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The joule ( , or ; symbol: J) is the unit of
energy Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...
in the
International System of Units The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official s ...
(SI). In terms of
SI base units The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which all ...
, one joule corresponds to one
kilogram The kilogram (also spelled kilogramme) is the base unit of mass in the International System of Units (SI), equal to one thousand grams. It has the unit symbol kg. The word "kilogram" is formed from the combination of the metric prefix kilo- (m ...
- metre squared per second squared One joule is equal to the amount of
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an ani ...
done when a force of one newton displaces a body through a distance of one
metre The metre (or meter in US spelling; symbol: m) is the base unit of length in the International System of Units (SI). Since 2019, the metre has been defined as the length of the path travelled by light in vacuum during a time interval of of ...
in the direction of that force. It is also the energy dissipated as heat when an
electric current An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. The moving particles are called charge c ...
of one
ampere The ampere ( , ; symbol: A), often shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One ampere is equal to 1 c ...
passes through a resistance of one
ohm Ohm (symbol Ω) is a unit of electrical resistance named after Georg Ohm. Ohm or OHM may also refer to: People * Georg Ohm (1789–1854), German physicist and namesake of the term ''ohm'' * Germán Ohm (born 1936), Mexican boxer * Jörg Ohm (1 ...
for one second. It is named after the English physicist James Prescott Joule (1818–1889).


Definition

According to the
International Bureau of Weights and Measures The International Bureau of Weights and Measures (, BIPM) is an List of intergovernmental organizations, intergovernmental organisation, through which its 64 member-states act on measurement standards in areas including chemistry, ionising radi ...
the joule is defined as "the work done when the point of application of 1 MKS unit of force ewtonmoves a distance of 1 metre in the direction of the force." In terms of
SI base units The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which all ...
and in terms of SI derived units with special names, the joule is defined as One joule is also equivalent to any of the following: * The work required to move an
electric charge Electric charge (symbol ''q'', sometimes ''Q'') is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative''. Like charges repel each other and ...
of one
coulomb The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). It is defined to be equal to the electric charge delivered by a 1 ampere current in 1 second, with the elementary charge ''e'' as a defining c ...
through an electrical potential difference of one volt, or one coulomb-volt (C⋅V). This relationship can be used to define the volt. * The work required to produce one watt of power for one second, or one watt-second (W⋅s) (compare
kilowatt-hour 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 comm ...
, which is 3.6 megajoules). This relationship can be used to define the watt.


