A kilowatt-hour is a basic unit of energy that applies especially to electricity. A watt is a volt times an amp, and there are 1000 watts in a kilowatt. A watt is a unit of power, which is the rate of energy used. When you multiply power by time you get a quantity of energy. Energy is measured in many different unit systems in different applications. Your electric utility company bills you for the kilowatt-hours you use. The energy content of batteries is given in amp-hours. The energy density of liquid fules is often given in British Thermal Units per gallon, or BTUs per gallon. A home gas bill usually reports usage in cubic feet (of gas), or therms. A therm is 100 cubic feet, and equivalent to 1000 BTU. Using the right conversion ratios, you can calculate the equivalent number of kilowatt-hours (KWH) in any amount of of energy measured in these other units. You can use the link in the Resources to calculate conversion ratios.
Calculate kilowatt-hours in natural gas. To compare the amount you pay for natural gas versus electricity, you need to convert between kilowatt-hours and therms. The conversion ratio is 0.0342 therms / 1 kilowatt-hour = 1. Electricity and natural gas prices vary greatly from region to region, but typical prices are 0.10 dollars per kilowatt-hour and 1 dollar per therm. Calculate (1 dollars / therm)*(0.0342 therm /1 kilowatt-hour) and cancel therms to get 0.0342 dollars/kilowatt-hour. In many places, natural gas is indeed cheaper per unit of energy. This is why, when it is available, many homes use gas for heating and cooking rather than electricity.
Calculate kilowatt-hours in a battery. A battery is usually labeled with how many milliamp-hours it has. Amp-hours are not technically a unit of energy. But when you multiply amp-hours by volts, you get watt-hours. There are 1000 watt-hours in a kilowatt-hour. A typical alkaline 1.5 volt AA battery supplies around 2000 milliamp-hours. If you multiply 2000 milliamp-hours x 1.5 volts you find that an alkaline AA battery contains 3 watt-hours, or 0.003 kilowatt-hours of energy. You can purchase AA batteries for as little as fifty cents apiece, or 0.5 dollars. To find the cost per kilowatt-hour, calculate (0.5 dollars / 3 watt-hours) x (1000 watt-hours / kilowatt-hour) = 167 dollars/kilowatt-hour. You can see why rechargeable batteries are good for the environment and your bank account.
Calculate kilowatt-hours in gasoline. Gasoline contains about 100,000 BTU of energy per gallon. The conversion ratio between BTU and kilowatt-hours is 3412 BTU / 1 kilowatt-hour = 1. So, gasoline contains (100,000 BTU / gallon) x (1 kilowatt-hour / 3412 BTU) = 29.3 kilowatt-hour/gallon. In 2013, the average price of gasoline was around 3.5 dollars/gallon. Calculate ( 3.5 dollars / 1 gallon ) x (1 gallon / 29.3 kilowatt-hours) = 0.12 dollars / kilowatt-hour. Roughly the same as for household electricity.