too. You can see this on the banner at the top of the page. If your battery is cold, then you will see three numbers for battery percentage. For instance, my page right now shows 58 (57) / 86. This means that I have the car set to charge to 86%. My power meter shows 58%, but my usable battery capacity is only 57%. To the right of that, it says my rated range (sic) is 182.24. The car shows 182 on the power display.

If I was in the car, I would calculate my "rated range" with 182/ .58 = 313.8.

Using the numbers on Teslafi I have two options:
182.25 / .58 = 314.2
182.25 / .57 = 319.7

Guess which one Teslafi uses in battery health. Yes. the lower one. That is because the charging data doesn't provide (or teslafi doesn't keep) the usable battery capacity, just the number that is shown on the screen.

Since even the usable battery capacity is given in 1% resolution there are two possible extremes with the above calculation. We could be at most .5% high or low on both numbers.
For instance we could actually be at 182.25 / .585 = 311.5
Or we could be at 182.25 / .565 = 322.6

That's 11 miles of range loss just from math errors due to resolution.

And, when the car gets really cold we can actually get more than 1 percent difference between usable and displayed percentage.

This is why you see in Teslafi and noisy battery health range. But then you see discrete jumps to a new noisy level.
The noise is because of math errors due to resolution and the discrete jumps are due to integer differences between usable and displayed battery percentage.
When you do the calculation yourself using the numbers on the screen it is slightly worse because the numerator is limited to 1 mile precision. Like in the above example, the display will show 182 instead of 182.25 so you lose the .25 in the numerator. .25 / .57 = .44 miles. Not much, but it can add up to another mile of loss range.

So what can you do? Well if it isn't cold outside then you can do this. Watch while charging for the percentage to go up by 1 and then get the range. Right as it goes up by 1% it should actually be right in the middle between the two percentages. So back to my original data.

37% 119 miles. 321.6
38% 119 miles. 313.2
38% 120 miles. 315.8
38% 121 miles. 318.4
38% 122 miles. 321.1
39% 122 miles. 312.8

If I do 38.5 122 miles = 316.9

It still isn't perfect because you can't tell whether the usable percentage is a different number or if the mileage shown is some fraction higher or lower.

DiminishedSeventh | 12. Februar 2020

Great write-up! Lots of detail and good explanations. Thanks for all the effort you put in!

TL;DR - just drive the damn car. :)

M-A-B-MCMLXXX | 12. Februar 2020

“ 2. Even with the above explanation, I'm definitely seeing a bigger step down in "rated range" then you are showing, especially in the winter.”

Is this an excerpt from another thread or did I miss something in your OP?

DiminishedSeventh | 12. Februar 2020

@MAB1980 I think that’s his second hypothetical scenario/argument that people make.

M-A-B-MCMLXXX | 12. Februar 2020

Roger that. It’s a “Yah but.”

Incidentally, what do you play (music reference)?

jallred | 13. Februar 2020

It wouldn’t take the full write up in the summary.

I noticed familiar patterns in teslafi battery health. After a little thought it was easy to find that there was the equivalent of a bit size deficiency in the calculations. Especiallly true with division.

Bottom line: can’t use these numbers to calculate “rated range” with any precision.

FISHEV | 13. Februar 2020

Nothing is wrong with Rated Range. It's just the ideal range of the car based on current battery capacity.

Only issue people have with Rated Range that we see a lot is they don't know what is the Rated Range for their car as Tesla is not doing a good job of handing people the car sticker which clearly stats Rated Range.

For how much range the car actually has just use Projected Range from the Energy/Consumption graph. When Rated Range says you have 56 miles to get to work but Projected Range says 31 miles left, Projected Range is right and get a charge.

M-A-B-MCMLXXX | 13. Februar 2020

“ Nothing is wrong with Rated Range.”

He didn’t say there is. He pointed out the inherent uncertainty in taking displayed numbers for range and energy remaining and extrapolating with them.

jallred | 13. Februar 2020

@MAB,

Not fair of you. For him to understand your post he would have to look up definitions of inherent, uncertainty, range, energy and extrapolating.

To top it off, his definition of rated range is all messed up. He says in his first paragraph that it is "based on the current battery capacity". But in the second paragraph he says "car sticker clearly stats (sic) Rated Range.

How is a sticker supposed to clearly state something based on the current battery capacity? More like a crystal ball then a sticker.

jallred | 13. Februar 2020

I've been trying to tell that fool for months that the power meter display is NOT rated range. And now he wants to say that rated range is a constant on the sticker.

HighlandPony | 13. Februar 2020

I think it would be awesome if Tesla changed the name of this displayed number to what it is commonly referred to in Norway, the country with the highest EV adoption rate. The GOM, guess-o-meter. Everyone there knows that this number is not to be trusted and can be wildly inaccurate. This is especially true for some makes and models of cars, only a fool would blindly trust it and make travel decisions based solely on it. Or make any kind of statement about battery health based solely on this value. At least the Norwegians have a sense of humor about it.

DiminishedSeventh | 13. Februar 2020

Lol @highlandpony I like that a lot more!

@MAB1980 I play sax, trumpet, and drums. Good catch :)

WW_spb | 13. Februar 2020

Gnome