History

The CGS system had been declared official in 1881, at the first
International Electrical Congress The International Electrical Congress was a series of international meetings, from 1881 to 1904, in the then new field of applied electricity. The first meeting was initiated by the French government, including official national representatives, le ...
. The
erg The erg is a unit of energy equal to 10−7joules (100Nano-, nJ). It is not an SI unit, instead originating from the centimetre–gram–second system of units (CGS). Its name is derived from (), a Greek language, Greek word meaning 'work' or ' ...
was adopted as its unit of energy in 1882. Wilhelm Siemens, in his inauguration speech as chairman of the
British Association for the Advancement of Science The British Science Association (BSA) is a Charitable organization, charity and learned society founded in 1831 to aid in the promotion and development of science. Until 2009 it was known as the British Association for the Advancement of Scienc ...
(23 August 1882) first proposed the ''joule'' as unit of
heat In thermodynamics, heat is energy in transfer between a thermodynamic system and its surroundings by such mechanisms as thermal conduction, electromagnetic radiation, and friction, which are microscopic in nature, involving sub-atomic, ato ...
, to be derived from the electromagnetic units
ampere The ampere ( , ; symbol: A), often shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One ampere is equal to 1 c ...
and
ohm Ohm (symbol Ω) is a unit of electrical resistance named after Georg Ohm. Ohm or OHM may also refer to: People * Georg Ohm (1789–1854), German physicist and namesake of the term ''ohm'' * Germán Ohm (born 1936), Mexican boxer * Jörg Ohm (1 ...
, in cgs units equivalent to . The naming of the unit in honour of James Prescott Joule (1818–1889), at the time retired and aged 63, followed the recommendation of Siemens: At the second International Electrical Congress, on 31 August 1889, the joule was officially adopted alongside the
watt The watt (symbol: W) is the unit of Power (physics), power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantification (science), quantify the rate of Work ...
and the ''quadrant'' (later renamed to henry). Joule died in the same year, on 11 October 1889. At the fourth congress (1893), the "international ampere" and "international ohm" were defined, with slight changes in the specifications for their measurement, with the "international joule" being the unit derived from them. In 1935, the
International Electrotechnical Commission The International Electrotechnical Commission (IEC; ) is an international standards organization that prepares and publishes international standards for all electrical, electronics, electronic and related technologies. IEC standards cover a va ...
(as the successor organisation of the International Electrical Congress) adopted the " Giorgi system", which by virtue of assuming a defined value for the
magnetic constant The vacuum magnetic permeability (variously ''vacuum permeability'', ''permeability of free space'', ''permeability of vacuum'', ''magnetic constant'') is the magnetic permeability in a classical vacuum. It is a physical constant, conventionall ...
also implied a redefinition of the joule. The Giorgi system was approved by the
International Committee for Weights and Measures The General Conference on Weights and Measures (abbreviated CGPM from the ) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established in 1875 under the terms of the Metre C ...
in 1946. The joule was now no longer defined based on electromagnetic unit, but instead as the unit of
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an ani ...
performed by one unit of force (at the time not yet named newton) over the distance of 1
metre The metre (or meter in US spelling; symbol: m) is the base unit of length in the International System of Units (SI). Since 2019, the metre has been defined as the length of the path travelled by light in vacuum during a time interval of of ...
. The joule was explicitly intended as the unit of energy to be used in both electromagnetic and mechanical contexts. The ratification of the definition at the ninth
General Conference on Weights and Measures The General Conference on Weights and Measures (abbreviated CGPM from the ) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established in 1875 under the terms of the Metre C ...
, in 1948, added the specification that the joule was also to be preferred as the unit of
heat In thermodynamics, heat is energy in transfer between a thermodynamic system and its surroundings by such mechanisms as thermal conduction, electromagnetic radiation, and friction, which are microscopic in nature, involving sub-atomic, ato ...
in the context of
calorimetry In chemistry and thermodynamics, calorimetry () is the science or act of measuring changes in '' state variables'' of a body for the purpose of deriving the heat transfer associated with changes of its state due, for example, to chemical reac ...
, thereby officially deprecating the use of the
calorie The calorie is a unit of energy that originated from the caloric theory of heat. The large calorie, food calorie, dietary calorie, kilocalorie, or kilogram calorie is defined as the amount of heat needed to raise the temperature of one liter o ...
. This is the definition declared in the modern
International System of Units The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official s ...
in 1960. The definition of the joule as J = kg⋅m2⋅s−2 has remained unchanged since 1946, but the joule as a derived unit has inherited changes in the definitions of the
second The second (symbol: s) is a unit of time derived from the division of the day first into 24 hours, then to 60 minutes, and finally to 60 seconds each (24 × 60 × 60 = 86400). The current and formal definition in the International System of U ...
(in 1960 and 1967), the
metre The metre (or meter in US spelling; symbol: m) is the base unit of length in the International System of Units (SI). Since 2019, the metre has been defined as the length of the path travelled by light in vacuum during a time interval of of ...
(in 1983) and the
kilogram The kilogram (also spelled kilogramme) is the base unit of mass in the International System of Units (SI), equal to one thousand grams. It has the unit symbol kg. The word "kilogram" is formed from the combination of the metric prefix kilo- (m ...
( in 2019).


Practical examples

One joule represents (approximately): * The typical energy released as heat by a person at rest every 1/60 s (~,
basal metabolic rate Basal metabolic rate (BMR) is the rate of energy expenditure per unit time by endothermic animals at rest.. In other words it is the energy required by body organs to perform normal It is reported in energy units per unit time ranging from watt ( ...
); about / day. * The amount of electricity required to run a device for . * The energy required to accelerate a mass at through a distance of . * The
kinetic energy In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Rober ...
of a
mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...
travelling at , or a mass travelling at . * The energy required to lift an apple up 1 m, assuming the apple has a mass of 101.97 g. * The
heat In thermodynamics, heat is energy in transfer between a thermodynamic system and its surroundings by such mechanisms as thermal conduction, electromagnetic radiation, and friction, which are microscopic in nature, involving sub-atomic, ato ...
required to raise the temperature of 0.239 g of water from 0 °C to 1 °C. * The
kinetic energy In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Rober ...
of a human moving very slowly (). * The kinetic energy of a tennis ball moving at . * The food energy (kcal) in slightly more than half of an ordinary-sized sugar crystal (/crystal).


