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Kilowatt-hour

## Summary

A kilowatt-hour (unit symbol: kW⋅h or kW h; commonly written as kWh) is a non-SI unit of energy equal to 3.6 megajoules (MJ) in SI units which is the energy delivered by one kilowatt of power for one hour. Kilowatt-hours are a common billing unit for electrical energy supplied by electric utilities. Metric prefixes are used for multiples and submultiples of the basic unit, the watt-hour (3.6 kJ).

kilowatt-hour
Residential electricity meter located in Canada
General information
Unit systemNon-SI metric
Unit ofEnergy
SymbolkW⋅h, kW h
Conversions
1 kW⋅h in ...... is equal to ...
SI units   3.6 MJ
CGS units   3.6×1013 erg
English Engineering units   2,655,224 ft⋅lbf
British Gravitational units   85,429,300 ft⋅pdl

## Definition

The kilowatt-hour is a composite unit of energy equal to one kilowatt (kW) sustained for (multiplied by) one hour. The International System of Units (SI) unit of energy meanwhile is the joule (symbol J). Because a watt is by definition one joule per second, and because there are 3,600 seconds in an hour, one kWh equals 3,600 kilojoules or 3.6 MJ.[1][2]

## Unit representations

A widely used representation of the kilowatt-hour is "kWh", derived from its component units, kilowatt and hour. It is commonly used in billing for delivered energy to consumers by electric utility companies, and in commercial, educational, and scientific publications, and in the media.[3][4] It is also the usual unit representation in electrical power engineering.[5] This common representation, however, does not comply with the style guide of the International System of Units (SI).[6]

Other representations of the unit may be encountered:

• "kW⋅h" and "kW h" are less commonly used, but they are consistent with the SI. The SI brochure[6] states that in forming a compound unit symbol, "Multiplication must be indicated by a space or a half-high (centred) dot (⋅), since otherwise some prefixes could be misinterpreted as a unit symbol." This is supported by a standard[7] issued jointly by an international (IEEE) and national (ASTM) organization, and by a major style guide.[8] However, the IEEE/ASTM standard allows "kWh" (but does not mention other multiples of the watt-hour). One guide published by NIST specifically recommends against "kWh" "to avoid possible confusion".[9]
• The United States official fuel-economy window sticker for electric vehicles uses the abbreviation "kW-hrs".[10]
• Variations in capitalization are sometimes encountered: KWh, KWH, kwh, etc., which are inconsistent with the International System of Units.
• The notation "kW/h" for the kilowatt-hour is incorrect, as it denotes kilowatt per hour.

The hour is a unit of time listed among the non-SI units accepted by the International Bureau of Weights and Measures for use with the SI.[6] Its combination with the kilowatt, a standard SI unit, is therefore permitted within the standard.[dubious ]

An electric heater consuming 1,000 watts (1 kilowatt) operating for one hour uses one kilowatt-hour of energy. A television consuming 100 watts operating continuously for 10 hours uses one kilowatt-hour. A 40-watt electric appliance operating continuously for 25 hours uses one kilowatt-hour.

## Electricity sales

Electrical energy is typically sold to consumers in kilowatt-hours. The cost of running an electrical device is calculated by multiplying the device's power consumption in kilowatts by the operating time in hours, and by the price per kilowatt-hour. The unit price of electricity charged by utility companies may depend on the customer's consumption profile over time. Prices vary considerably by locality. In the United States prices in different states can vary by a factor of three.[11]

While smaller customer loads are usually billed only for energy, transmission services, and the rated capacity, larger consumers 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 peak power. These charges are billed as demand changes.[12] Industrial users may also have extra charges according to the power factor of their load.

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. A 365-day year equals 8,760 hours, so over a period of one year, power of one gigawatt equates to 8.76 terawatt-hours of energy. Conversely, one terawatt-hour is equal to a sustained power of about 114 megawatts for a period of one year.

