Kilowatt-hour
{{Use dmy dates|date=August 2023}}
{{Short description|Unit of energy, often used for electrical billing}}
{{Redirect|KWH}}
{{Infobox unit
| bgcolor =
| name = kilowatt-hour
| image = Hydro quebec meter.JPG
| caption = Residential electricity meter located in Canada
| standard = Non-SI metric
| quantity = Energy
| symbol = kW⋅h
| symbol2 = kW h
| extralabel =
| extradata =
| units1 = SI units
| inunits1 = {{convert|1|kW.h|sigfig=2|disp=out}}
| units2 = CGS units
| inunits2 = {{convert|1|kW.h|erg|lk=out|disp=out}}
| units3 = Imperial units
| inunits3 = ≈{{thinsp}}{{convert|1|kW.h|ftpdl|sigfig=7|lk=out|disp=out}}
| units4 = English Engineering units (US only)
| inunits4 = ≈{{thinsp}}{{convert|1|kW.h|ft.lbf|sigfig=7|lk=out|disp=out}}
}}
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).
Definition
The kilowatt-hour is a composite unit of energy equal to one kilowatt (kW) multiplied by (i.e., sustained for) 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.Thompson, Ambler and Taylor, Barry N. (2008). [http://physics.nist.gov/cuu/pdf/sp811.pdf Guide for the Use of the International System of Units (SI)] {{webarchive |url=https://web.archive.org/web/20160603203340/http://physics.nist.gov/cuu/pdf/sp811.pdf |date=3 June 2016 }} (Special publication 811). Gaithersburg, MD: National Institute of Standards and Technology. 12."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.) [http://physics.nist.gov/Pubs/SP330/sp330.pdf The International System of Units.] {{webarchive|url=https://web.archive.org/web/20160603215953/http://physics.nist.gov/Pubs/SP330/sp330.pdf |date=3 June 2016 }} (Special publication 330). Gaithersburg, MD: National Institute of Standards and Technology. 20.
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.[http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=131-11-58 IEC Electropedia, Entry 131-11-58] {{webarchive |url=https://web.archive.org/web/20160314215740/http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=131-11-58 |date=14 March 2016 }}See for example: [http://www.windpower.org/en/stat/unitsene.htm Wind Energy Reference Manual Part 2: Energy and Power Definitions] {{webarchive |url= https://web.archive.org/web/20071126132157/http://www.windpower.org/en/stat/unitsene.htm |date=26 November 2007 }} Danish Wind Energy Association. Retrieved 9 January 2008; [http://www.businessdictionary.com/definition/Kilowatt-Hour-kWh.html "Kilowatt-Hour (kWh)"] {{webarchive|url=https://web.archive.org/web/20160302222956/http://www.businessdictionary.com/definition/Kilowatt-Hour-kWh.html |date=2 March 2016 }} BusinessDictionary.com. Retrieved 9 January 2008; [http://www.world-nuclear.org/info/inf41.html "US Nuclear Power Industry"] {{webarchive|url=https://web.archive.org/web/20071126132157/http://www.world-nuclear.org/info/inf41.html |date=26 November 2007 }} www.world-nuclear.org. Retrieved 9 January 2008; [http://eeru.open.ac.uk/natta/energy.html#4 "Energy. A Beginners Guide: Making Sense of Units"] {{webarchive | url= https://web.archive.org/web/20071126132157/http://eeru.open.ac.uk/natta/energy.html |date=26 November 2007 }} Renew On Line (UK). The Open University. Retrieved 9 January 2008. It is also the usual unit representation in electrical power engineering.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)" This common representation, however, does not comply with the style guide of the International System of Units (SI).{{cite web |title=The International System of Units (SI) |url=https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf#page=33 |publisher=International Bureau of Weights and Measures (BIPM) |access-date=7 April 2020 |page=147 |date=2019}}
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 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 standardStandard 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. issued jointly by an international (IEEE) and national (ASTM) organization, and by a major style guide.{{cite book |title=The Chicago Manual of Style |date=2017 |publisher=University of Chicago Press |location=Chicago |edition=17 |url=https://www.chicagomanualofstyle.org/book/ed17/part2/ch10/psec058.html |access-date=1 April 2020 |chapter=10.57: Units derived from SI base units}} 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".{{cite web | url= https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication811e2008.pdf | title= Guide for the Use of the International System of Units (SI) | publisher = National Institute of Standards and Technology | year= 2008 | quote = 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; | access-date= 6 April 2020}}
- In 2014, the United States official fuel-economy window sticker for electric vehicles used the abbreviation kW-hrs.{{cite web|title=Electric Vehicles: Learn More About the New Label |url= http://www.fueleconomy.gov/feg/label/learn-more-electric-label.shtml |website=fueleconomy.gov|publisher=US Department of energy|access-date=10 August 2014}}
- 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.
