Joule

# Joule

Overview
The joule; symbol J) is a derived unit
SI derived unit
The International System of Units specifies a set of seven base units from which all other units of measurement are formed, by products of the powers of base units. These other units are called SI derived units, for example, the SI derived unit of area is square metre , and of density is...

of energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

or work in the International System of Units
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

. It is equal to the energy expended (or work done) in applying a force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

of one newton through a distance of one metre
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

(1 newton metre or N·m), or in passing an electric current of one ampere
Ampere
The ampere , often shortened to amp, is the SI unit of electric current and is one of the seven SI base units. It is named after André-Marie Ampère , French mathematician and physicist, considered the father of electrodynamics...

through a resistance of one ohm
Ohm
The ohm is the SI unit of electrical resistance, named after German physicist Georg Simon Ohm.- Definition :The ohm is defined as a resistance between two points of a conductor when a constant potential difference of 1 volt, applied to these points, produces in the conductor a current of 1 ampere,...

for one second. It is named after the English physicist James Prescott Joule
James Prescott Joule
James Prescott Joule FRS was an English physicist and brewer, born in Salford, Lancashire. Joule studied the nature of heat, and discovered its relationship to mechanical work . This led to the theory of conservation of energy, which led to the development of the first law of thermodynamics. The...

(1818–1889).

In terms firstly of base SI units and then in terms of other SI units:

where N is the newton, m is the metre
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

, kg is the kilogram
Kilogram
The kilogram or kilogramme , also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram , which is almost exactly equal to the mass of one liter of water...

, s is the second
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....

, Pa is the pascal
Pascal (unit)
The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre...

, and W is the watt
Watt
The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...

.

One joule can also be defined as:
• The work required to move an electric charge
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

of one coulomb through an electrical potential difference
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

of one volt
Volt
The volt is the SI derived unit for electric potential, electric potential difference, and electromotive force. The volt is named in honor of the Italian physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery.- Definition :A single volt is defined as the...

, or one '"coulomb volt" (C·V).
Discussion

Encyclopedia
The joule; symbol J) is a derived unit
SI derived unit
The International System of Units specifies a set of seven base units from which all other units of measurement are formed, by products of the powers of base units. These other units are called SI derived units, for example, the SI derived unit of area is square metre , and of density is...

of energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

or work in the International System of Units
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

. It is equal to the energy expended (or work done) in applying a force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

of one newton through a distance of one metre
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

(1 newton metre or N·m), or in passing an electric current of one ampere
Ampere
The ampere , often shortened to amp, is the SI unit of electric current and is one of the seven SI base units. It is named after André-Marie Ampère , French mathematician and physicist, considered the father of electrodynamics...

through a resistance of one ohm
Ohm
The ohm is the SI unit of electrical resistance, named after German physicist Georg Simon Ohm.- Definition :The ohm is defined as a resistance between two points of a conductor when a constant potential difference of 1 volt, applied to these points, produces in the conductor a current of 1 ampere,...

for one second. It is named after the English physicist James Prescott Joule
James Prescott Joule
James Prescott Joule FRS was an English physicist and brewer, born in Salford, Lancashire. Joule studied the nature of heat, and discovered its relationship to mechanical work . This led to the theory of conservation of energy, which led to the development of the first law of thermodynamics. The...

(1818–1889).

In terms firstly of base SI units and then in terms of other SI units:

where N is the newton, m is the metre
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

, kg is the kilogram
Kilogram
The kilogram or kilogramme , also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram , which is almost exactly equal to the mass of one liter of water...

, s is the second
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....

, Pa is the pascal
Pascal (unit)
The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre...

, and W is the watt
Watt
The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...

.

One joule can also be defined as:
• The work required to move an electric charge
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

of one coulomb through an electrical potential difference
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

of one volt
Volt
The volt is the SI derived unit for electric potential, electric potential difference, and electromotive force. The volt is named in honor of the Italian physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery.- Definition :A single volt is defined as the...

, or one '"coulomb volt" (C·V). This relationship can be used to define the volt.
• The work required to produce one watt
Watt
The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...

of power
Power (physics)
In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...

for one second
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....

