# Kilowatt hour

(Redirected from Watt-hour)

The kilowatt hour (symbol: kW⋅h or kW h; commonly but incorrectly symbolized as kWh) is a unit of energy equal to 3.6 megajoules. If energy is transmitted or used at a constant rate (power) over a period of time, the total energy in kilowatt hours is equal to the power in kilowatts multiplied by the time in hours. The kilowatt hour is commonly used as a billing unit for energy delivered to consumers by electric utilities.

Kilowatt hour
Residential electricity meter located in Canada
General information
Unit systemNon-SI metric
Unit ofEnergy
SymbolkW⋅h, kW h
Conversions
1 kW⋅h, 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 with 1 kW⋅h being equivalent to 1 kilowatt (1 kW) of power sustained for 1 hour. One watt is equal to 1 J/s. One kilowatt hour is 3.6 megajoules,[1][2] which is the amount of energy converted if work is done at an average rate of one thousand watts for one hour.

The derived unit of energy within the International System of Units (SI) is the joule. The hour is a unit of time "outside the SI", making the kilowatt hour a non-SI unit of energy. The kilowatt hour is not listed among the non-SI units accepted by the BIPM for use with the SI, although the hour, from which the kilowatt hour is derived, is.[3]

## Examples

An electric heater consuming 1000 watts (1 kilowatt), and operating for one hour uses one kilowatt hour of energy. A television consuming 100 watts operating for 10 hours continuously uses one kilowatt hour. A 40-watt electric appliance operating continuously for 25 hours uses one kilowatt hour. In terms of human power, a healthy adult male manual laborer will perform work equal to about half a kilowatt hour over an eight-hour day.

Electrical energy is typically sold to consumers in kilowatt hours. The cost of running an electric device is calculated by multiplying the device's power consumption in kilowatts by the running time in hours and then by the price per kilowatt hour. The unit price of electricity may depend upon the rate of consumption and the time of day. Prices vary considerably by locality. In the United States prices in different states can vary by a factor of three.[4]

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.[5] 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 (TW⋅h) 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.

## Symbol and abbreviations for kilowatt hour

The symbol "kWh", though incorrect, is commonly used in commercial, educational, scientific and media publications,[6][7] and is the usual practice in electrical power engineering.[8]

Other abbreviations and symbols may be encountered:

• "kW h" is less commonly used. It is consistent with SI standards.[9] 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[10] issued jointly by an international (IEEE) and national (ASTM) organization. However, at least one major usage guide[11] and the IEEE/ASTM standard allow "kWh" (but do not mention other multiples of the watt hour). One guide published by NIST specifically recommends against "kWh" "to avoid possible confusion".[12]
• "kW⋅h" is, like "kW h", consistent with (and preferred by) SI standards, but it is less commonly used in practice.
• The US official fuel-economy window sticker for electric vehicles uses the abbreviation "kW-hrs".[13]
• Variations in capitalization are sometimes seen: KWh, KWH, kwh, etc.; these are inconsistent with the International System of Units.
• The notation "kW/h" is not a correct symbol for kilowatt hour, as it denotes kilowatt per hour instead.

## 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 = 3.6 × 103 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 = 4.2 1.163 × 10−3 1.163 × 10−6 2.613 × 1019 1

## Watt hour multiples and billing units

All the SI prefixes are commonly applied to the watt hour: a kilowatt hour is 1,000 W⋅h (symbols kW⋅h or kW h); a megawatt hour is 1 million W⋅h (symbols MW⋅h or MW h); a milliwatt hour is 1/1000 W⋅h (symbols mW⋅h or mW h) 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 (MW⋅h), gigawatt hours (GW⋅h), and terawatt hours (TW⋅h) are often used for metering larger amounts of electrical energy to industrial customers and in power generation. The terawatt hour and petawatt hour (PW⋅h) units are large enough to conveniently express the annual electricity generation for whole countries and the world energy consumption.

Submultiples Multiples Value Symbol Name Value 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

Petawatt hours can describe the output of nuclear power plants across decades. For example, the Gravelines Nuclear Power Station in France became in 2010 the first power plant to ever deliver a cumulative petawatt-hour of electricity.[14][15]

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

Power and energy are frequently confused: power is the rate of delivery of energy; energy is the work performed.

Power is measured in watts, or joules per second. Energy is measured in joules, or watt seconds.

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

In a given period of time, a higher level of power means that more energy is used. For a given power level, a longer run period causes more energy to be used. For a given amount of energy, a higher level of power means that that energy is used in less time.