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.[https://www.eia.gov/electricity/monthly/epm_table_grapher.php?t=epmt_5_6_a Average Price of Electricity to Ultimate Customers by End-Use Sector], U.S. Energy Information Administration, April 2018
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.[https://www.nationalgridus.com/niagaramohawk/non_html/eff_elec-demand.pdf "Understanding Electric Demand"] {{webarchive |url=https://web.archive.org/web/20160606043318/https://www.nationalgridus.com/niagaramohawk/non_html/eff_elec-demand.pdf |date=6 June 2016 }}, National Grid 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, often a calendar year or financial year. A 365-day year equals 8,760 hours, so one gigawatt sustained over a year corresponds to 8.76 terawatt-hours of energy. Conversely, one terawatt-hour is equal to the 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.{{cite web|title=How much electricity does an American home use?|url=https://www.eia.gov/tools/faqs/faq.php?id=97&t=3#:~:text=How%20much%20electricity%20does%20an,about%20893%20kWh%20per%20month.|publisher=U.S. Energy Information Administration|access-date=11 June 2022|date=7 October 2021}}
Raising the temperature of 1 litre of water from room temperature to the boiling point with an electric kettle takes about 0.1 kWh.
A 12-watt LED lamp lit constantly uses about 0.3 kWh per 24 hours and about 9 kWh per month.
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.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
Conversions
{{Further|Conversion of units#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.
| class="wikitable"
! ! Joule ! Watt-hour ! Kilowatt-hour ! Calorie |
| {{rh|align=right}} | 1 J = 1 kg⋅m2⋅s−2 =
| 1 | 2.77778 × 10−4 | 2.77778 × 10−7 | 6.241 × 1018 | 0.239 |
|---|
| {{rh|align=right}} | 1 Wh =
| 3.6 × 103 | 1 | 0.001 | 2.247 × 1022 | 859.8 |
| {{rh|align=right}} | 1 kWh =
| 3.6 × 106 | 1,000 | 1 | 2.247 × 1025 | 8.598 × 105 |
| {{rh|align=right}} | 1 eV =
| 1.602 × 10−19 | 4.45 × 10−23 | 4.45 × 10−26 | 1 | 3.827 × 10−20 |
| {{rh|align=right}} | 1 cal =
| 4.184 | 1.162 × 10−3 | 1.162 × 10−6 | 2.612 × 1019 | 1 |
==Watt-hour multiples {{anchor|Multiples}}==
{{Further|Metric prefix}}
| class="wikitable floatright" style="text-align: center;"
|+ SI multiples of watt-hour (W⋅h) | ||
| scope="col" | Value
! scope="col" | Symbol ! scope="col" | Name | ||
|---|---|---|
| {{10^ | ||
| 6}} | μW⋅h | microwatt-hour |
| {{10^ | ||
| 3}} | mW⋅h | milliwatt-hour |
| {{10^|0}} | W⋅h | watt-hour |
| {{10^|3}} | kW⋅h | kilowatt-hour |
| {{10^|6}} | MW⋅h | megawatt-hour |
| {{10^|9}} | GW⋅h | gigawatt-hour |
| {{10^|12}} | TW⋅h | terawatt-hour |
| {{10^|15}} | PW⋅h | petawatt-hour |
All the SI prefixes are commonly applied to the watt-hour: a kilowatt-hour (kWh) is 1,000 Wh; a megawatt-hour (MWh) is 1 million Wh; a milliwatt-hour (mWh) is {{nowrap|1/1,000 Wh}} 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 {{val|8760|u=h|up=yr}}.
Thus, {{nowrap|1 GWh/yr}} = {{nowrap|1 GWh/8760 h}} ≈ {{val|114.12|u=kW}}.
=Misuse of watts per hour{{anchor|Watt 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 {{val|1|u=MW}} from {{val|0|u=MW}} in 15 minutes has a ramp-up rate of {{val|4|u=MW|up=h}}.
Other uses of terms such as watts per hour are likely to be errors.{{Cite book |last=Woofenden |first=Ian |url=https://books.google.com/books?id=iYktDwAAQBAJ&dq=%22watts+per+hour%22+%22nonsensical+phrase%22&pg=PA48 |title=Wind Power For Dummies |date=5 October 2009 |publisher=John Wiley & Sons |isbn=978-0-470-49637-4 |pages=48 |language=en |quote=Much too often, I hear people say something like ... 'watts per hour'...}}{{Cite book |url=https://books.google.com/books?id=NvRIAQAAIAAJ&q=%22watts+per+hour%22+(mistake+OR+error+OR+blunder) |title=Home Power |date=2007 |publisher=Electron Connection |language=en |quote="Watts per hour. This nonsensical phrase tops my electrical terminology pet peeve list."}}
See also
References
{{Reflist}}
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