garsh's Official Model 3 Battery Pack Capacity Calculation Thread

garsh

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#1
Given all of the recent talk about Model 3 battery pack capacities that erupted after Elon's tweet:
I decided to attempt an actual calculation of the largest possible battery pack that will fit into a Model 3. So... LOTS of caveats. Since we have no official dimensions of any kind, I'm making a lot of assumptions and educated guesses. So whenever you see me provide a size for something related to the Model 3, it is a guess - an approximation.

First, consider the battery pack from a P100D. It's been hinted that the cell arrangement in the 100D battery pack is a precursor to how the Model 3's battery pack will be organized. So here's a Model S battery pack:

It contains 16 battery modules - two stacked in front, and the rest in a 7x2 arrangement.
Here's what one of those modules looks like from a P100D (with a P85D module above it):

Model S: Arrangement of Cells in a Module
There are 516 cells in that module (8256 cells total). Each cell is 18mm in diameter.
From any of the various ebay auctions, the dimensions of a module are approximately 685mm x 280mm.
Looking at the picture above, we see that we have 16 rows of cell, each row with 32-34 cells.
Taking the width of 280mm and dividing by 16, we get 17.5mm.
Taking the length of 685mm and dividing by 34, we get 20mm.
The rows are staggered to allow 18mm diameter cells to be placed 17.5mm apart.
So, I'm going to assume that the Model 3 battery modules will have a similar arrangement, where the cells in a row have about 2mm in between, but the rows are staggered and overlap by 0.5mm.

Model S: Percentage of the Floor taken by Battery Modules
Ignoring the two stacked modules, the other 14 modules fit in a space in between the front & rear axles. I couldn't find the dimensions of the entire pack, but seven modules would be 1960mm == 77". The wheelbase of a Model S is 116.5", and the tire diameter is 28.5". Add a few inches within the wheel arches, and that leaves 84" to fit the battery pack. So we have ~7" of overhead between and around the modules. Roughly 10% of the space in between the axles. The width of a Model S is 77.3" (1963mm). Two modules together would have a length of 54" (1370mm). So width-wise, we have about 30% overhead. I'm going to assume that the Model 3 has similar 10% length and 30% width overhead values.

The Model 3
Now comes all of the approximations. How big is the Model 3 battery pack? How many modules does it contain? How big are those modules, and how many cells will fit in each module? Let me take a shot at this:

From the Model 3 reveal, we know that the pack will consist of 8 modules. Unlike the S, the 3's modules are arranged so that there are four modules side-to-side, and two modules front-to-back.

Model 3: Battery Module Size
Randy Carlson of seeking alpha approximates the size of the modules as 42"x14" (1067mm x 356mm). How did he come up with this? I don't know. Let's try to figure out what fits ourselves. The "approximate" Model 3 dimensions given by MotorTrend (I still think they took a tape measure to the photo shoot, but weren't allowed to say so) are:
  • Width: 74.2" (1885 mm)
  • Wheelbase: 113" (2870 mm)
  • Tire (275/30-20) diameter: 26.5" (673 mm)
Let's take 70% of the width (52", 1320mm), divide by 4, and we get module widths of 13" (330mm).
Take wheelbase - tire diameter (86.5"), remove a bit more for wheel arches (82.5"), and then remove 10% overhead, to get 74.25" (1886mm). That gives module lengths of 37" (940mm). So, we'll assume that the modules are 37"x13" (940mm x 330mm).

Model 3: Number of Cells
The cells for the Model 3 are 21mm in diameter. Let's assume they get packed in a manner similar to the 100D battery modules. So it would have rows that are 20.5mm apart, with 2mm gaps between cells in the same row. Then, a single module could hold (330mm/20.5mm=) 16 rows of (940mm/23mm=) 40 cells. That gives (16x40=) 640 cells per module, and (640x8=) 5120 cells for the whole battery pack.

