What's the difference between kW and kWh?

Understanding electric and plug-in vehicles requires a slightly different knowledge set than what mechanics and drivers have needed to know for decades. One of the most obvious new concepts is the large battery pack and electric motor added to the car. The capacity values of these devices can be written using kW (kilowatt) and kWh (kilowatt hours), but don't think that a 90 kW motor is anything like a 90 kWh battery pack. That little h makes a big difference. Exactly what is the difference? Well, that's what we investigate in this week's Greenlings. Follow us after the jump to learn more.

[Sources: Idaho National Lab]
Photo by Vince Alongi. Licensed under Creative Commons license 2.0.


Defining kW and kWh

The simplest definitions of kW and kWh are as follows:

• kW = one thousand watts (and a watt is one joule of energy per second)
• kWh = using a thousand watts for an hour (3,600,000 joules).

That may make kW and kWh look like they're easily connected, but, as Wolfram Alpha says, "kW (kilowatts) and kWh (kilowatt hours) are not compatible units, so cannot be compared." Kilowatts are a unit of power, while kWh is a unit of energy. Think of it this way: kW defines how much energy a device uses or generates in a given amount of time. Meanwhile kWh defines how much energy that device actually used or generates. So, a 100-watt light bulb that is on for 10 hours needs 1 kWh (1,000 watt-hours). This is the same as ten 100-watt bulbs burning for one hour.

Both kW and kWh are SI (metric) units and can be applied to any type of machine or energy storage system respectively. That means a gas engine or electric motor can both have a kW rating. Similarly since kWh is a measure of energy, you can define the capacity of a tank of liquid fuel or a battery in kWh.

In battery terms, a kWh rating defines how much energy the battery pack has available to provide to the electric motor and, thus, sort of, how far the car can go before needing to be recharged. In order to make batteries last longer (in terms of durability rather than range) they are typically not used to their full capacity. GM engineers have opted to only use half of the capacity of the Chevy Volt's 16 kWh battery pack in order to help it last for 10 years / 150,000 miles. That means it will only provide 8 kWh of usable energy to get a 40-mile nominal electric-only range.

Still, since we don't know the usable capacity of all the battery packs used in plug-in vehicles, we'll use total capacity to compare some of the more popular EVs:

Model	Battery Capacity	EV Range (official estimates)	Miles per kWh
Chevy Volt	16 kWh	40 miles	2.5
Ford Focus BEV	23 kWh	75 miles	3.2
Tesla Model S (base model)	42 kWh	160 miles	3.8
Nissan Leaf	24 kWh	100 miles	4.1
Tesla Roadster	53 kWh	244 miles	4.6
Citroën C-ZERO	16 kWh	80 miles	5
A123 PHEV Prius	5 kWh	30-40 miles (top speed, 35 mph)	6-8

Note that these battery packs are being used in very different types of vehicles, which accounts for some of the difference in miles per kWh.

Be mindful of these numbers since, as we mentioned, the Volt only uses 50 percent of its capacity while the Tesla Roadster can use 100 percent of its 53 kWh. The Tesla battery pack is only expected to retain at best about 70 percent of capacity after 4-5 years while the Volt is being developed to still have 100 percent of its rated capacity after 10 years.

In battery terms, a kWh rating tells us how much energy the pack has to give to the electric motor. So, the 24 kWh pack in the Nissan Leaf could provide 24 kW for one hour, not taking into account what it's actually being asked for by the electric motor or what connectors are in it to regulate the flow. The kWh number is also important in plug-in cars because it's used as a way to talk about how expensive a battery is: the cost per kWh currently sits at around $1,000, but the big automakers are working hard to drop this to $600 or $500 or lower. Just for comparison one gallon of gasoline has a capacity of about 36 kWh and currently costs about $2.65 in southeast Michigan.

Batteries are in a unique position compared to many other devices. While they are primarily energy storage devices measured in kWh, they also have power ratings in kW. The power rating of a battery describes how fast it can release or absorb energy. Think of it in terms of a fuel tank. A high capacity, low power battery would be like a big tank with a pin-hole for the fuel to pour out of. A high power battery would have a larger opening for the fuel to come out of (or go into). We'll have more on this in a future installment of Greenlings.

This brings us to electric motors, which are also given a kW rating. If you're coming to EVs from standard gasoline vehicles, understanding a motor's kW rating is simpler than understanding kWh because a kilowatt is equal to around 1.34 horsepower. Therefore, it is possible (and easy) to translate electric motor strength into hp, more commonly used to define liquid-powered engine power. A 100 kW motor puts out 134 hp.

Cost Per Mile

One reason it's important to understand all of this is that it will help to determine how much it will cost you to drive your plug-in vehicle. Right now, knowing your mpg and the cost of gasoline will do the trick. Determining the cost per mile of an EV requires knowing your utility's rates and how much juice your car will require to fill up. For example, a charger that uses two kW and takes eight hours draws 16 kWh of electricity. If your utility charges a dime per kWh, then to "fill up" costs you $1.60. Then, you take this number and divide it by how far you can go on to determine your cost per mile.

The Idaho National Lab has also provided a handy chart for this (download the PDF). It's slightly out of date because it can only help us calculate costs for an EV that get 2, 3, or 4 miles per kWh, but if gives you can idea. Here's how to read the chart:

The fuel cost of driving an electric vehicle depends on the cost of electricity per kilowatt-hour (kWh) and the energy efficiency of the vehicle. For example, to determine the energy cost per mile of an electric vehicle, select the location on the left axis (Electricity Cost per kWh) at 9 cents in the graph below. Draw a horizontal line to the right until you bisect the EV 3 mi/kWh line. Now draw a vertical line down until you bisect the bottom axis (Energy Cost per Mile). This tells you that the fuel for an electric vehicle with an energy efficiency of 3 miles per kWh costs about 3.0 cents per mile when electricity costs 9 cents per kWh.

kW and Hydrogen Fuel Cells

Just as with any other machine, kilowatts are also used to explain the output of a fuel cell stack. Unlike a battery, the stack does not store energy, it simply transforms it from chemical to electrical. Therefore the power rating describes the rate at which it can produce electrical energy. The power output range varies tremendously depending on what kind of fuel cell we're talking about. Proton Exchange Membrane (PEM) fuel cells are often used in hydrogen cars, and generally range from 50 to 250 kW. Since fuel cells send their electricity to the electric motor, the kW rating of the motor defines how much of this energy is actually required at any given moment. And, instead of being limited by the kWh in the battery pack, the range of a hydrogen car is limited by the amount of fuel in the storage tank which can also be defined in terms of kWh (1 kg of compressed hydrogen gas has a capacity of about 39.7 kWh), but that's a different subject.