Kilowatt hour

"KWH" redirects here. For other uses, see KWH (disambiguation).

Residential electricity meter located in Canada

The kilowatt hour (symbol kWh, kW·h, or kW h) is a derived unit of energy equal to 3.6 megajoules. If the energy is being transmitted or used at a constant rate (power) over a period of time, the total energy in kilowatt-hours is the product of the power in kilowatts and the time in hours. The kilowatt-hour is commonly used as a billing unit for energy delivered to consumers by electric utilities.

Definition

The kilowatt-hour (symbolized kW⋅h) is a unit of energy equivalent to one kilowatt (1 kW) of power sustained for one hour.

$\mathrm{kW \cdot h}=(3600\,\mathrm{s}) \lbrack \mathrm{kW}\rbrack=3600\, \lbrack \mathrm{s}\rbrack\Bigg \lbrack \frac{\mathrm{kJ}}{\mathrm{s}}\Bigg\rbrack=3600\,\mathrm{kJ}=3.6\,\mathrm{MJ}$

One watt is equal to 1 J/s. One kilowatt-hour is 3.6 megajoules, which is the amount of energy converted if work is done at an average rate of one thousand watts for one hour.

Note that the international standard SI unit of energy is the joule. The hour is a unit of time "outside the SI", so the kilowatt-hour is a non-SI unit of energy. It is not listed among the non-SI units accepted by the BIPM for use with the SI.

Examples

An electric heater rated at 1000 watts (1 kilowatt), operating for one hour uses one kilowatt-hour (equivalent to 3.6 megajoules) of energy. A television rated at 100 watts operating for 10 hours continuously uses one kilowatt-hour. A 40-watt light bulb operating continuously for 25 hours uses one kilowatt-hour.

Electrical energy is sold in kilowatt-hours; cost of running equipment is the product of power in kilowatts multiplied by running time in hours and price per kilowatt-hour. The unit price of electricity may depend upon the rate of consumption and the time of day. Industrial users may also have extra charges according to their peak usage and the power factor.

Symbol and abbreviation for kilowatt hour

The symbol "kWh" is commonly used in commercial, educational, scientific and media publications, and is the usual practice in electrical power engineering.

Other abbreviations and symbols may be encountered:

• "kW h" is less commonly used. It is consistent with SI standards (but note that the kilowatt-hour is a non-SI unit). The international standard for SI states that in forming a compound unit symbol, "Multiplication must be indicated by a space or a half-high (centered) dot (·), since otherwise some prefixes could be misinterpreted as a unit symbol" (i.e., kW h or kW·h). This is supported by a voluntary standard issued jointly by an international (IEEE) and national (ASTM) organization. However, at least one major usage guide and the IEEE/ASTM standard allow "kWh" (but do not mention other multiples of the watt hour). One guide published by NIST specifically recommends avoiding "kWh" "to avoid possible confusion".
• The US official fuel-economy window sticker for electric vehicles uses the abbreviation "kW-hrs", though the related website uses the more usual "kWh".
• Variations in capitalization are sometimes seen: KWh, KWH, kwh etc.
• "kW·h" is, like "kW h", preferred with SI standards, but it is very rarely used in practice.
• The notation "kW/h", as a symbol for kilowatt-hour, is not correct.

Conversions

Further information: Conversion of units of energy

To convert a quantity measured in a unit in the left column to the units in the top row, multiply by the factor in the cell where the row and column intersect.

	joule	watt hour	kilowatt hour	electronvolt	calorie
1 J = 1 kg·m2 s−2 =	1	2.77778 × 10−4	2.77778 × 10−7	6.241 × 1018	0.239
1 W·h =	3,600	1	0.001	2.247 × 1022	859.8
1 kW·h =	3.6 × 106	1,000	1	2.247 × 1025	8.598 × 105
1 eV =	1.602 × 10−19	4.45 × 10−23	4.45 × 10−26	1	3.827 × 10−20
1 cal =	4.1868	1.163 × 10−3	1.163 × 10−6	2.613 × 1019	1

Watt hour multiples and billing units

The kilowatt-hour is commonly used by electrical distribution providers for purposes of billing, since the monthly energy consumption of a typical residential customer ranges from a few hundred to a few thousand kilowatt-hours. Megawatt-hours (MWh), gigawatt-hours (GWh), and terawatt-hours (TWh) are often used for metering larger amounts of electrical energy to industrial customers and in power generation. The terawatt-hour and petawatt-hour (PWh) units are large enough to conveniently express the annual electricity generation for whole countries.

SI multiples for watt hour (W·h)

Submultiples				Multiples
Value	Symbol	Name		Value	Symbol	Name
10−3	mW·h	milliwatt hour		103	kW·h	kilowatt hour
10−6	µW·h	microwatt hour		106	MW·h	megawatt hour
				109	GW·h	gigawatt hour
				1012	TW·h	terawatt hour
				1015	PW·h	petawatt hour

Confusion of kilowatt-hours (energy) and kilowatts (power)

The terms power and energy are frequently confused. Physical power can be defined as work per unit time, measured in units of joules per second or watts. To produce power over any given period of time requires energy. Either higher levels of power (for a given period) or longer periods of run time (at a given power level) require more energy.

