Joule Unit

What is joule?

Joule is the SI unit of energy or work (energy and work are interconvertible). Its symbol is “J”. It is named after a Scientist James Prescott Joule who worked on the conversion of enegy which led to the law of conservation of energy.

Equivalent units of joule:

The formula of work / energy is,

W=F.d →1

Where W stands for work, F represents force and d is the distance. We know that the unit of force is newton and in SI system distance is measured in meters so according to this, Joule is equal to N.m

Joule=Newton×meter (N.m) →2

Another equivalent unit for joule can be derived by opening the formula of force in equation 1.



Here m stands for mass and a is the acceleration. Mass is measured in kilograms and unit of acceleration is m/s2 so Joule is also equal to Kgm^2/s^2


Joule=(Kg.m^2)⁄s^2 →3

Definition of joule:

Joule can be defined in many ways.

  1. According to the second equation, the amount of work that is done by 1 newton of force in moving an object through a distance of 1 meter is equivalent to 1 joule.
  2. According to the third equation, the amount of work that is done when 1kg of object is moved 1 meter with an acceleration of 1m/s2 is equal to 1 joule.

joule is equal to N.m

Joule in terms of potential difference:

Let’s see the formula of electric potential difference.

V=W/q →4

V is the potential difference and q stands for charge. The units of potential difference and charge are volt and coulomb (C). This gives us another equivalent unit of joule that is,


joule in terms of potential difference

Definition of joule:

The above equation has given us another definition of joule. The amount of work done on 1 coulomb of charge when there is potential difference of 1 volt. is equal to 1 joule.

Joule in terms of power:


P is power here and t is for time. Let’s look in to the units. The SI unit of power is watt and time is measured in seconds so Joule is also equivalent to power x time


Definition of joule:

Joule can also be that amount of work which is done in 1 second with power of 1 watt.

Joule into Kilowatt-hour:

Commercially energy is measured in Kilowatt-hour. 1 kilowatt-hour is equal to 36x10^5 joules.

1 Kilowatt-hour=〖10〗^3×36×〖10〗^2=36×〖10〗^5 Joules

Conversion of joule into erg:

In CGs (centimeter gram second) system the unit of energy or work is erg.

1 erg=〖10〗^(-7) Joule

Conversion of joule into Calorie:

Another unit of energy in CGS system is calorie.

1 cal=4.18 Joule

Conversion of joule into

Dyne (represented as dyn) is the unit of force in CGS system and in this system distance is measured in cm. According to the formula of energy / work (equation 1) in CGS another unit of energy can be

1×〖10〗^(-7) Joules

The above equation also shows that the unit is equal to erg.

Conversion of joule into BTU:

BTU stands for british thermal unit. To convert joule into BTU multiply the value in joule with 1055.

1 BTU=1055 Joule

Conversion of joule into lb.ft:

In FPS system (foot pound second) the distance is measured in foot (represented as ft) and the unit of force is pound (symbol lb). According to equation 1, in FPS system the unit of energy will be lb.ft.

1 lb.ft=1.356 Joules

Atomic unit of Energy:

Joule and other units are not convinient to describe the energy of very small particles like electrons and protons. So scientist developed another unit to measure very small energy changes. They called it “Electron Volt”.

atomic unit of energy

Definition of electron volt:

The amount of energy required by an electron to move in an electric field when the potential difference is of 1 volt.

Conversion of joule into electron volt:

According to equation 4 (formula of potential difference),

1 ev=1.6×〖10〗^(-19) coulomb ×1 volt

1 ev=1.6×〖10〗^(-19) Joules

Read also:
Watt hour
Energy conservation

James Joule played the major role in establishing the conservation of energy, or the first law of thermodynamics, as a universal, all-pervasive principle of physics. He was an experimentalist par excellence and his place in the development of thermodynamics is unarguable. This article discusses Joule’s life and scientific work culminating in the 1850 paper, where he presented his detailed measurements of the mechanical equivalent of heat using his famous paddle-wheel apparatus. Joule’s long series of experiments in the 1840s leading to his realisation that the conservation of energy was probably of universal validity is discussed in context with the work of other pioneers, notably Sadi Carnot, who effectively formulated the principle of the second law of thermodynamics a quarter of a century before the first law was accepted. The story of Joule’s work is a story of an uphill struggle against a critical scientific establishment unwilling to accept the mounting evidence until it was impossible to ignore. His difficulties in attracting funding and publishing in reputable journals despite the quality of his work will resonate with many young scientists and engineers of the present day. This commentary was written to celebrate the 350th anniversary of the journal *Philosophical Transactions of the Royal. Outside the scientific and engineering communities the name of James Prescott Joule is not widely known although virtually every packet of food purchased in a supermarket lists the energy value of the contents in the now standard SI unit, the joule . But old habits die hard and the superseded unit, the calorie , still finds greater favour with the general public. When, for example, did you last hear someone declare, ‘there were far too many joules in that pudding’? Until 1853, when William Rankine coined the terms potential energy and actual (i.e. kinetic) energy , Joule himself would not have been familiar with the word energy as a precisely defined scientific quantity. He would, however, have recognized calorie as being related to the caloric theory of heat , a theory that was accepted by almost all scientists of the time (then called natural philosophers ) and which Joule was instrumental in overturning and replacing by the axiomatic principle we now call the conservation of energy or the first law of thermodynamics . James Joule (1818–1889) was born in Salford near Manchester, the heartland of the industrial revolution. In the words of the English experimental physicist Patrick Blackett, Salford was ‘one of those towns in which so much of the nation’s wealth has been made and on which so little of it has been spent’. Nevertheless, Joule’s family enjoyed a good life for they owned and operated a local brewery which became the largest in the region. They were prosperous and middle class, and they lived well in a substantial house with several servants. In 1823, the family moved to Swinton nearby. The young James Joule was not a healthy child and a spinal weakness gave him a slight, though not pronounced, deformity. He did not attend school and was tutored at home where he made slow progress. Unsurprisingly, he was shy in company. Indeed, Joule was never able to command respect by the force of a strong personality and this may well account for his comparative obscurity outside the scientific community. He needed the support of someone who possessed the gifts he lacked, but it was not until 1847 that he found that person in the shape of William Thomson, later Lord Kelvin (1824–1907), who, although 6 years younger, had no trouble with self-publicity. Until then Joule struggled, publishing papers of major scientific importance but making almost no impact whatsoever. The definitive account of Joule’s life and work is the book by Donald Cardwell. In Cardwell’s description of Joule’s formative years, he stresses the important influence of John Dalton (1766–1844), a local teacher and natural philosopher with radical scientific ideas who was an early proponent of the billiard-ball atomic theory of gases. From 1834 to 1837, James and his elder brother Benjamin studied under Dalton, receiving twice weekly sessions on arithmetic, geometry, chemistry and physics. Joule’s fascination with experimental work started in this period but he did not acquire his obsession with experimental precision from Dalton. According to Humphry Davy, Dalton was a ‘very coarse experimenter’ and he often used rough and inaccurate instruments even when better ones were available. Nevertheless, Dalton was greatly celebrated in his own lifetime and on his death 40 000 people filed past his coffin as he lay in state in Manchester Town Hall, an astonishing accolade that almost certainly would have horrified the man himself who was quiet and retiring. Given Joule’s burgeoning scientific talents, it was a remarkable stroke of good fortune that a man of John Dalton’s abilities was retained to tutor the two brothers. Dalton was a Fellow of the Royal Society and knew many of the leading scientists of the day. But he was also a scientifically independent thinker and it may well have been this characteristic which impressed the young Joule to such an extent that, when he was developing his own views about energy transformation, he was prepared to stand firm in print when almost every other natural philosopher in the world disagreed with him. Nowadays, it is