, or one "watt second" (W·s) (compare kilowatt hour). This relationship can be used to define the watt.

## Confusion with newton metre

Although the joule has the same dimensions as the newton-metre (1 J = 1 N·m = 1 kg·m2·s−2), these units are not interchangeable as the newton-metre (N·m) is the unit of torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....

and joules the unit of energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

. Torque and energy are related to each other using the equation

where E is the energy, τ is magnitude of the torque, and θ is the angle moved (in radian
Radian is the ratio between the length of an arc and its radius. The radian is the standard unit of angular measure, used in many areas of mathematics. The unit was formerly a SI supplementary unit, but this category was abolished in 1995 and the radian is now considered a SI derived unit...

s). Since radians are dimensionless, it follows that torque and energy have the same dimensions.

The use of newton-metres for torque and joules for energy is useful in helping avoid misunderstandings and miscommunications.

Torque and energy have the same dimension because both torque and work (a type of energy) can be calculated by multiplying a force by a distance. However, the details are quite different in the two cases. For torque, the multiplication of force and distance is a vector cross product, while for work it is a dot product
Dot product
In mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers and returns a single number obtained by multiplying corresponding entries and then summing those products...

. Also, for torque, the distance involved is the length of the lever arm, while for energy it is the distance traveled by the object undergoing the force.

## Practical examples

One joule in everyday life is approximately:
• the energy required to lift a small apple one metre straight up. (A mass of about 102 g =  kg)
• the energy released when that same apple falls one metre to the ground.
• the energy released as heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...

by a person at rest, every 1/60th of a second.
• the kinetic energy of a 50 kg human moving very slowly (0.2 m/s).
• the kinetic energy of a tennis ball moving at 23 km/h (14 mph).

## Multiples

For additional examples, see: Orders of magnitude (energy)
Orders of magnitude (energy)
This list compares various energies in joules , organized by order of magnitude.-SI multiples:-See also:*Conversion of units of energy*Energies per unit mass*List of energy topics*Metric system*TNT equivalent*Scientific notation-Notes:...

### Nanojoule

The nanojoule (nJ) is equal to one billionth of one joule. One nanojoule is about 1/160 of the kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...

of a flying mosquito.

### Microjoule

The microjoule (μJ) is equal to one millionth of one joule. The Large Hadron Collider
The Large Hadron Collider is the world's largest and highest-energy particle accelerator. It is expected to address some of the most fundamental questions of physics, advancing the understanding of the deepest laws of nature....

(LHC) is expected to produce collisions on the order of 1 microjoule (7 TeV) per particle.

### Kilojoule

The kilojoule (kJ) is equal to one thousand (103) joules. Food labels in some countries express food energy
Food energy
Food energy is the amount of energy obtained from food that is available through cellular respiration.Food energy is expressed in food calories or kilojoules...

in kilojoules.

One kilojoule per second (1000 watts) is approximately the amount of solar radiation received by one square metre of the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

in full daylight.

### Megajoule

The megajoule (MJ) is equal to one million (106) joules, or approximately the kinetic energy of a one-tonne
Tonne
The tonne, known as the metric ton in the US , often put pleonastically as "metric tonne" to avoid confusion with ton, is a metric system unit of mass equal to 1000 kilograms. The tonne is not an International System of Units unit, but is accepted for use with the SI...

vehicle moving at 160 km/h (100 mph).

Because 1 watt times one second equals one joule, 1 kilowatt-hour is 1000 watts times 3600 seconds, or 3.6 megajoules.

### Gigajoule

The gigajoule (GJ) is equal to one billion (109) joules. Six gigajoules is about the amount of potential chemical energy
Chemical energy
Chemical energy is the potential of a chemical substance to undergo a transformation through a chemical reaction or, to transform other chemical substances...

in a barrel
Barrel of oil equivalent
The barrel of oil equivalent is a unit of energy based on the approximate energy released by burning one barrel of crude oil. The US Internal Revenue Service defines it as equal to 5.8 × 106 BTU...

of oil, when combusted.