Multiples

; : . The minimal energy needed to change a bit of data in computation at around room temperature – approximately – is given by the Landauer limit. ; : is about the
kinetic energy In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Rober ...
of a flying mosquito. ; : The
Large Hadron Collider The Large Hadron Collider (LHC) is the world's largest and highest-energy particle accelerator. It was built by the CERN, European Organization for Nuclear Research (CERN) between 1998 and 2008, in collaboration with over 10,000 scientists, ...
(LHC) produces collisions of the microjoule order (7 TeV) per particle. ; : Nutritional food labels in most countries express energy in kilojoules (kJ). One square metre of the
Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...
receives about of
solar radiation Sunlight is the portion of the electromagnetic radiation which is emitted by the Sun (i.e. solar radiation) and received by the Earth, in particular the visible light perceptible to the human eye as well as invisible infrared (typically p ...
every second in full daylight. A human in a sprint has approximately 3 kJ of kinetic energy, while a cheetah in a (76 mph) sprint has approximately 20 kJ. . ; : The megajoule is approximately the kinetic energy of a one megagram (tonne) vehicle moving at (100 mph). The energy required to heat of liquid water at constant pressure from to is approximately . . ; : is about the
chemical energy Chemical energy is the energy of chemical substances that is released when the substances undergo a chemical reaction and transform into other substances. Some examples of storage media of chemical energy include batteries, Schmidt-Rohr, K. (20 ...
of combusting of
petroleum Petroleum, also known as crude oil or simply oil, is a naturally occurring, yellowish-black liquid chemical mixture found in geological formations, consisting mainly of hydrocarbons. The term ''petroleum'' refers both to naturally occurring un ...
. 2 GJ is about the Planck energy unit. . ; : The terajoule is about (which is often used in energy tables). About of energy was released by Little Boy. The
International Space Station The International Space Station (ISS) is a large space station that was Assembly of the International Space Station, assembled and is maintained in low Earth orbit by a collaboration of five space agencies and their contractors: NASA (United ...
, with a mass of approximately and orbital velocity of , has a
kinetic energy In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Rober ...
of roughly . In 2017,
Hurricane Irma Hurricane Irma was an extremely powerful and devastating tropical cyclone that was the first Category 5 hurricane to strike the Leeward Islands on record, followed by Hurricane Maria, Maria two weeks later. At the time, it was considered ...
was estimated to have a peak wind energy of . . ; : is about of TNT, which is the amount of energy released by the
Tsar Bomba The Tsar Bomba (code name: ''Ivan'' or ''Vanya''), also known by the alphanumerical designation "AN602", was a Thermonuclear weapon, thermonuclear aerial bomb, and by far the most powerful nuclear weapon ever created and tested. The Soviet phy ...
, the largest man-made explosion ever. . ; : The
2011 Tōhoku earthquake and tsunami On 11 March 2011, at 14:46:24 Japan Standard Time, JST (05:46:24 UTC), a  9.0–9.1 Submarine earthquake, undersea megathrust earthquake occurred in the Pacific Ocean, east of the Oshika Peninsula of the Tōhoku region. It lasted approx ...
in Japan had of energy according to its rating of 9.0 on the
moment magnitude scale The moment magnitude scale (MMS; denoted explicitly with or Mwg, and generally implied with use of a single M for magnitude) is a measure of an earthquake's magnitude ("size" or strength) based on its seismic moment. was defined in a 1979 paper ...
. Yearly U.S. energy consumption amounts to roughly , and the world final energy consumption was in 2021. One petawatt-hour of electricity, or any other form of energy, is . ; : The zettajoule is somewhat more than the amount of energy required to heat the
Baltic Sea The Baltic Sea is an arm of the Atlantic Ocean that is enclosed by the countries of Denmark, Estonia, Finland, Germany, Latvia, Lithuania, Poland, Russia, Sweden, and the North European Plain, North and Central European Plain regions. It is the ...
by 1 °C, assuming properties similar to those of pure water. Human annual world energy consumption is approximately . The energy to raise the temperature of Earth's atmosphere 1 °C is approximately . ; : The yottajoule is a little less than the amount of energy required to heat the
Indian Ocean The Indian Ocean is the third-largest of the world's five oceanic divisions, covering or approximately 20% of the water area of Earth#Surface, Earth's surface. It is bounded by Asia to the north, Africa to the west and Australia (continent), ...
by 1 °C, assuming properties similar to those of pure water. The thermal output of the
Sun The Sun is the star at the centre of the Solar System. It is a massive, nearly perfect sphere of hot plasma, heated to incandescence by nuclear fusion reactions in its core, radiating the energy from its surface mainly as visible light a ...
is approximately per second.