difficult to empathize with the scientific and technical culture of the early nineteenth century. In Britain, no science degrees were awarded and there were no professional scientific qualifications. Only a small minority of those who published scientific papers were gainfully employed in science and Joule himself conducted most of his experiments in the cellar of his house as a private individual. However, the development of the steam engine, most notably by James Watt in the late eighteenth century, was stimulating an interest, particularly among engineers, in the fundamental principles of the technology. Natural philosophy was divided into the finished sciences (Newtonian mechanics, planetary astronomy and optics) and the progressive sciences (botany, physiology, zoology, geology, chemistry, heat, electricity and magnetism). Electricity and heat were regarded as part of chemistry and thermal effects were thought to be due to the action of a subtle fluid called caloric which could be stored in bodies and transferred from one to the other. The caloric theory of heat held sway throughout the late eighteenth and the first half of the nineteenth century. Virtually all natural philosophers accepted the concept that caloric could pass from one body to another by conduction and was conserved in the process. This theory was given convincing credibility in The Analytical Theory of Heat by the French mathematician and physicist Joseph Fourier (1768–1830). Fourier’s treatise was a mathematical tour de force introducing, as it did, the solution of the heat conduction equation using what are now known as Fourier series to represent arbitrary functions which could even have discontinuities. Fourier claimed that, given the thermal properties, state and form of a body, he could predict its thermal state at any time in the future and had thus essentially completed the scientific study of heat. But, although the work was hugely influential, it was seriously restricted because it ignored the situation whereby heat was applied and mechanical work was performed in an engine. Given the huge success of the steam engine in powering the industrial revolution, this was a remarkable, indeed inexplicable, oversight on the part of Fourier and his contemporaries. By the 1820s, few scientists had questioned the caloric theory. The most famous of the dissenters was the American military adventurer and physicist Benjamin Thompson (1753–1814), better known as Count Rumford. Rumford had a remarkable life. He fought in the American War of Independence, moved to London where he received a knighthood from King George III, and then spent nine years as the minister charged with re-organizing the Bavarian army. Nevertheless, it was his famous cannon boring experiment which has secured his place in history. Rumford observed that the frictional heat generated by boring cannon in the arsenal in Munich was apparently limitless. To demonstrate this he immersed a cannon barrel in water and, using a specially blunted boring tool, found that the water boiled in under 3 hours. He then argued that this seemingly unlimited generation of heat was incompatible with the caloric theory and concluded that the only thing communicated to the barrel was motion. Rumford himself did not attempt to calculate the so-called mechanical equivalent of heat (usually given the symbol J) and his description was essentially qualitative. However, Joule made a rough estimate from the data in Rumford’s original paper and concluded that, ‘the heat required to raise a lb. of water 1°F will be equivalent to the force represented by 1034 foot-pounds’. Before the mid-nineteenth century, the term force was often used to denote what we now call work (though clearly the unit foot-pound does not represent a force). The heat required to raise the temperature of 1 lb. of water by 1°F is now called a British thermal unit (Btu) and the currently accepted value for J is 778.0 foot-pounds per Btu. So, Rumford’s data did give a value of the correct order of magnitude. James Joule had no doubt that the caloric theory was fundamentally flawed. He arrived at this conclusion with growing conviction through a long series of experimental investigations starting in the late 1830s and extending through the 1840s. In fact, Joule’s suspicions concerning the relation between heat and work may stem from an even earlier period. In 1813, the engineer Peter Ewart published a paper in the Manchester Memoirs urging his readers to accept the principle of the conservation of vis viva. The term vis viva literally means living force and was defined as mass multiplied by velocity squared, i.e. twice the kinetic energy. Ewart wrote, ‘If we could get rid of all the imperfections in our steam engines we should find that a certain amount of heat always yielded a fixed equivalent of work’. The notable point is that John Dalton helped to write this paper and so it may have been through Dalton The 1830s was a decade of great advances in the science and application of electricity. In 1831, Michael Faraday (1791–1867) discovered the phenomenon of electromagnetic induction and this was rapidly followed by the invention of the electric motor and generator, clear demonstrations of the inter-convertibility of mechanical and electrical work. The world was suddenly transfixed by the possibilities of electricity and James Joule was no exception. Most of his early experiments were electrically based and he acquired a laboratory stocked with electric batteries, electromagnets, motors, generators and