### Terajoule

The terajoule (TJ) is equal to one trillion (1012) joules. About 63 terajoules were released by the atomic bomb that exploded over Hiroshima
Little Boy
"Little Boy" was the codename of the atomic bomb dropped on Hiroshima on August 6, 1945 by the Boeing B-29 Superfortress Enola Gay, piloted by Colonel Paul Tibbets of the 393rd Bombardment Squadron, Heavy, of the United States Army Air Forces. It was the first atomic bomb to be used as a weapon...

. The International Space Station
International Space Station
The International Space Station is a habitable, artificial satellite in low Earth orbit. The ISS follows the Salyut, Almaz, Cosmos, Skylab, and Mir space stations, as the 11th space station launched, not including the Genesis I and II prototypes...

, at completion, with a mass of 450,000kg and orbital velocity of 7.7 km/s, will have a kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...

of roughly 13 terajoules.

### Petajoule

The petajoule (PJ) is equal to 1015 joules. 210 PJ is equivalent to about 50 megatons of TNT. This is the amount of energy released by the Tsar Bomba
Tsar Bomba
Tsar Bomba is the nickname for the AN602 hydrogen bomb, the most powerful nuclear weapon ever detonated. It was also referred to as Kuz'kina Mat , in this usage meaning "something that has not been seen before"....

, the largest man-made nuclear explosion ever.

### Exajoule

The exajoule (EJ) is equal to 1018 joules. The 2011 Tōhoku earthquake and tsunami
2011 Tōhoku earthquake and tsunami
The 2011 earthquake off the Pacific coast of Tohoku, also known as the 2011 Tohoku earthquake, or the Great East Japan Earthquake, was a magnitude 9.0 undersea megathrust earthquake off the coast of Japan that occurred at 14:46 JST on Friday, 11 March 2011, with the epicenter approximately east...

in Japan had 1.41 EJ of energy according to its 9.0 on the moment magnitude scale
Moment magnitude scale
The moment magnitude scale is used by seismologists to measure the size of earthquakes in terms of the energy released. The magnitude is based on the seismic moment of the earthquake, which is equal to the rigidity of the Earth multiplied by the average amount of slip on the fault and the size of...

. Energy in the United States used per year is roughly 94 EJ.

### Zettajoule

The zettajoule (ZJ) is equal to 1021 joules. Annual global energy consumption
World energy resources and consumption
]World energy consumption in 2010: over 5% growthEnergy markets have combined crisis recovery and strong industry dynamism. Energy consumption in the G20 soared by more than 5% in 2010, after the slight decrease of 2009. This strong increase is the result of two converging trends...

is approximately 0.5 ZJ

### Yottajoule

The yottajoule (YJ) is equal to 1024 joules. This is approximately the amount of energy required to heat the entire volume of water on Earth by 1 °Celsius.

## Conversions

1 joule is equal to: (exactly) (electronvolt
Electronvolt
In physics, the electron volt is a unit of energy equal to approximately joule . By definition, it is equal to the amount of kinetic energy gained by a single unbound electron when it accelerates through an electric potential difference of one volt...

s) (thermochemical gram calorie
Calorie
The calorie is a pre-SI metric unit of energy. It was first defined by Nicolas Clément in 1824 as a unit of heat, entering French and English dictionaries between 1841 and 1867. In most fields its use is archaic, having been replaced by the SI unit of energy, the joule...

s or small calories) (thermochemical kilocalories, kilogram calories, large calories or food calories) (British thermal unit
British thermal unit
The British thermal unit is a traditional unit of energy equal to about 1055 joules. It is approximately the amount of energy needed to heat of water, which is exactly one tenth of a UK gallon or about 0.1198 US gallons, from 39°F to 40°F...

) (foot-pounds force) (foot-poundal
Poundal
The poundal is a unit of force that is part of the foot-pound-second system of units, in Imperial units introduced in 1877, and is from the specialized subsystem of English Absolut ....

s) (mass-energy equivalence) (exactly)

Units defined exactly in terms of the joule include:
• 1 thermochemical calorie = 4.184 J
• 1 International Table calorie = 4.1868 J
• 1 watt hour = 3600 J
• 1 kilowatt hour = (or 3.6 MJ)
• 1 watt second =
• 1 ton TNT = 4.184 GJ