Conversions

1 joule is equal to (approximately unless otherwise stated): * (exactly) * * * (foot-pound) * (foot-poundal) Units with exact equivalents in joules include: * 1 thermochemical
calorie The calorie is a unit of energy that originated from the caloric theory of heat. The large calorie, food calorie, dietary calorie, kilocalorie, or kilogram calorie is defined as the amount of heat needed to raise the temperature of one liter o ...
= 4.184JThe adoption of joules as units of energy
FAO/WHO Ad Hoc Committee of Experts on Energy and Protein, 1971. A report on the changeover from calories to joules in nutrition.
* 1 International Table calorie = 4.1868J * 1W⋅h = * 1kW⋅h = * 1W⋅s = * 1 ton TNT = * 1 foe =


Newton-metre and torque

In
mechanics Mechanics () is the area of physics concerned with the relationships between force, matter, and motion among Physical object, physical objects. Forces applied to objects may result in Displacement (vector), displacements, which are changes of ...
, the concept of
force In physics, a force is an influence that can cause an Physical object, object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the Magnitu ...
(in some direction) has a close analogue in the concept of
torque In physics and mechanics, torque is the rotational analogue of linear force. It is also referred to as the moment of force (also abbreviated to moment). The symbol for torque is typically \boldsymbol\tau, the lowercase Greek letter ''tau''. Wh ...
(about some angle): A result of this similarity is that the SI unit for torque is the
newton-metre The newton-metre or newton-meter (also non-hyphenated, newton metre or newton meter; symbol N⋅m or N m) is the unit of torque (also called ) in the International System of Units (SI). One newton-metre is equal to the torque resulting fr ...
, which works out
algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...
ically to have the same
dimension In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coo ...
s as the joule, but they are not interchangeable. The
General Conference on Weights and Measures The General Conference on Weights and Measures (abbreviated CGPM from the ) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established in 1875 under the terms of the Metre C ...
has given the unit of
energy Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...
the name ''joule'', but has not given the unit of torque any special name, hence it is simply the newton-metre (N⋅m) – a compound name derived from its constituent parts. The use of newton-metres for torque but joules for energy is helpful to avoid misunderstandings and miscommunication. The distinction may be seen also in the fact that energy is a scalar quantity – the
dot product In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a Scalar (mathematics), scalar as a result". It is also used for other symmetric bilinear forms, for example in a pseudo-Euclidean space. N ...
of a force
vector Vector most often refers to: * Euclidean vector, a quantity with a magnitude and a direction * Disease vector, an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematics a ...
and a displacement vector. By contrast, torque is a vector – the
cross product In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E), and ...
of a force vector and a distance vector. Torque and energy are related to one another by the equation E = \tau \theta\, , where ''E'' is energy, ''τ'' is (the
vector magnitude In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and ze ...
of) torque, and ''θ'' is the angle swept (in
radian The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. It is defined such that one radian is the angle subtended at ...
s). Since plane angles are dimensionless, it follows that torque and energy have the same dimensions.


Watt-second

A watt-second (symbol W s or W⋅s) is a
derived unit A base unit of measurement (also referred to as a base unit or fundamental unit) is a unit of measurement adopted for a '' base quantity''. A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the ...
of
energy Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...
equivalent to the joule. The watt-second is the energy equivalent to the power of one
watt The watt (symbol: W) is the unit of Power (physics), power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantification (science), quantify the rate of Work ...
sustained for one
second The second (symbol: s) is a unit of time derived from the division of the day first into 24 hours, then to 60 minutes, and finally to 60 seconds each (24 × 60 × 60 = 86400). The current and formal definition in the International System of U ...
. While the watt-second is equivalent to the joule in both units and meaning, there are some contexts in which the term "watt-second" is used instead of "joule", such as in the rating of photographic electronic flash units.


References


External links

* {{Footer energy James Prescott Joule SI derived units Units of energy