Model 3: Energy Stored in Cells
How much energy do the Model S's 18650 cells hold? If a Model S's 100kWh pack has 8256 cells, then I guess each 18650 cell can hold about (100,000Wh/8256=) 12.1 watt-hours. As a lower bound, if we assume each of the Model 3's 5120 cells can also hold only 12.1 watt-hours, that gives a pack size of 62kWh.

But, we know that the new 2170 cells can hold more energy than the 18650 cells. So, how much energy can the 2170 cell hold compared to the 18650? The 2170 has about 46% more volume than the 18650 (24,245 mm³ vs 16,575 mm³). Assuming it could hold 46% more energy, that would give us a 90.5kWh pack. So I think it will be quite reasonable to expect an 85kWh pack - maybe even a 90kWh pack - to be offered as the top option for the Model 3.
 
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BigBri

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#4
Seems like the right idea to me. Considering the 100KWH pack is their newest (we can speculate that the M3 pack will have more in common with it then an older Model S pack) then 90 makes sense given the 100KWH has a bit over 100kwh of capacity rather then the older packs that had a bit under the advertised capacity.
 

TrevP

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#5
Thanks for doing this. I didn't really do any math but figured the pack is 85-90% the size of a Model S and given the new cells are indeed larger I figured there'd be less of them but the volume makes up for the pack size loss so I always figured 85kWh would be the upper capacity.

I have a feeling the base pack will be 55kWh and a mid pack coming in at 70kWh giving their cars a 15kWh spread between options. If Tesla indeed has their costs in check then we could see just 2 offerings: 70 and 85kWh physical packs with the base being software limited to 55kWh with a OTA unlock possible.
 

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#6
I'm glad you both reach the same conclusions. This underlines the probability that something like this will be the outcome.

If Tesla has the costs in check that would also mean that the costs for extra battery size will be moderate, I think. Especially since range is such a big factor in BEV acceptance.
(Together with fast charging ability.)
A happy prospect!
 

Mike

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#7
Given all of the recent talk about Model 3 battery pack capacities that erupted after Elon's tweet:
I decided to attempt an actual calculation of the largest possible battery pack that will fit into a Model 3. So... LOTS of caveats. Since we have no official dimensions of any kind, I'm making a lot of assumptions and educated guesses. So whenever you see me provide a size for something related to the Model 3, it is a guess - an approximation.

First, consider the battery pack from a P100D. It's been hinted that the cell arrangement in the 100D battery pack is a precursor to how the Model 3's battery pack will be organized. So here's a Model S battery pack:

It contains 16 battery modules - two stacked in front, and the rest in a 7x2 arrangement.
Here's what one of those modules looks like from a P100D (with a P85D module above it):

Model S: Arrangement of Cells in a Module
There are 516 cells in that module (8256 cells total). Each cell is 18mm in diameter.
From any of the various ebay auctions, the dimensions of a module are approximately 685mm x 280mm.
Looking at the picture above, we see that we have 16 rows of cell, each row with 32-34 cells.
Taking the width of 280mm and dividing by 16, we get 17.5mm.
Taking the length of 685mm and dividing by 34, we get 20mm.
The rows are staggered to allow 18mm diameter cells to be placed 17.5mm apart.
So, I'm going to assume that the Model 3 battery modules will have a similar arrangement, where the cells in a row have about 2mm in between, but the rows are staggered and overlap by 0.5mm.

Model S: Percentage of the Floor taken by Battery Modules
Ignoring the two stacked modules, the other 14 modules fit in a space in between the front & rear axles. I couldn't find the dimensions of the entire pack, but seven modules would be 1960mm == 77". The wheelbase of a Model S is 116.5", and the tire diameter is 28.5". Add a few inches within the wheel arches, and that leaves 84" to fit the battery pack. So we have ~7" of overhead between and around the modules. Roughly 10% of the space in between the axles. The width of a Model S is 77.3" (1963mm). Two modules together would have a length of 54" (1370mm). So width-wise, we have about 30% overhead. I'm going to assume that the Model 3 has similar 10% length and 30% width overhead values.