## Examples

In 2020, the average household in the United States consumed 893 kWh per month.[13]

In terms of human power, a healthy adult male manual laborer performs work equal to about half a kilowatt-hour over an eight-hour day.[14]

## 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 Wh = 3.6 × 103 1 0.001 2.247 × 1022 859.8
1 kWh = 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 = 4.184 1.162 × 10−3 1.162 × 10−6 2.612 × 1019 1

## Watt-hour multiples

SI multiples of watt-hour (W⋅h)
Value Symbol Name
10−6 μW⋅h microwatt-hour
10−3 mW⋅h milliwatt-hour
100 W⋅h watt-hour
103 kW⋅h kilowatt-hour
106 MW⋅h megawatt-hour
109 GW⋅h gigawatt-hour
1012 TW⋅h terawatt-hour
1015 PW⋅h petawatt-hour

All the SI prefixes are commonly applied to the watt-hour: a kilowatt-hour is 1,000 Wh (kWh); a megawatt-hour is 1 million Wh (MWh); a milliwatt-hour is 1/1,000 Wh (mWh) and so on. The kilowatt-hour is commonly used by electrical energy 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 and the world energy consumption.

## Distinction between kWh (energy) and kW (power)

A kilowatt is a unit of power (rate of flow of energy per unit of time). A kilowatt hour is a unit of energy. Kilowatt per hour would be a rate of change of power flow with time.

Work is the amount of energy transferred to a system; power is the rate of delivery of energy. Energy is measured in joules, or watt-seconds. Power is measured in watts, or joules per second.

For example, a battery stores energy. When the battery delivers its energy, it does so at a certain power, that is, the rate of delivery of the energy. The higher the power, the quicker the battery's stored energy is delivered. A higher power output will cause the battery's stored energy to be depleted in a shorter time period.

### Annualized power

Electric energy production and consumption are sometimes reported on a yearly basis, in units such as megawatt-hours per year (MWh/yr) gigawatt-hours/year (GWh/yr) or terawatt-hours per year (TWh/yr). These units have dimensions of energy divided by time and thus are units of power. They can be converted to SI power units by dividing by the number of hours in a year, about 8760 h/yr.

Thus, 1 GWh/yr = 1 GWh/8760 h ≈ 114.12 kW.

### Misuse of watts per hour

Many compound units for various kinds of rates explicitly mention units of time to indicate a change over time. For example: miles per hour, kilometres per hour, dollars per hour. Power units, such as kW, already measure the rate of energy per unit time (kW=kJ/s). 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, i.e. an acceleration in the delivery of energy. It is used to measure the daily variation of demand (e.g. the slope of the duck curve), or 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.

Other uses of terms such as watts per hour are likely to be errors.[15][16]

## Other related energy units

Several other units related to kilowatt-hour are commonly used to indicate power or energy capacity or use in specific application areas.

Average annual energy production or consumption can be expressed in kilowatt-hours per year. This is used with loads or output that vary during the year but whose annual totals are similar from one year to the next. For example, it is useful to compare the energy efficiency of household appliances whose power consumption varies with time or the season of the year. Another use is to measure 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 ampere-hour (Ah) to watt-hours (Wh), the ampere-hour value must be multiplied by the voltage of the power source. This value is approximate, since the battery voltage is not constant during its discharge, and because higher discharge rates reduce the total amount of energy that the battery can provide. In the case of devices that output a different voltage than the battery, it is the battery voltage (typically 3.7 V for Li-ion) that must be used to calculate rather than the device output (for example, usually 5.0 V for USB portable chargers). This results in a 500 mA USB device running for about 3.7 hours on a 2,500 mAh battery, not five hours.

The Board of Trade unit (B.T.U.)[17] 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.[18] This should not be confused with a British Thermal Unit (BTU) which is 1055 J.

