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garsh's Official Model 3 Battery Pack Capacity Calculation Thread

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#1 · (Edited)
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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#3 ·
Funny... I saw the title of the thread and guessed 85 kWh...

And then read your calculations...
 
#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.
 
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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.
 
#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!
 
#8 ·
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.
 
#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. :)
 
#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.
 
#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 :)
 
#24 ·
Software Locked 55 unlocked to 70
Tesla has already said that it will have less than 60 actual kWh. No software unlocking to 70.

Also much more likely to have free unlimited supercharging.
Unlimited free supercharging is gone, don't expect it will ever return. It disallows all sorts of things like vehicle-to-grid and commercial fleets (not to mention being a rent-seeking economic problem).

The conclusion is still the same, but with 85kWh looking even more likely than 90kWh.
I think we can expect some increase in capacity going from old 18650 to new 2170. 90 might be reasonable (95 seems unlikely only in that Elon was so emphatic that 100 was not (yet) possible).

Thank you kindly.
 
#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.
 
#21 ·
No, selling is selling... or?
The difference is in the ulterior motive. Selling as a goal, or selling as a means.
 
#25 ·
Someone posted that they thought Tesla would start at a battery pack of 55 and then do 15 step increments, (55,70,85) I'm having difficulty remembering why everybody thinks the Model 3 will have a base pack of 55? Why not starting at what Tesla already has, a 60...Then a 75 and then a 90?

Whatever Tesla decides to do, I just wish they would hurry up and kick out some possible costs associated with the options. Not everybody has a ton of money sitting around...lots of us have to save up and time is running out.
 
#32 · (Edited)
So Randy Carlson has posted another article on Seeking Alpha:
Tesla: Model 3 Update - What To Look For

In this article, he wonders if Tesla can get away with arranging the cells horizontally instead of vertically. In particular, he wonders if chemistry improvements might allow Tesla to get away with having only a single layer of horizontal cells in the packs. Given my calculations of module size above, we could then fit at most (940mm/70mm=) 13 by (330mm/21mm=) 15, or 195 cells/module (Randy estimates 220 cells/module).

This gives (195*8=) 1560 cells for the whole vehicle. In order to get even a 70kWh pack out of this arrangement (since we've heard rumors that this pack size does exist), then each cell must be capable of holding (70000/1560=) 44.9 watt-hours. This would be a HUGE jump from the 12.1 watt-hours contained in current 18650 cells.

Even a double-layer of cells would require 22.5 watt-hours to be contained within each cell. That would allow the battery pack to be 28.5mm thinner (assuming a 0.5mm overlap in rows), which is something, but not a huge win. And this is at least within striking distance of the 18 watt-hours per cell that I calculated above, which assumes that the cell chemistry hasn't changed from the 18650 so that only the volume difference is important. But that would also dash my dreams of owning a P85D Model 3. We shall see.
 
#33 ·
So Randy Carlson has posted another article on Seeking Alpha:
Tesla: Model 3 Update - What To Look For
(...) We shall see.
@garsh , thank you. Had posted the same article in the Mixed Bag of Analysts Opinion yet without the deeply grounded analysis you provide here... unfortunately lacking that knowledge...
Also, I like how you end your post... Exactly what I wrote on the other debate re wheels sizes... Time will tell :)
 
#37 ·
Holy crap, @TrevP! I didn't realize that you could blow up that still image large enough to make out more than modules! It does kind of look like it's showing individual cells.

But I don't think it really is. Recall that I calculated that Tesla can fit 16 rows of 40 cells into each module. From this picture, it looks like each module only contains 8 rows of very, very large cells. So, next best guess is that each of the round bumps at the ends of of the modules is actually a bend in the cooling loop, which spans two rows of cells:


So I agree, it certainly does look like the cells are vertical, and I think this provides further proof that the modules likely contain 16 rows of cells. That makes me feel a bit more confident in my calculations. Furthermore, it appears that 4 of the 16 rows have fewer than the maximum number of cells that would fit within the module's rectangular area. This also occurs in the Model S modules, and provides more reason to believe that a 90kWh battery is not very likely.

Also from the blown-up picture, there appear to be 3 rows of 5 "holes" running down each battery module. There doesn't appear to be anything equivalent in the Model S battery pack, so I'm not sure what to make of these.
 
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