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):

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.

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.

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.

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:

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).

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.

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

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)

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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