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.[19][20]

## References

1. ^ Thompson, Ambler and Taylor, Barry N. (2008). Guide for the Use of the International System of Units (SI) Archived 3 June 2016 at the Wayback Machine (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. Archived 3 June 2016 at the Wayback Machine (Special publication 330). Gaithersburg, MD: National Institute of Standards and Technology. 20.
3. ^ IEC Electropedia, Entry 131-11-58 Archived 14 March 2016 at the Wayback Machine
4. ^ See for example: Wind Energy Reference Manual Part 2: Energy and Power Definitions Archived 26 November 2007 at the Wayback Machine Danish Wind Energy Association. Retrieved 9 January 2008; "Kilowatt-Hour (kWh)" Archived 2 March 2016 at the Wayback Machine BusinessDictionary.com. Retrieved 9 January 2008; "US Nuclear Power Industry" Archived 26 November 2007 at the Wayback Machine www.world-nuclear.org. Retrieved 9 January 2008; "Energy. A Beginners Guide: Making Sense of Units" Archived 26 November 2007 at the Wayback Machine Renew On Line (UK). The Open University. Retrieved 9 January 2008.
5. ^ ASTM SI10-10, IEEE/ASTM SI 10 American National Standard for Metric Practice, ASTM International, West Conshohocken, PA, 2010, [www.astm.org] "The symbols for certain compound units of electrical power engineering are usually written without separation, thus: watthour (Wh), kilowatthour (kWh), voltampere (VA), and kilovoltampere (kVA)"
6. ^ a b c "The International System of Units (SI)" (PDF). International Bureau of Weights and Measures (BIPM). 2019. p. 147. Retrieved 7 April 2020.
7. ^ 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.
8. ^ "10.57: Units derived from SI base units". The Chicago Manual of Style (17 ed.). Chicago: University of Chicago Press. 2017. Retrieved 1 April 2020.
9. ^ "Guide for the Use of the International System of Units (SI)" (PDF). National Institute of Standards and Technology. 2008. Retrieved 6 April 2020. Reference [4: ISO 31-0] suggests that if a space is used to indicate units formed by multiplication, the space may be omitted if it does not cause confusion. This possibility is reflected in the common practice of using the symbol kWh rather than kW⋅h or kW h for the kilowatt-hour. Nevertheless, this Guide takes the position that a half-high dot or a space should always be used to avoid possible confusion;
10. ^ "Electric Vehicles: Learn More About the New Label". fueleconomy.gov. US Department of energy. Retrieved 10 August 2014.
11. ^ Average Price of Electricity to Ultimate Customers by End-Use Sector, U.S. Energy Information Administration, April 2018
12. ^ "Understanding Electric Demand" Archived 6 June 2016 at the Wayback Machine, National Grid
13. ^ "How much electricity does an American home use?". U.S. Energy Information Administration. 7 October 2021. Retrieved 11 June 2022.
14. ^ Eugene A. Avallone et al., (ed), Marks' Standard Handbook for Mechanical Engineers 11th Edition , Mc-Graw Hill, New York 2007 ISBN 0-07-142867-4 page 9-4
15. ^ Woofenden, Ian (5 October 2009). Wind Power For Dummies. John Wiley & Sons. p. 48. ISBN 978-0-470-49637-4. Much too often, I hear people say something like ... 'watts per hour'...
16. ^ Home Power. Electron Connection. 2007. Watts per hour. This nonsensical phrase tops my electrical terminology pet peeve list.
17. ^ E. M. Kirkpatrick, ed. (1983). Chambers 20th Century Dictionary (New ed.). Edinburgh: Chambers. p. 137. ISBN 0550102345.
18. ^ "The Board of Trade 1621-1970". Archived from the original on 4 March 2010.
19. ^ "Get enlightened about electricity". The Financial Express. 20 December 2004. Archived from the original on 8 September 2012. Retrieved 29 November 2009.
20. ^ "BHEL manufactured units generate record power". The Hindu. Press Trust of India. 24 July 2008. Archived from the original on 7 November 2012. Retrieved 29 November 2009.