The Model 3
Now comes all of the approximations. How big is the Model 3 battery pack? How many modules does it contain? How big are those modules, and how many cells will fit in each module? Let me take a shot at this:

From the Model 3 reveal, we know that the pack will consist of 8 modules. Unlike the S, the 3's modules are arranged so that there are four modules side-to-side, and two modules front-to-back.

Model 3: Battery Module Size
Randy Carlson of seeking alpha approximates the size of the modules as 42"x14" (1067mm x 356mm). How did he come up with this? I don't know. Let's try to figure out what fits ourselves. The "approximate" Model 3 dimensions given by MotorTrend (I still think they took a tape measure to the photo shoot, but weren't allowed to say so) are:
  • Width: 74.2" (1885 mm)
  • Wheelbase: 113" (2870 mm)
  • Tire (275/30-20) diameter: 26.5" (673 mm)
Let's take 70% of the width (52", 1320mm), divide by 4, and we get module widths of 13" (330mm).
Take wheelbase - tire diameter (86.5"), remove a bit more for wheel arches (82.5"), and then remove 10% overhead, to get 74.25" (1886mm). That gives module lengths of 37" (940mm). So, we'll assume that the modules are 37"x13" (940mm x 330mm).

Model 3: Number of Cells
The cells for the Model 3 are 21mm in diameter. Let's assume they get packed in a manner similar to the 100D battery modules. So it would have rows that are 20.5mm apart, with 2mm gaps between cells in the same row. Then, a single module could hold (330mm/20.5mm=)16 rows of (940mm/23mm=) 40 cells. That gives (16x40=) 640 cells per module, and (640x8=) 5120 cells for the whole battery pack.

Model 3: Energy Stored in Cells
How much energy do the Model S's 18650 cells hold? If a Model S's 100kWh pack has 8256 cells, then I guess each 18650 cell can hold about 12.1 watt-hours. As a lower bound, if we assume each of the Model 3's 5120 cells can also hold only 12.1 watt-hours, that gives a pack size of 62kWh.

But, we know that the new 2170 cells can hold more energy than the 18650 cells. So, how much energy can the 2170 cell hold compared to the 18650? The 2170 has about 50% more volume than the 18650. Assuming it could hold 50% more energy, that would give us a 93kWh pack. So I think it will be quite reasonable to expect an 85kWh pack - maybe even a 90kWh pack - to be offered as the top option for the Model 3.
Nice work. Thanks. :)
 

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#8
I'm glad you both reach the same conclusions. This underlines the probability that something like this will be the outcome.

If Tesla has the costs in check that would also mean that the costs for extra battery size will be moderate, I think. Especially since range is such a big factor in BEV acceptance.
(Together with fast charging ability.)
A happy prospect!
As an almost 5 year EV driver (23-February), battery size to give 150 miles and access to rapid charging in some the winning combo... doubling the pack size is the sweet spot to knock down 95% of the naysayers...

As I've been known to say, I stop on long range EV drives because I have to... and the car still has enough charge/range... and that's on an 85kWh Model S.
 

Gary Moore

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#9
By SWAG (aka Kentucky windage), I was thinking the desirability of having an acceptable Ludicrous package for Model 3 would prompt the engineers to be asked: Can we safely stack at least 85kwh in there? From a marketing perspective, if the Model S buyer is paying the bigger bucks, you sanely don't want him greatly upstaged by someone buying a Model 3. I realize we're talking the real Elon here, but as the Puzo's Godfather was wont to say, "It's strictly business."

Thanks for all the estimation effort and presentation.
 

Mike

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#11
...you sanely don't want him greatly upstaged by someone buying a Model 3. I realize we're talking the real Elon here, but as the Puzo's Godfather was wont to say, "It's strictly business."
Something I've been bringing to various online conversations: that moment when resale values of current Model S' take a hit because the next gen architecture of Model 3 is so much improved. My first home PC (386/20) suffered the same fate.....

The real cash for Tesla will be the millions of Model 3's, like Henry Fords Model T......

Great line from a great movie by the way :)
 

Twiglett

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#12
Something I've been bringing to various online conversations: that moment when resale values of current Model S' take a hit because the next gen architecture of Model 3 is so much improved. My first home PC (386/20) suffered the same fate.....

