Like most other electric and hybrid vehicles on the market, the Tesla [NSDQ:TSLA] Model S and Model X are both fitted with a system that allows them to recapture energy and put it back into the battery pack.
The most common manner in which this is done is through a regenerative braking system. Whenever you apply the brakes, you're creating energy due to the heat from the braking friction. Your batteries are thirsty for electrons, and this is a means in which you can give them a delicious taste. You'll find the largest regenerative braking gains happen when you're coming down a mountainous highway pass. But could a really large slope be enough to fully recharge your battery pack? Jason from Engineering Explained decided to do the math and find out.
In order to determine just how far a Tesla would have to travel down a slope, Jason decided to start with a Model S equipped with the 60-kilowatt-hour battery pack. You have to convert the potential energy that can be stored in that pack into joules, and then you're on your way along this mathematical adventure. And boy does this one involve a good deal of math.
Using the listed curb weight of a Model S and the potential energy available in the battery pack, Jason discovered that a Model S would need a slope 10.5 kilometers long in order to go from no charge to a full charge. The problem there is that this doesn't account for the energy lost through the transfer from the wheels all the way to the battery pack. You have a gear reduction that feeds to a motor and that in turn moves the energy to an inverter and it eventually gets to the battery. You're going to receive 60 percent of the initial energy being fed into the system.
Taking that into account, you'll find that you need a slope that's 17.4-km tall. That's about double the height of Mount Everest, so that is probably a bit outside the scope of what's possible here in reality. It's an interesting thought experiment, but you won't be recharging your Tesla completely with any hills here on Earth.