Joule

This article is about the unit of energy. For other uses, see Joule (disambiguation).

joule
Unit system	SI derived unit
Unit of	Energy
Symbol	J
Named after	James Prescott Joule
Conversions
1 J in ...	... is equal to ...
SI base units	kg⋅m2⋅s−2
CGS units	1×107 erg
kilowatt hours	2.78×10−7 kW⋅h
kilocalories (thermochemical)	2.390×10−4 kcalth
BTUs	9.48×10−4 BTU
electronvolts	6.24×1018 eV

The joule (/dʒaʊl/; /dʒuːl/; symbol: J) is a derived unit of energy in the International System of Units. It is equal to the energy transferred to (or work done on) an object when a force of one newton acts on that object in the direction of its motion through a distance of one metre (1 newton metre or N⋅m). It is also the energy dissipated as heat when an electric current of one ampere passes through a resistance of one ohm for one second. It is named after the English physicist James Prescott Joule (1818–1889).

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

${\text{J}}={\frac {{\text{kg}}{\cdot }{\text{m}}^{2}}{{\text{s}}^{2}}}={\text{N}}{\cdot }{\text{m}}={\text{Pa}}{\cdot }{\text{m}}^{3}={\text{W}}{\cdot }{\text{s}}={\text{C}}{\cdot }{\text{V}},$

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 – 3.6 megajoules). This relationship can be used to define the watt.

Usage

The joule is named after James Prescott Joule. As with every SI unit named for a person, its symbol starts with an upper case letter (J), but when written in full, it follows the rules for capitalisation of a common noun; i.e., joule becomes capitalised at the beginning of a sentence and in titles but is otherwise in lower case.

Exception of newton metre

Main article: Newton metre

In mechanics, the concept of force (in some direction) has a close analog in the concept of torque (about some angle):

Linear	Angular
Force	Torque
Mass	Moment of inertia
Displacement (sometimes position)	Angle

A result of this similarity is that the SI unit for torque is the newton metre, which works out algebraically to have the same dimensions as the joule. But they 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 it is simply the newton metre (N⋅m) – a compound name derived from its constituent parts. The use of newton metres for torque and joules for energy is helpful to avoid misunderstandings and miscommunications.

The distinction may be seen also in the fact that energy is a scalar – the dot product of a vector force and a vector displacement. By contrast, torque is a vector – the cross product of a distance vector and a force vector. Torque and energy are related to one another by the equation

$E=\tau \theta \ ,$

where E is energy, τ is (the vector magnitude of) torque, and θ is the angle swept (in radians). Since radians are dimensionless, it follows that torque and energy have the same dimensions.

Practical examples

One joule in everyday life represents approximately:

• The energy required to lift a medium-sized tomato up 1 metre (3 ft 3 in) (assume the tomato has a mass of approximately 100 grams (3.5 oz)).
• The energy released when that same tomato falls back down one metre.
• The energy required to accelerate a 1 kg mass at 1 m⋅s⁻² through a distance of 1 m.
• The heat required to raise the temperature of 1 g of water by 0.24 °C.
• The typical energy released as heat by a person at rest every 1/60 s (approximately 17 ms).
• The kinetic energy of a 50 kg human moving very slowly (0.2 m/s or 0.72 km/h).
• The kinetic energy of a 56 g tennis ball moving at 6 m/s (22 km/h).
• The kinetic energy of an object with mass 1 kg moving at √2 ≈ 1.4 m/s.
• The amount of electricity required to light a 1 W LED for 1 s.

Since the joule is also a watt-second and the common unit for electricity sales to homes is the kW⋅h (kilowatt-hour), a kW⋅h is thus 1000 W × 3600 s = 3.6 MJ (megajoules).

Multiples

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

SI multiples of joule (J) Submultiples Multiples Value SI symbol Name Value SI 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 10−27 J rJ rontojoule 1027 J RJ ronnajoule 10−30 J qJ quectojoule 1030 J QJ quettajoule Common multiples are in bold face

Yoctojoule

The yoctojoule (yJ) is equal to (10⁻²⁴) of one joule.

Zeptojoule

The zeptojoule (zJ) is equal to one sextillionth (10⁻²¹) of one joule. 160 zeptojoules is about one electronvolt.

Attojoule

The attojoule (aJ) is equal to (10⁻¹⁸) of one joule.

Femtojoule

The femtojoule (fJ) is equal to (10⁻¹⁵) of one joule.

Picojoule

The picojoule (pJ) is equal to one trillionth (10⁻¹²) of one joule.

