# Kilowatt hour

(Redirected from KWh)
Residential electricity meter located in Canada

The kilowatt hour, or kilowatt-hour, (symbol kW·h, kW h or kWh) is a unit of energy equal to 1000 watt-hours or 3.6 megajoules.[1][2] For constant power, energy in watt-hours is the product of power in watts and time in hours. The kilowatt-hour is most commonly known as a billing unit for energy delivered to consumers by electric utilities.

## Definition

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

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

Inversely, 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.

## Examples

A heater rated at 1000 watts (1 kilowatt), operating for one hour uses one kilowatt-hour (equivalent to 3.6 megajoules) of energy. A 60-watt light bulb consumes 0.06 kilowatt-hours of energy per hour. Electrical energy is sold in kilowatt-hours; cost of running equipment is the product of power in kilowatts multiplied by running time and price per kilowatt-hour. The unit price of electricity may depend upon the rate of consumption and the time of day.

## Symbol and abbreviation for kilowatt hour

The international standard for SI[3] 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[4] issued jointly by an international (IEEE) and national (ASTM) organization. However, at least one major usage guide[5] 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".[6] Nonetheless, it is commonly used in commercial, educational, scientific and media publications.[7]

## Conversions

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, gigawatt-hours, and terawatt-hours are often used for metering larger amounts of electrical energy to industrial customers and in power generation. The terawatt-hour and petawatt-hour are large enough to conveniently express 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

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.[8][9]

## 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 may be 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.[10] 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.[citation needed]

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.[citation needed]

## 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 100W is turned on for one hour, the energy used is 100 watt hours (W·h), 0.1 kilowatt-hour, or 360 kJ. 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 MJ.

Major energy production or consumption is often expressed as terawatt-hours (TWh) 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[11] may be widespread.

## References

1. ^ Thompson, Ambler and Taylor, Barry N. (2008). Guide for the Use of the International System of Units (SI) (Special publication 811). Gaithersburg, MD: National Institute of Standards and Technology. 12.
2. ^ "Half-high dots or spaces are used to express a derived unit formed from two or more other units by multiplication." Barry N. Taylor. (2001 ed.) The International System of Units. (Special publication 330). Gaithersburg, MD: National Institute of Standards and Technology. 20.
3. ^ The International System of Units (SI). (2006, 8th ed.) Paris: International Bureau of Weights and Measures. 130.
4. ^ Standard for the Use of the International System of Units (SI): The Modern Metric System. (1997). (IEEE/ASTM SI 10-1997). New York and West Conshohocken, PA: Institute of Electrical and Electronics Engineers and ASTM. 15.
5. ^ Chicago Manual of Style. (14th ed., 1993) University of Chicago Press. 482.
6. ^ Guide for the Use of the International System of Units (SI) p.12
7. ^ See for example: Wind Energy Reference Manual Part 2: Energy and Power Definitions Danish Wind Energy Association. Retrieved 9 January 2008; "Kilowatt-Hour (kWh)" BusinessDictionary.com. Retrieved 9 January 2008; "US Nuclear Power Industry" www.world-nuclear.org. Retrieved 9 January 2008; "Energy. A Beginners Guide: Making Sense of Units" Renew On Line (UK). The Open University. Retrieved 9 January 2008.
8. ^ "Get enlightened about electricity". The Financial Express. December 20, 2004. Retrieved 29 November 2009.
9. ^ "BHEL manufactured units generate record power". The Hindu. Press Trust of India. July 24, 2008. Retrieved 29 November 2009.
10. ^
11. ^ "Inverter Selection". Northern Arizona Wind and Sun. Retrieved 27 March 2009.