# Joule

joule
Unit systemSI derived unit
Unit ofEnergy
SymbolJ
Named afterJames Prescott Joule
Conversions
1 J in ...... is equal to ...
SI base units   kgm2s−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 (/l/; symbol: J) is a derived unit of energy in the International System of Units.[1] 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).[2][3][4]

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

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

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

This SI unit is named after James Prescott Joule. As with every International System of Units (SI) unit named for a person, the first letter of its symbol is upper case (J). However, when an SI unit is spelled out in English, it is treated as a common noun and 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 material using title case.

## Exception of 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.[5] The use of newton metres for torque and joules for energy is helpful to avoid misunderstandings and miscommunications.[5]

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

${\displaystyle E=\tau \theta \ ,}$

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.[6]
• The typical energy released as heat by a person at rest every 1/60 s (approximately 17 ms).[7]
• 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).[8]
• 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)
Submultiples Multiples Value SI symbol Name Value 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
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.[9]
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).[10]
One square metre of the Earth receives about 1.4 kilojoules of solar radiation every second in full daylight.[11]
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.[12] 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.[13] The International Space Station, with a mass of approximately 450 megagrams and orbital velocity of 7.7 km/s,[14] has a kinetic energy of roughly 13 TJ. In 2017 Hurricane Irma was estimated to have a peak wind energy of 112 TJ.[15][16]
Petajoule
The petajoule (PJ) is equal to one quadrillion (1015) joules. 210 PJ is about 50 megatons of TNT. This 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

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 l⋅atm (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[17]
• 1 International Table calorie = 4.1868 J[18]
• 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.[19] 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

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.

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

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.[20]

## Notes and references

1. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 120, ISBN 92-822-2213-6, archived (PDF) from the original on 2017-08-14
2. ^ American Heritage Dictionary of the English Language, Online Edition (2009). Houghton Mifflin Co., hosted by Yahoo! Education.
3. ^ The American Heritage Dictionary, Second College Edition (1985). Boston: Houghton Mifflin Co., p. 691.
4. ^ McGraw-Hill Dictionary of Physics, Fifth Edition (1997). McGraw-Hill, Inc., p. 224.
5. ^ a b "Units with special names and symbols; units that incorporate special names and symbols". International Bureau of Weights and Measures. Archived from the original on 28 June 2009. Retrieved 18 March 2015. A derived unit can often be expressed in different ways by combining base units with derived units having special names. Joule, for example, may formally be written newton metre, or kilogram metre squared per second squared. This, however, is an algebraic freedom to be governed by common sense physical considerations; in a given situation some forms may be more helpful than others. In practice, with certain quantities, preference is given to the use of certain special unit names, or combinations of unit names, to facilitate the distinction between different quantities having the same dimension.
6. ^ "Units of Heat – BTU, Calorie and Joule". Engineeringtoolbox.com. Retrieved 2013-09-16.
7. ^ This is called the basal metabolic rate. It corresponds to about 5,000 kJ (1,200 kcal) per day. The kilocalorie (symbol kcal) is also known as the dietary calorie. "At rest" means awake but inactive.
8. ^ Ristinen, Robert A.; Kraushaar, Jack J. (2006). Energy and the Environment (2nd ed.). Hoboken, NJ: John Wiley & Sons. ISBN 0-471-73989-8.
9. ^ "Physics - CERN". public.web.cern.ch. Archived from the original on 2012-12-13.
10. ^ "You Say Calorie, We Say Kilojoule: Who's Right?". Retrieved 2 May 2017.
11. ^ "Construction of a Composite Total Solar Irradiance (TSI) Time Series from 1978 to present". Archived from the original on 2011-08-22. Retrieved 2005-10-05.
12. ^
13. ^ Malik, John (September 1985). "Report LA-8819: The yields of the Hiroshima and Nagasaki nuclear explosions" (PDF). Los Alamos National Laboratory. Archived from the original (PDF) on 11 October 2009. Retrieved 18 March 2015.
14. ^ "International Space Station Final Configuration" (PDF). European Space Agency. Archived from the original (PDF) on 21 July 2011. Retrieved 18 March 2015.
15. ^ Bonnie Berkowitz; Laris Karklis; Reuben Fischer-Baum; Chiqui Esteban (11 September 2017). "Analysis - How big is Hurricane Irma?". Washington Post. Retrieved 2 November 2017.
16. ^ "Irma unleashes its fury on south Florida", Financial Times, accessed 10-Sept-2017 (subscription required)
17. ^ The 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.
18. ^ Feynman, Richard (1963). "Physical Units". Feynman's Lectures on Physics. Retrieved 2014-03-07.
19. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 39–40, 53, ISBN 92-822-2213-6, archived (PDF) from the original on 2017-08-14
20. ^