galvanometers, most of which he made himself. In 1839, Joule performed a series of experiments in which he discovered two electrical energy relationships, though he made no claim to originality. Firstly, he noted that the power output from his electric motor was proportional to the product of the current and the electromotive force. Secondly, he found that the heat produced by an electric current was proportional to the square of the current and the resistance of the wire (Joule heating) and was independent of the shape, size or form of the circuit. Some of this work was submitted to Philosophical Transactions of the Royal Society and was rejected. Joule later said , ‘I was not surprised. I could imagine those gentlemen in London sitting round a table and saying to each other, “What good can come out of a town where they dine in the middle of the day?”.’ In the early 1840s, Joule applied his experimental expertise to investigate the generation of heat in electrical, chemical, mechanical and fluid systems. With this broader remit he began to realize that the results from a variety of quite different experiments were indicative of an underlying principle of much greater generality. The experiments involved measurements on electric generators and motors to calculate the mechanical equivalent of heat but the accuracy was not good and he obtained a variety of values between 587 and 1040 foot-pounds per Btu. He also devised an experiment in which water was heated by being forced through narrow tubes and obtained a value of 770 foot-pounds per Btu. When writing up this work he stated that he would lose no time in repeating and extending the experiments, ‘being satisfied that the grand agents of nature are, by the Creator’s fiat, indestructible, and that wherever mechanical force is expended, an exact equivalent of heat is always obtained’ This was an early qualitative statement of the conservation of energy, albeit backed up by some questionable religious evidence. Despite the mediocre accuracy, Joule now suspected that he had discovered a universal constant of physics governing the conversion of work into heat and vice versa. He presented his results at a British Association meeting in Cork in Ireland society publishing but the scientific community ignored his paper; it was still believed that Fourier had finalized the theory of heat in his treatise of 1822. Arguments supporting a kinetic theory of heat continued to appear sporadically but there was little support from the universities and influential institutions such as the Royal Society. In 1846, the scientific grandee Sir John Herschel, replying to John Waterston (a pioneer of the kinetic theory of gases), brushed him aside with, ‘I trust however that you will excuse me if I say that I have no time for the subject’. Undeterred, Joule ploughed on. This time he investigated the changes in temperature produced by the expansion and compression of air. The experiments were carried out with two cylinders joined via a stopcock. One side was pressurized and the cylinders were placed in a water bath. When the valve was opened there was no change in the water temperature (because no overall work was done and the internal energy of the air remained the same) but further measurements showed that the cylinder subject to the expansion was cooled while that subject to the compression was heated by almost exactly the same amount. The experiments gave values for J of 820, 814 and 760 foot-pounds per Btu.
James Prescott Joule (1818 − 1889) was a self-educated British physicist and brewer whose work in the mid nineteenth century contributed to the establishment of the energy concept. The international unit of energy bears
his name:
1 Joule [J] = 1 Watt-second [Ws] = 1 V A s = 1 N m = 1 kg m2s−2.
It takes about 1 J to raise a 100-g-apple 1 m. Energy units can be preceded
by various factors, including the following:
kilo (k=103), mega (M=106), giga (G=109), tera (T=1012), peta (P=1015),
Exa (E=1018).
Thus, a kiloJoule (kJ) is 1000 Joules and a mega Joule (MJ) is 1,000,000 Joules.
A related unit is the Watt, which is a unit of power (energy per unit time). Power units can be converted to energy units through multiplication by seconds [s], hours, [h], or years [yr].
For example, 1 kWh [kilowatt hour] = 3.6 MJ [mega Joule]. With 1 kWh, about 10 liters of water can be heated from 20 ºC to the boiling point.
There are many other energy units besides the “Systèm International d’Unités (SI)”. A “ton of coal equivalent” (tce) is frequently used in the energy business. 1 tce equals 8.141 MWh. It means that the combustion of 1 kg of coal produces the same amount of heat as electrical heating for one hour at a rate of 8.141 kW.
More Units of Energy:
1 calIT = 4.1868 J, International Table calorie
1 calth = 4.184 J, thermochemical calorie
1 cal15 ≈ 4.1855 J, calories to heat from 14.5 °C to 15.5 °C
1 erg = 10−7 J, cgs [centimeter-gram-second] unit
1 eV ≈ 1.60218 × 10−19 J, electron volt
1 Eh ≈ 4.35975 × 10−18 J, Hartree, atomic energy unit
1 Btu = 1055.06 J, British thermal unit according to ISO, to heat 1 pound water from 63 °F to 64 °F
1 tce = 29.3076 × 109 J, ton of coal equivalent, 7000 kcalIT
1 toe = 41.868 × 109 J, ton of oil equivalent, 10000 kcalIT
Calories and/or kilocalories [cal and/or kcal] were historically often used to measure heat (energy) and are still used fot thi sometimes today. Heating a gram of water 1 ºC requires 1 cal. Different definitions are often the result of inconsistent starting temperatures of the heating.
Multiplication Table of Units:

