Every vehicle that Tesla has made, to date, has used the 18650 Lithium ion battery cells. This was true for the Roadster, Model S, and Model X. Each car uses about seven thousand 18650s. Model 3 will be different.
For the Model 3, Tesla will be making the batteries themselves in the Gigafactory and they have already said that the battery will be different. The only details about the difference that has been mentioned is that cells will be bigger in each dimension and it will have better energy density than the battery cells that are being made today.
The 18650 is so named because it is 18 mm in diameter by 65 mm height and there is no Z-dimension because it is a cylinder, not a rectangular prism.
So how much difference would 20% size increase make? The answer is more than you might think. Volumetrically it resulted in far more than a 20% increase.
Let's compare the old battery cell and the potencial new one.
Volume of the 18650
Letting our friends at Wolfram Alpha do the math, the volume of 18650 is about 16.5 millimeters.
Volume of the New Tesla Battery Cell
A 20% increase in diameter is 21.6mm and a 20% increase in height is 78mm. Going back to Wolfram:
The new volume is about 28.6 milliliters. That is ~170% of the old battery cell volume. That is 70% more room for anodes, cathodes, and all the things that make a battery work.
How Many Battery Cells Will Be In The Model 3?
As Tesla's smallest vehicle, the Model 3 will be the most aerodynamic vehicle they make when it comes out. To have 215+ miles of range the car will need at least 50kWh of battery capacity. For a given range, Model 3 will only need about 2/3rds the capacity of its Model S big brother. This along with battery cells that hold 70% more capacity means that Model 3 will need far fewer battery cells per vehicle.Starting with the 7,000 cells in Model S, then reducing it by 2/3rds for the smaller car and then reducing it by 40% for the higher capacity yields ~2750 battery cells for Model 3.
These are, of course, rough guesses based on a single comment from Elon Musk during a quarterly results conference call, but I think it is safe to say that Model 3 will have less than half the number of battery cells compared to the current 7,000 of Model S/X.
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