The joule (/ˈdʒuːl/ or sometimes /ˈdʒaʊl/), symbol J, is a derived unit of energy, work, or amount of heat in the International System of Units.^[1] It is equal to the energy expended (or work done) in applying a force of one newton through a distance of one metre (1 newton metre or N·m), or in passing an electric current of one ampere through a resistance of one ohm for one second. It is named after the English physicist James Prescott Joule (1818–1889).^[2][3][4]

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

where kg is the kilogram, m is the metre, s is the second, N is the newton, Pa is the pascal, W is the watt, C is the coulomb, and V is the volt.

One joule can also be defined as:

• The work required to move an electric charge of one coulomb 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). This relationship can be used to define the watt.

Usage

This SI unit is named after James Prescott Joule. As with every International System of Units (SI) unit whose name is derived from the proper name of a person, the first letter of its symbol is upper case (J). However, when an SI unit is spelled out in English, it should always begin with a lower case letter (joule), except in a situation where any word in that position would be capitalized, such as at the beginning of a sentence or in capitalized material such as a title. Note that “degree Celsius” conforms to this rule because the “d” is lowercase. —Based on The International System of Units, section 5.2.

Confusion with newton-metre

In angular mechanics, torque is analogous to the linear Newtonian mechanics parameter of force, moment of inertia to mass, and angle to distance. Energy is the same in both systems. Thus, although the joule has the same dimensions as the newton-meter (1 J = 1 N·m = 1 kg·m²·s⁻²), these units are not interchangeable: the CGPM has given the unit of energy the name “joule”, but has not given the unit of torque any special name, hence the unit of torque is known as the newton-metre (N·m) – a compound name derived from its constituent parts.^[5] Torque and energy are related to each other using the equation

where E is the energy, τ is the torque, and θ is the angle moved (in radians). 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.^[5]

An additional solution is to realize that joules are scalars – they are the dot product of a vector force and a vector displacement whereas torque is a vector. Torque is the cross product of a distance vector and a force vector. Drawing a traditional vector arrow over “newton-meter” in a torque resolves the ambiguity.

Practical examples

One joule in everyday life represents approximately:

• the energy required to lift a small apple (with a mass of approximately 100 g) vertically through one meter of air.
• the energy released when that same apple falls one meter to the ground.
• the heat required to raise the temperature of 1 g of water by 0.24 K.^[6]
• the typical energy released as heat by a person at rest, every 1/60th of a second.^[7]
• 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 (6.4 m/s).^[8]
• the kinetic energy of 1 kg moving √2 m/s.

Since the joule is also a watt-second and the common unit for electricity sales to homes is the kWh (kilowatt-hour), a kWh is thus 1000 (kilo) x 3600 seconds = 3.6 MJ (megajoules).

Multiples

For additional examples, see: Orders of magnitude (energy)

SI multiples for joule (J) Submultiples Multiples Value Symbol Name Value Symbol Name 10−1 J dJ decijoule 101 J daJ decajoule 10−2 J cJ centijoule 102 J hJ hectojoule 10−3 J mJ millijoule 103 J kJ kilojoule 10−6 J µJ microjoule 106 J MJ megajoule 10−9 J nJ nanojoule 109 J GJ gigajoule 10−12 J pJ picojoule 1012 J TJ terajoule 10−15 J fJ femtojoule 1015 J PJ petajoule 10−18 J aJ attojoule 1018 J EJ exajoule 10−21 J zJ zeptojoule 1021 J ZJ zettajoule 10−24 J yJ yoctojoule 1024 J YJ yottajoule Common multiples are in bold face

Nanojoule

The nanojoule (nJ) is equal to one billionth of one joule. One nanojoule is about 1/160 of the kinetic energy of a flying mosquito.^[9]

Microjoule

The microjoule (μJ) is equal to one millionth of one joule. The Large Hadron Collider (LHC) is expected to produce collisions on the order of 1 microjoule (7 TeV) per particle.

Millijoule

The millijoule (mJ) is equal to one thousandth of a joule.

Kilojoule

The kilojoule (kJ) is equal to one thousand (10³) joules. Nutritional food labels in certain countries express energy in standard kilojoules (kJ).

One kilojoule per second (1 kilowatt) is approximately the amount of solar radiation received by one square metre of the Earth in full daylight.^[10]

Megajoule

The megajoule (MJ) is equal to one million (10⁶) joules, or approximately the kinetic energy of a one-ton 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 in a barrel of oil, when combusted.^[11]

Terajoule

The terajoule (TJ) is equal to one trillion (10¹²) joules. About 63 terajoules were released by the atomic bomb that exploded over Hiroshima.^[12] The International Space Station, with a mass of approximately 450,000 kg and orbital velocity of 7.7 km/s,^[13] has a kinetic energy of roughly 13.34 terajoules.

Petajoule

The petajoule (PJ) is equal to one quadrillion (10¹⁵) joules. 210 PJ is equivalent to about 50 megatons of TNT. This is the amount of energy released by the Tsar Bomba, the largest man-made nuclear explosion ever.

Exajoule

The exajoule (EJ) is equal to one quintillion (10¹⁸) joules. The 2011 Tōhoku earthquake and tsunami in Japan had 1.41 EJ of energy according to its 9.0 on the moment magnitude scale. Energy in the United States used per year is roughly 94 EJ.

Zettajoule

The zettajoule (ZJ) is equal to one sextillion (10²¹) joules. Annual global energy consumption is approximately 0.5 ZJ.

Yottajoule

The yottajoule (YJ) is equal to one septillion (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:

• 1×10⁷ ergs (exactly)
• 6.24150974×10¹⁸ eV (electronvolts)
• 0.2390 cal (thermochemical gram calories or small calories)
• 2.3901×10⁻⁴ kcal (thermochemical kilocalories, kilogram calories, large calories or food calories)
• 9.4782×10⁻⁴ BTU (British thermal unit)
• 0.7376 ft·lb (foot-pounds)
• 23.7 ft·pdl (foot-poundals)
• 2.7778×10⁻⁷ kilowatt-hour
• 2.7778×10⁻⁴ watt-hour
• 9.8692×10⁻³ litre–atmosphere
• 11.1265 femtograms (mass-energy equivalence)
• 1×10⁻⁴⁴ foe (exactly)

Units defined exactly in terms of the joule include:

• 1 thermochemical calorie = 4.184 J^[14]
• 1 International Table calorie = 4.1868 J^[15]
• 1 watt hour = 3600 J
• 1 kilowatt hour = 3.6×10⁶ J (or 3.6 MJ)
• 1 watt second = 1 J
• 1 ton TNT = 4.184 GJ