Nanojoule

The nanojoule (nJ) is equal to one billionth (10⁻⁹) of one joule. 160 nanojoules is about the kinetic energy of a flying mosquito.

Microjoule

The microjoule (μJ) is equal to one millionth (10⁻⁶) of one joule. The Large Hadron Collider (LHC) produces collisions of the microjoule order (7 TeV) per particle.

Millijoule

The millijoule (mJ) is equal to one thousandth (10⁻³) of a joule.

Kilojoule

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

One square metre of the Earth receives about 1.4 kilojoules of solar radiation every second in full daylight.

Megajoule

The megajoule (MJ) is equal to one million (10⁶) joules, or approximately the kinetic energy of a one megagram (tonne) vehicle moving at 161 km/h.

The energy required to heat 10 liters of liquid water at constant pressure from 0 °C (32 °F) to 100 °C (212 °F) is approximately 4.2 MJ.

One kilowatt hour of electricity is 3.6 megajoules.

Gigajoule

The gigajoule (GJ) is equal to one billion (10⁹) joules. 6 GJ is about the chemical energy of combusting 1 barrel (159 L) of crude oil. 2 GJ is about the Planck energy unit.

Terajoule

The terajoule (TJ) is equal to one trillion (10¹²) joules; or about 0.278 GWh (which is often used in energy tables). About 63 TJ of energy was released by the atomic bomb that exploded over Hiroshima. The International Space Station, with a mass of approximately 450 megagrams and orbital velocity of 7.7 km/s, has a kinetic energy of roughly 13 TJ. In 2017 Hurricane Irma was estimated to have a peak wind energy of 112 TJ.

Petajoule

The petajoule (PJ) is equal to one quadrillion (10¹⁵) joules. 210 PJ is about 50 megatons of TNT which is the amount of energy released by the Tsar Bomba, the largest man-made 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 rating of 9.0 on the moment magnitude scale. Yearly U.S. energy consumption amounts to roughly 94 EJ.

Zettajoule

The zettajoule (ZJ) is equal to one sextillion (10²¹) joules. The human 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 all the water on Earth by 1 °C. The thermal output of the Sun is approximately 400 YJ per second.

Conversions

Main article: Conversion of units of energy

1 joule is equal to (approximately unless otherwise stated):

• 1×10⁷ erg (exactly)
• 6.24150974×10¹⁸ eV
• 0.2390 cal (gram calories)
• 2.390×10⁻⁴ kcal (food calories)
• 9.4782×10⁻⁴ BTU
• 0.7376 ft⋅lb (foot-pound)
• 23.7 ft⋅pdl (foot-poundal)
• 2.7778×10⁻⁷ kW⋅h (kilowatt-hour)
• 2.7778×10⁻⁴ W⋅h (watt-hour)
• 9.8692×10⁻³ latm (litre-atmosphere)
• 11.1265×10⁻¹⁵ g (by way of mass-energy equivalence)
• 1×10⁻⁴⁴ foe (exactly)

Units defined exactly in terms of the joule include:

• 1 thermochemical calorie = 4.184 J
• 1 International Table calorie = 4.1868 J
• 1 W⋅h = 3600 J (or 3.6 kJ)
• 1 kW⋅h = 3.6×10⁶ J (or 3.6 MJ)
• 1 W⋅s = 1 J
• 1 ton TNT = 4.184 GJ

Watt second

A watt second (also watt-second, symbol W s or W·s) is a derived unit of energy equivalent to the joule. The watt-second is the energy equivalent to the power of one watt sustained for one second. 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".

Photography

See also: Guide number

In photography, the unit for flashes is the watt-second. A flash can be rated in watt-seconds (e.g. 300 W⋅s) or in joules (different names for the same thing), but historically the term "watt-second" has been used and continues to be used. An on-camera flash, using a 1000 microfarad capacitor at 300 volts, would be 45 watt-seconds. Studio flashes, using larger capacitors and higher voltages, are in the 200–2000 watt-second range.

${\text{Energy of a flash in joules or watt-seconds}}={\dfrac {1}{2}}\cdot {\text{capacitance of the storage capacitor in farads}}\cdot {\text{working voltage}}^{2}$

The energy rating a flash is given is not a reliable benchmark for its light output because there are numerous factors that affect the energy conversion efficiency. For example, the construction of the tube will affect the efficiency, and the use of reflectors and filters will change the usable light output towards the subject. Some companies specify their products in "true" watt-seconds, and some specify their products in "nominal" watt-seconds.

See also

• Fluence