Symbol Exponential Prefix Quantity
k 103 kilo thousand
M 106 mega million
G 109 giga billion
T 1012 tera trillion
P 1015 peta quadrillion
E 1018 exa quintillion

The unit Megagram is not used, since there is a special
name for one million grams, one ton (t): 1 t = 1000 kg.
Multiplication of the Units of Power with Units of Time:
When the Watt is multiplied by a unit of time, an energy unit is formed as follows: 1 Ws = 1 J.
The use of the kilowatt-hour is more common: 1 kWh = 3600 kWs = 3.6 MJ. Besides the second [s] and the hour [h], the day [d] and the year [yr] are also used,
with 1 yr = 365.2425 d = 31,556,952 s. So, for example, energy of one Megawatt-year can be written as 1 MWyr = 31.557952 TJ (TeraJoule).
The annual consumption of 1 toe/yr corresponds to the daily consumption of about 31.56 kWh/d.The annual consumption of 1 GJ/yr corresponds to the daily consumption of about 0.7605 kWh/d.
Conversion of Energy Units:
The unit conversions indicated on this page can be performed with a calculator. One can also find conversion calculators on the internet such as the International Energy Agency, unit conversion.or and at Robert Fogt.
Joule , unit of work or energy in the International System of Units (SI); it is equal to the work done by a force of one newton acting through one metre. Named in honour of the English physicist James Prescott Joule , it equals 107 ergs, or approximately 0.7377 foot-pounds.
The theory for electrical energy and power was developed using the principles of
mechanical energy, and the units of energy are the same for both electrical and
mechanical energy. However, heat energy is typically measured in quantities that are
separately defined from the laws of mechanics and electricity and magnetism. Sir James
Joule first studied the equivalence of these two forms of energy and found that there was
a constant of proportionality between them and this constant is therefore referred to as the
Joule equivalent of heat and given the symbol J. The Joule equivalent of heat is the
amount of mechanical or electrical energy contained in a unit of heat energy. The factor
is to be determined in this experiment.
Power is defined as the rate of doing work, and electrical power is defined as the amount
of electrical energy being expended per unit time. The work ∆W (mechanical energy)
required to move an electrical charge ∆Q through a potential difference V is given by
∆ =∆ × W QV (1)
and power is P is given by
W Qso that
PVI = × . (3)
In an electrical circuit the energy ∆W expended in a increment of time, ∆t , in a
resistance is given by
∆ = ×∆ WP t (4)
which can be written as
∆ = × ×∆ WVI t (5)
when Equation (3) is substituted for P.
Electrical and mechanical energy is measured in units of joules in the SI system of units,
but heat energy is measured in units of kilocalories.
The change in heat energy of a material, ∆Q , is directly proportional to the change in
temperature of the material and depends on the type of material and its mass. The change
is heat energy, ∆Q , for a given change of temperature, ∆T , is given by
∆= ∆ Q mc T (6)
where m is the mass of the material and c the specific heat of the material. If electrical
energy is transformed into heat energy then the equivalence of the electrical energy and
heat energy is given by
∆ = ×∆ WJ Q (7)
where J is the Joule equivalent of heat or the mechanical energy equivalent of heat
energy. In SI units, J = 4186 Joules/kilocalorie .
In this experiment a constant current I will be used to flow through a resistive heating
element and a constant potential drop V across the element will be maintained. The
electrical energy expended in the heating element will be transformed into heat energy
that is will increase the temperature of a quantity of water and the container in which it is
kept. The change in heat energy of the container and water will be the sum of the heat
energies of each and will be given by
∆ = ∆+ ∆ Q mc T m c T cc ww (8)
where mc and mw are the masses of the container and water respectively, and cc and cw are
the specific heats of the material of the container and water.
VI t J m c T m c T ×∆ = ∆ + ∆ ( cc ww ). P V