# Kilowatt hour

(Redirected from Watt hours)
Kilowatt hour
Residential electricity meter located in Canada
Unit information
Unit system Non-SI metric
Unit of Energy
Symbol kW⋅h
Unit conversions
1 kW⋅h in ... ... is equal to ...
SI units    3.6 MJ
English Engineering units    2,655,224 ft·lbf

The kilowatt-hour (symbol kWh,[1] kW⋅h or kW h[2]) is a derived unit of energy equal to 3.6 megajoules.[3][4] 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 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.

## Definition

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

${\displaystyle 1\,\mathrm {kW\cdot h} =(3600\,\mathrm {s} )\lbrack \mathrm {kW} \rbrack =3600\,\lbrack \mathrm {s} \rbrack {\Bigg \lbrack }{\frac {\mathrm {kJ} }{\mathrm {s} }}{\Bigg \rbrack }=3600\,\mathrm {kJ} =3.6\,\mathrm {MJ} }$

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.

The base 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.[5]

## 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 often sold in kilowatt-hours. The cost of running an electric device is calculated by multiplying the device's power in kilowatts, by the running time in hours, by the 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 abbreviations for kilowatt-hour

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

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[5] 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[8] issued jointly by an international (IEEE) and national (ASTM) organization. However, at least one major usage guide[9] 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".[10]
• "kW·h" is, like "kW h", preferred with SI standards, but it is very rarely used in practice.
• The US official fuel-economy window sticker for electric vehicles uses the abbreviation "kW-hrs".[11]
• Variations in capitalization are sometimes seen: KWh, KWH, kwh, etc. these are inconsistent with International System of Units.
• The notation "kW/h", as a symbol for kilowatt-hour, is not correct.

## 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, 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. 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 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

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

The terms power and energy are frequently confused. Power is the rate of delivery of energy. Power is work performed per unit of time. Energy is the work performed (over a period of time).

Power is measured using the unit watts, or joules per second. Energy is measured using the unit watt-hours, or joules.

A common household battery contains 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.

For a given period of time, a higher level of power causes more energy to be 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 causes that energy to be used is less time.

An electrical load (e.g. a lamp, TV-set, or electric motor) has a rated power, which is usually measured 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. The amount of energy that is consumed (at that rate) depends on how long the device is operated. However, its power requirement is constant while running. The unit of energy used for residential electrical billing, the kilowatt-hour, shows the cumulative amount of electrical energy used during the billing period, regardless of the power drawn at any moment during the billing period.

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), which is equal to 0.1 kilowatt-hours. This same amount of energy would light a 50-watt bulb for 2 hours, a 40-watt bulb for 2.5 hours, or a 10-watt bulb for 10 hours. A power station's 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 peak power. These charges are billed as demand charges.[12]

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[13] 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.

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, and because higher discharge rates reduce the total amount of energy 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 for Li-ion) that must be used to calculate rather than the device output (usually 5.0 for USB portable chargers), since use of the lower figure allows manufacturers of such devices to overstate the capacity or run-time, inflating it by 35% (53.7=1.35). This results in a 500mA USB device running for only about 3.7 hours on a 2500mAh battery, rather than the expected 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.[14] 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.

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.[15][16]

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. ^ IEC Electropedia, Entry 131-11-58 Archived March 14, 2016, on Wayback Machine.
2. ^ "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;
3. ^ Thompson, Ambler and Taylor, Barry N. (2008). Guide for the Use of the International System of Units (SI) Archived June 3, 2016, on Wayback Machine. (Special publication 811). Gaithersburg, MD: National Institute of Standards and Technology. 12.
4. ^ "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, on Wayback Machine. (Special publication 330). Gaithersburg, MD: National Institute of Standards and Technology. 20.
5. ^ a b The International System of Units (SI) Archived April 29, 2016, on Wayback Machine.. (2006, 8th ed.) Paris: International Bureau of Weights and Measures. 130.
6. ^ See for example: Wind Energy Reference Manual Part 2: Energy and Power Definitions Archived November 26, 2007, on Wayback Machine. Danish Wind Energy Association. Retrieved 9 January 2008; "Kilowatt-Hour (kWh)" Archived March 2, 2016, on Wayback Machine. BusinessDictionary.com. Retrieved 9 January 2008; "US Nuclear Power Industry" Archived November 26, 2007, on Wayback Machine. www.world-nuclear.org. Retrieved 9 January 2008; "Energy. A Beginners Guide: Making Sense of Units" Archived November 26, 2007, on Wayback Machine. Renew On Line (UK). The Open University. Retrieved 9 January 2008.
7. ^ 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)"
8. ^ 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.
9. ^ Chicago Manual of Style. (14th ed., 1993) University of Chicago Press. 482.
10. ^
11. ^ "Electric Vehicles: Learn More About the New Label". fueleconomy.gov. US Department of energy. Retrieved 10 August 2014.
12. ^ " Understanding Electric Demand" Archived June 6, 2016, on Wayback Machine., National Grid
13. ^ "Inverter Selection". Northern Arizona Wind and Sun. Retrieved 27 March 2009.
14. ^ "The Board of Trade 1621-1970". Archived from the original on 2010.
15. ^ "Get enlightened about electricity". The Financial Express. December 20, 2004. Archived from the original on September 8, 2012. Retrieved 29 November 2009.
16. ^ "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.