The real cash for Tesla will be the millions of Model 3's, like Henry Fords Model T......

Great line from a great movie by the way :)
I don't think they will take too much of a hit - they will very likely drop, but they're still a bigger car in a different class.
Also much more likely to have free unlimited supercharging.
 

Mike

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#13
I don't think they will take too much of a hit - they will very likely drop, but they're still a bigger car in a different class.
Also much more likely to have free unlimited supercharging.
I admit I'm no subject matter expert in economics and the economics of the automotive sector.

I'm too close to this, emotionally, so I can only go by my gut instinct (which is often not a good way to stay solvent), but......

....I can't help but wonder what Elon must be factoring into all the early marketing decisions of the Model 3 without hollowing out the Model S. There has to be a corporate recognition that if the Model 3 is artificially held back to maintain the Model S' perceived value, the company may ultimately take a bigger hit with the loss of some potential Model 3 sales.
 

AEDennis

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#15
I admit I'm no subject matter expert in economics and the economics of the automotive sector.

I'm too close to this, emotionally, so I can only go by my gut instinct (which is often not a good way to stay solvent), but......

....I can't help but wonder what Elon must be factoring into all the early marketing decisions of the Model 3 without hollowing out the Model S. There has to be a corporate recognition that if the Model 3 is artificially held back to maintain the Model S' perceived value, the company may ultimately take a bigger hit with the loss of some potential Model 3 sales.
Considering that Tesla does not do any marketing... I don't think you have to worry about this.

The Model S and Model 3 are going after different markets once the 3 is out. I doubt that the 60kWh-75kWh Model S will survive... which means starting prices for Model S will go up from their current levels as the top end Model 3 will fill in that spot.

Just a thought.
 

MichelT3

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#16
I don't really understand the worrying. Every carmaker has price-overlapping models. On purpose, because different models have different characteristics, applying to different customers. By having overlapping prices it's easier to satisfy different demands.

It's just a problem from our perspective, because we are totally Model 3 minded.

I can imagine someone saying: "I want a big Tesla, but without a huge range and the most advanced technical specifications. Why care that for the same price I can get a smaller car which has frills? I want a BIG Tesla."

I expect the Model Y to overlap prices of both 3 and S, maybe even X. Just as X overlaps S.
 

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#17
Considering that Tesla does not do any marketing... I don't think you have to worry about this.
I'm not a salesman, but my father spent 42 years in sales and marketing and he finds the whole Tesla marketing (his term) model brilliant.

I agree with you that the classical, Madison-Avenue-sells-ICE-to-the-crowd model of marketing is not being employed here.

IMHO, everything that Elon does, information flow wise for the Model 3, is marketing. Everything.
 

garsh

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#18
The difference in volume between the old & new cells is actually 1.46. I've updated the last calculation of possible pack size. The conclusion is still the same, but with 85kWh looking even more likely than 90kWh.
 

MichelT3

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#19
I'm not a salesman, but my father spent 42 years in sales and marketing and he finds the whole Tesla marketing (his term) model brilliant.

I agree with you that the classical, Madison-Avenue-sells-ICE-to-the-crowd model of marketing is not being employed here.

IMHO, everything that Elon does, information flow wise for the Model 3, is marketing. Everything.
By calling it marketing, it sounds to me like it's done with the purpose to sell.
While I'm convinced that the ulterior motive is not to sell and make money, but to spread EV's and renewable energy to better the world. That you can only do that if the new products are better than the fossil ones. And that is what people realise and what makes Tesla so attractive. The philosophy behind the make and its products.
 

Rick59

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#20
By calling it marketing, it sounds to me like it's done with the purpose to sell.
While I'm convinced that the ulterior motive is not to sell and make money, but to spread EV's and renewable energy to better the world. That you can only do that if the new products are better than the fossil ones. And that is what people realise and what makes Tesla so attractive. The philosophy behind the make and its products.
Marketing is brand promotion, advertising is selling.