The kilowatt hour (symbol kWh, kW⋅h or kW h) is a unit of
energy equal to 3.6 megajoules. 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 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.
Contents
1 Definition
2 Examples
3 Symbol and abbreviations for kilowatt hour
4 Conversions
5
Watt
Watt hour multiples and billing units
6 Confusion of kilowatt hours (energy) and kilowatts (power)
7 Misuse of watts per hour
8 Other energy-related units
9 See also
10 References
11 External links
Definition[edit]
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. 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 base unit of energy within the
International System of Units
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
SI unit of energy. The kilowatt hour is not listed
among the non-SI units accepted by the
BIPM
BIPM for use with the SI,
although the hour, from which the kilowatt hour is derived, is.[3]
Examples[edit]
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 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 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.
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.[4]
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 to 8,760 hours, therefore over a
period of one year, a power of one gigawatt equates to 8.76 terawatt
hours of energy. Conversely, one terawatt hour is equal to a sustained
power of approximately 114 megawatts for a period of one year.
Symbol and abbreviations for kilowatt hour[edit]
The symbol "kWh" is commonly used in commercial, educational,
scientific and media publications,[5][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.[8] 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[9] issued jointly
by an international (IEEE) and national (ASTM) organization. However,
at least one major usage guide[10] and the IEEE/
ASTM
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".[11]
"kW⋅h" is, like "kW h", preferred by 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".[12]
Variations in capitalization are sometimes seen: KWh, KWH, kwh, etc.;
these are inconsistent with International System of Units.
The notation "kW/h" is not a correct symbol for kilowatt hour, as it
denotes kilowatt per hour instead.
Conversions[edit]
Further information: Conversion of units of 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.
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
Watt hour multiples and billing units [edit]
Further information: Metric prefix
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.
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
Confusion of kilowatt hours (energy) and kilowatts (power)[edit]
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
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 in less time.
Misuse of watts per hour[edit]
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
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[edit]
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
USB portable chargers). This results
in a 500 mA
USB
USB device running for about 3.7 hours on a
2500 mAh battery, not five hours.
The
Board of Trade
Board of Trade unit (BOTU) is an obsolete UK synonym for kilowatt
hour. The term derives from the name of the
Board of Trade
Board of Trade which
regulated the electricity industry until 1942 when the Ministry of
Power took over.[14]
The
British thermal unit or BTU (not to be confused with BOTU), is a
unit of thermal energy with several definitions, all about 1055 Joule
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 TWh or 1.055
exajoule (EJ).
A
TNT equivalent
TNT equivalent is a measure of energy released in the detonation of
trinitrotoluene. A tonne of
TNT equivalent
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]
See also[edit]
Energy
Energy portal
Ampere-hour
Watt
Joule
Watt
Watt second
Orders of magnitude (energy)
Electric energy consumption
IEEE Std 260.1-2004
References[edit]
^ Thompson, Ambler and Taylor, Barry N. (2008). Guide for the Use of
the
International System of Units
International System of Units (SI) Archived June 3, 2016, at the
Wayback Machine. (
Special
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.) The International System of Units. Archived June 3, 2016,
at the Wayback Machine. (
Special
Special publication 330). Gaithersburg, MD:
National Institute of Standards and Technology. 20.
^ a b The
International System of Units
International System of Units (SI) Archived April 29, 2016,
at the Wayback Machine.. (2006, 8th ed.) Paris: International Bureau
of Weights and Measures. 130.
^ "Understanding Electric Demand" Archived June 6, 2016, at the
Wayback Machine., National Grid
^ IEC Electropedia, Entry 131-11-58 Archived March 14, 2016, at the
Wayback Machine.
^ See for example: Wind
Energy
Energy Reference Manual Part 2:
Energy
Energy and
Power Definitions Archived November 26, 2007, at the Wayback Machine.
Danish Wind
Energy
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.
^
ASTM
ASTM SI10-10, IEEE/
ASTM
ASTM SI 10 American National Standard for Metric
Practice,
ASTM
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)"
^ "Guide for the Use of the
International System of Units
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;
^ Standard for the Use of the
International System of Units
International System of Units (SI): The
Modern Metric System. (1997). (IEEE/
ASTM
ASTM SI 10-1997). New York and
West Conshohocken, PA: Institute of Electrical and Electronics
Engineers and ASTM. 15.
^ Chicago Manual of Style. (14th ed., 1993) University of Chicago
Press. 482.
^ Guide for the Use of the
International System of Units
International System of Units (SI) p.12
Archived March 4, 2016, at the Wayback Machine.
^ "Electric Vehicles: Learn More About the New Label".
fueleconomy.gov. US Department of energy. Retrieved 10 August
2014.
^ "Inverter Selection". Northern Arizona Wind and Sun. Retrieved 27
March 2009.
^ "The
Board of Trade
Board of Trade 1621-1970". Archived from the original on
2010.
^ "Get enlightened about electricity". The Financial Express. December
20, 2004. Archived from the original on September 8, 2012. Retrieved
29 November 2009.
^ "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.
External links[edit]
Prices per kilowatt hour in the USA,
Energy
Energy Information Ad