Energy Density and Power Density in Batteries and Electric Vehicles

Power density is the core measure controlling the speed and range you can get with a given vehicle. Power density controls the quantity of electricity you can store within a given space, and is measured two ways: (For more about these units see http://visforvoltage.org/book/ev-batteries/13232)

volume = the size of the area for batteries
weight = the carrying capacity of the vehicle

These are usually measured as

volume energy density = kilowatt-hours / liter = kwh / l
weight energy density = kilowatt-hours / kilogram = kwh / kg
volume power density = kilowatt-hours / liter = kw / l
weight power density = kilowatt-hours / kilogram = kw / kg

Remember that

1 kilowatt-hour = 1 kilowatt used over 1 hour = kwh
1 kilowatt = 1,000 watts

And remember that, as an electric vehicle moves down the road, it consumes electricity. Say the vehicle has a 120 volt electrical system, and uses 30 amps to cruise, therefore the vehicle cruises at 3.6 kilowatts. If the vehicle is run for an hour, it consumes 3.6 kilowatt hours of electricity.

The main measurement controlling the range capability of a given battery pack in a given vehicle is, how many kilowatt-hours can you carry in the vehicle. Hence, the power density of the chosen battery pack directly determines the kilowatt-hours in the vehicle. Obviously the batteries have to fit within the physical dimensions of the vehicle, hence the "volume power density" measure given above. Another consideration is how much weight the vehicle can carry on its frame, tires, and suspension system, maybe you have lots of room for batteries but you'd overload the car if you filled it to capacity. Hence the "weight power density" measure given above.