Joule

The joule, symbol J, is the coherent derived unit of energy, work, and heat in the International System of Units (SI). One joule is the work done by a force of one newton when its point of application moves one metre in the force’s direction. It also equals the energy transferred by one watt of power in one second. The unit is named after James Prescott Joule, whose experiments investigated the quantitative relationship between mechanical work and heating. (bipm.org)

Definition and dimensions

In terms of SI units,

Here N denotes the newton, the SI unit of force, while kg, m, and s denote the kilogram, metre, and second. The joule is therefore a derived unit rather than a base unit: its dimensions are mass multiplied by length squared and divided by time squared. Calling it coherent means that its expression in base units requires no numerical conversion factor other than one. (nist.gov)

The definition concerns force and displacement, not simply moving a particular mass through a particular distance. For a constant force acting at an angle $\theta$ to a straight displacement, work is $W=Fd\cos\theta$. A perpendicular force does no work; a force opposing motion does negative work. Thus, specifying displacement alone cannot determine an energy transfer. (openstax.org)

Mechanical interpretation

In classical mechanics, the joule measures both kinetic energy and potential energy. For a body of mass $m$ moving at speed $v$, its translational kinetic energy is

As a calculated illustration, a 2 kg body moving at 1 m/s has 1 J of kinetic energy. The work–energy theorem states that the net work done on a body equals the change in its kinetic energy. This connects the force-and-displacement definition directly with energy associated with motion. (openstax.org)

Although torque has the same base-unit dimensions as energy, its SI unit is written newton metre, N m, rather than joule. Torque describes a force’s rotational effect; energy describes a different physical quantity. Equal dimensions do not make quantities interchangeable, and retaining distinct unit expressions helps identify what is being measured. (bipm.org)

Electrical energy and power

The joule also connects mechanical energy measurements with electrical quantities:

A coulomb of electric charge transferred through an electric potential difference of one volt corresponds to one joule of energy. The watt, symbol W, measures power—the rate of energy transfer—and equals one joule per second. Energy and power therefore answer different questions: how much is transferred, and how rapidly it is transferred. (nist.gov)

For constant power $P$ maintained over a time interval $t$, the transferred energy is $E=Pt$. A calculated example is a device operating at 100 W for 10 s, which transfers 1,000 J. A watt second is an energy unit equivalent to a joule; it must not be confused with a watt per second, which measures a rate of change of power. (openstax.org)

Heat and thermodynamics

In thermodynamics, heat and work are modes of energy transfer, whereas internal energy is a property of a system. All three are expressed in joules. Under the convention that $Q$ is heat supplied to a system and $W$ is work done by it, the first law of thermodynamics is

The common unit permits thermal and mechanical transfers to be included in the same energy balance. (openstax.org)

Energy should not be confused with temperature. A specified energy input does not imply a universal temperature increase: the response depends on the substance, amount of material, and process. In calorimetry, heating measurements relate transferred energy to temperature changes and thermal properties. (openstax.org)

The joule also appears in compound units. Heat capacity and entropy are measured in J/K, using the kelvin; molar energy is measured in J/mol, using the mole; and energy density is measured in J/m³. These expressions describe different quantities, not alternative magnitudes of energy itself. (bipm.org)

Multiples and conversions

SI prefixes provide convenient scales: a kilojoule (kJ) is $10^3$ J, a megajoule (MJ) is $10^6$ J, and a gigajoule (GJ) is $10^9$ J. Common conversions include:

Different historical calorie definitions have slightly different conversion factors, so precision requires specifying the convention. (nist.gov)

The electronvolt is exactly $1.602176634\times10^{-19}$ J. Its very small size provides another scale for expressing energy without changing the underlying physical quantity. (physics.nist.gov)

Historical basis and notation

Joule’s paddle-wheel experiments used falling weights to stir liquids. He compared the mechanical work supplied with the resulting heating, reporting detailed measurements in his 1850 paper On the Mechanical Equivalent of Heat. In 1948, the General Conference on Weights and Measures ratified the mechanical definition of the joule and identified it as the unit of quantity of heat. (commons.princeton.edu)

The name joule is normally lowercase, but its symbol J is uppercase because the unit commemorates a person. Symbols are upright, do not take plural endings, and are separated from numerical values by a space: 25 J, not 25 Js. Prefix symbols attach directly, as in 25 kJ. (nist.gov)