An electrical load (e.g. a lamp, toaster, electric motor, etc.) has a rated "size" in watts. This is its running power level, which equates to the instantaneous rate at which energy must be generated and consumed to run the device. How much energy is consumed at that rate depends on how long you run the device. However, its power level requirements are basically constant while running. The unit of energy for residential electrical billing, kilowatt-hours, integrates changing power levels in use at the residence over the past billing period (nominally 720 hours for a 30-day month), thus showing cumulative electrical energy use for the month.

For another example, when a light bulb with a power rating of 100 watts is turned on for one hour, the energy used is 100 watt hours (W·h), 0.1 kilowatt-hour, or 360 kilojoules. This same amount of energy would light a 40-watt bulb for 2.5 hours, or a 10-watt low-energy bulb for 10 hours. A power station electricity output at any particular moment would be measured in multiples of watts, but its annual energy sales would be in multiples of watt-hours. A kilowatt-hour is the amount of energy equivalent to a steady power of 1 kilowatt running for 1 hour, or 3.6 megajoules.

Energy cost can be illustrated in a similar example: a 100-watt (i.e. 0.1 kilowatt) light bulb turned on for 8 hours uses 800 W⋅h or 0.8 kW⋅h. If the energy cost is 25 cents per kilowatt-hour, it would cost 0.1 kW × 8 h × $0.25/kW⋅h = $0.20.

Whereas individual homes only pay for the kilowatt-hours consumed, commercial buildings and institutions also pay for peak power consumption (the greatest power recorded in a fairly short time, such as 15 minutes). This compensates the power company for maintaining the infrastructure needed to provide higher-than-normal power. These charges show up on electricity bills in the form of demand charges.

Major energy production or consumption is often expressed as terawatt-hours (TW⋅h) for a given period that is often a calendar year or financial year. One terawatt-hour is equal to a sustained power of approximately 114 megawatts for a period of one year.

Misuse of watts per hour

Power units measure the rate of energy per unit time. Many compound units for rates explicitly mention units of time, for example, miles per hour, kilometers per hour, dollars per hour. Kilowatt-hours are a product of power and time, not a rate of change of power with time. Watts per hour (W/h) is a unit of a change of power per hour. It might be used to characterize the ramp-up behavior of power plants. For example, a power plant that reaches a power output of 1 MW from 0 MW in 15 minutes has a ramp-up rate of 4 MW/h. Hydroelectric power plants have a very high ramp-up rate, which makes them particularly useful in peak load and emergency situations.

The proper use of terms such as watts per hour is uncommon, whereas misuse may be widespread.

Other energy-related units

Several other units are commonly used to indicate power or energy capacity or use in specific application areas. All the SI prefixes are commonly applied to the watt-hour: a kilowatt-hour is 1,000 W·h (symbols kW·h, kWh or kW h; a megawatt-hour is 1 million W·h, (symbols MW·h, MWh or MW h); a milliwatt-hour is 1/1000 W·h (symbols mW·h, mWh or mW h) and so on.

Average annual power production or consumption can be expressed in kilowatt-hours per year; for example, when comparing the energy efficiency of household appliances whose power consumption varies with time or the season of the year, or the energy produced by a distributed power source. One kilowatt-hour per year equals about 114.08 milliwatts applied constantly during one year.

The energy content of a battery is usually expressed indirectly by its capacity in ampere-hours; to convert watt-hours (W·h) to ampere-hour (A·h), the watt-hour value must be divided by the voltage of the power source. This value is approximate since the voltage is not constant during discharge of a battery.

The Board of Trade unit (BOTU) is an obsolete UK synonym for kilowatt-hour. The term derives from the name of the Board of Trade which regulated the electricity industry until 1942 when the Ministry of Power took over. The B.O.T.U. should not be confused with the British thermal unit or BTU, which is a much smaller quantity of thermal energy. To further the confusion, at least as late as 1937, Board of Trade unit was simply abbreviated BTU.

In India, the kilowatt-hour is often simply called a Unit of energy. A million units, designated MU, is a gigawatt-hour and a BU (billion units) is a terawatt-hour.

Burnup of nuclear fuel is normally quoted in megawatt-days per tonne (MW·d/MTU), where tonne refers to a metric ton of uranium metal or its equivalent, and megawatt refers to the entire thermal output, not the fraction which is converted to electricity.

See also

• Ampere-hour
• Watt
• Joule
• Orders of magnitude (energy)
• Electric energy consumption
• Watt second

External links

• Prices per kilowatt hour in the USA, Energy Information Administration