### Annualized power

Electric energy production and consumption are sometimes reported on a yearly basis, in units such as megawatt-hours per year (MW⋅h/yr) gigawatt-hours/year (GW⋅h/yr) or terawatt-hours per year (TW⋅h/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 8766 h/yr.

Thus, 1 GW⋅h/yr ≈ 114.08 kW.

### Misuse of watts per hour

Power units measure the rate of energy per unit time. Many compound units for various kinds of rates explicitly mention units of time: for example, miles per hour, kilometres 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, 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. Hydroelectric power plants have a very high ramp-up rate, which makes them particularly useful in peak load and emergency situations. Other uses of terms such as watts per hour are likely to be errors.

## Other use

By definition of the units, a consumption of 1 kW⋅h/100 km is exactly equivalent to a resistance force of 36 N (newtons),[16] an idea taken up by the von Kármán–Gabrielli diagram.

## Other energy-related units

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

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 ampere-hour (A⋅h) to watt hours (W⋅h), 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 2500 mA⋅h battery, not five hours.

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.[17]

The British thermal unit or BTU (not to be confused with BOTU), is a unit of thermal energy with several definitions, all of which are about 1055 joules or 0.293 watt hour. The quad, short for quadrillion BTU, or 1015 BTU, is sometimes used in national-scale energy discussions in the United States. One quad is approximately 293 TW⋅h or 1.055 exajoule (EJ).

A TNT equivalent is a measure of energy released in the detonation of trinitrotoluene. A tonne of TNT equivalent is approximately 4.184 gigajoules or 1,163 kilowatt hours.

A tonne of oil equivalent is the amount of energy released by burning one tonne of crude oil. It is approximately 41.84 gigajoules or 11,630 kilowatt hours.

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.[18][19]

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]

## References

1. ^ Thompson, Ambler and Taylor, Barry N. (2008). Guide for the Use of the International System of Units (SI) Archived June 3, 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 June 3, 2016, at the Wayback Machine (Special publication 330). Gaithersburg, MD: National Institute of Standards and Technology. 20.
3. ^ a b The International System of Units (SI) Archived April 29, 2016, at the Wayback Machine. (2006, 8th ed.) Paris: International Bureau of Weights and Measures. 130.
4. ^ Average Price of Electricity to Ultimate Customers by End-Use Sector, U.S. Energy Information Administration, April 2018
5. ^ "Understanding Electric Demand" Archived June 6, 2016, at the Wayback Machine, National Grid
6. ^ IEC Electropedia, Entry 131-11-58 Archived March 14, 2016, at the Wayback Machine
7. ^ See for example: Wind Energy Reference Manual Part 2: Energy and Power Definitions Archived November 26, 2007, at the Wayback Machine Danish Wind Energy Association. Retrieved 9 January 2008; "Kilowatt-Hour (kWh)" Archived March 2, 2016, at the Wayback Machine BusinessDictionary.com. Retrieved 9 January 2008; "US Nuclear Power Industry" Archived November 26, 2007, at the Wayback Machine www.world-nuclear.org. Retrieved 9 January 2008; "Energy. A Beginners Guide: Making Sense of Units" Archived November 26, 2007, at the Wayback Machine Renew On Line (UK). The Open University. Retrieved 9 January 2008.
8. ^ 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)"
9. ^ "Guide for the Use of the International System of Units (SI)" (PDF). physics.nist.gov. National Institute of Standards and Technology. 2008. Archived (PDF) from the original on 3 June 2016. Retrieved 25 January 2017. 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. ^ 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.
11. ^ Chicago Manual of Style. (14th ed., 1993) University of Chicago Press. 482.
12. ^
13. ^ "Electric Vehicles: Learn More About the New Label". fueleconomy.gov. US Department of energy. Retrieved 10 August 2014.
14. ^ "French nuclear plant reaches landmark". World Nuclear News. 2 November 2010. Retrieved 22 June 2018. The six-unit Gravelines nuclear power plant near Dunkerque in northern France has become the first nuclear plant in the world to deliver 1000 billion kilowatt-hours (one petawatt-hour) of electricity.
15. ^ "French nuclear reactor reaches 1 petawatt-hour generation landmark". www.power-eng.com.
16. ^ Useful data - Cambridge repository website repository.cam.ac.uk; see page 328.
17. ^ "The Board of Trade 1621-1970". Archived from the original on 2010.
18. ^ "Get enlightened about electricity". The Financial Express. December 20, 2004. Archived from the original on September 8, 2012. Retrieved 29 November 2009.
19. ^ "BHEL manufactured units generate record power". The Hindu. Press Trust of India. July 24, 2008. Archived from the original on November 7, 2012. Retrieved 29 November 2009.