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# kilowatt-hour (kWh)

The kilowatt-hour (symbolized kWh) is a unit of energy equivalent to one kilowatt (1 kW) of power expended for one hour (1 h) of time. The kilowatt-hour is not a standard unit in any formal system, but it is commonly used in electrical applications.

An energy expenditure of 1 kWh represents 3,600,000 joules (3.600 x 106 J). To obtain joules when kilowatt-hours are known, multiply by 3.600 x 106. To obtain kilowatt-hours when joules are known, multiply by 2.778 x 10-7.

In general, energy (E) is equivalent to power (P) multiplied by time (t). To determine E in kilowatt-hours, P must be expressed in kilowatts and t must be expressed in hours. Suppose a 1.5-kW electric heater runs for 3 h. Then P = 1.5 and t = 3, so the energy E in kilowatt-hours is:

E = Pt = 1.5 x 3 = 4.5 kWh

If P and t are not specified in kilowatts and hours respectively, then they must be converted to those units before determining E in kilowatt-hours.

The consumption of electrical energy by homes and small businesses is usually measured in kilowatt-hours. Larger businesses and institutions sometimes use the megawatt-hour (MWh), where 1 MWh = 1,000 kWh. The energy outputs of large power plants over long periods of time, or the energy consumption of states or nations, can be expressed in gigawatt hours (GWh), where 1 GWh = 1,000 MWh = 106 kWh.

The kilowatt-hour is rarely used to express energy in any form other than electrical. A quantity of gasoline, oil, or coal contains potential energy that is liberated when the fuel is burned. The heat energy resulting from combustion of such fuels is usually expressed in joules according to the International System of Units (SI) or in British thermal units (Btus) according to the foot-pound-second (fps) or English system. If this energy is used to operate an electric generator, the output of the generator over a certain period of time can be expressed in kilowatt-hours.

Compare watt-hour. Also see energy, joule, International System of Units (SI), and Table of Physical Units.

This was last updated in September 2006

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