Joule
SI derived unit · quantity: energy, work, quantity of heat
01 · Definition
The work of a force of one newton along a path of one metre. About what it takes to lift an apple from the table to shoulder height.
A single definition serves three quantities at once: work, energy and quantity of heat. This came about not from carelessness but from the substance of the matter — all three convert into one another without loss or remainder. Until the middle of the nineteenth century heat was held to be a special substance and measured in calories, work in kilogram-metres, and the link between the two scales had to be established by experiment. Joule showed that this link is constant, and after him the separate units became unnecessary: one joule was left for every form of energy, from a raised weight to warmed water to a charged capacitor.
Work arises when a force acts along a displacement; torque when the force is applied across a lever arm and displaces nothing. The dimension in both cases is kilogram times metre squared per second squared, but the units must not be substituted for one another: bolt tightening torque is written in newton metres and work in joules, and the standard fixes that distinction. A spanner that has tightened a bolt to forty newton metres has done almost no work — the bolt turned a quarter of a revolution.
02 · Conversion
Joules, calories, kilowatt-hours
The factors are exact by definition, but the calorie calls for care: there are several of them and they differ in the third figure. The table uses the international one — four point one eight six eight.
The dietary Calorie is in fact a kilocalorie, a thousand small calories, and European labelling always sets a kilojoule figure beside it. Fifteen hundred kilocalories of daily food come to six point three megajoules. The international calorie is defined as exactly four point one eight six eight joules, the thermochemical one as four point one eight four, and the two are sometimes confused in calculations.
| Unit | Name | Value | Where it is met |
|---|---|---|---|
| J | joule, the SI unit | 1 | physics and engineering |
| kJ | kilojoule | 0.001 | food labelling |
| MJ | megajoule | 1·10⁻⁶ | heat engineering |
| GJ | gigajoule | 1·10⁻⁹ | heating bills |
| W·h | watt-hour | 2.778·10⁻⁴ | batteries |
| kW·h | kilowatt-hour | 2.778·10⁻⁷ | the electricity meter |
| cal | international calorie | 0.2388 | heat engineering, older calculations |
| kcal | kilocalorie, the dietary Calorie | 2.388·10⁻⁴ | food labels |
| Gcal | gigacalorie | 2.388·10⁻¹⁰ | heating bills in Russia |
| erg | erg, the CGS system | 1·10⁷ | physics before the SI |
| BTU | British thermal unit | 9.478·10⁻⁴ | English-language heat engineering |
| kgf·m | kilogram-force metre | 0.102 | older mechanical calculations |
The joule, the watt-second and the newton metre are one and the same. The kilowatt-hour is handier for electricity bills because the power of household appliances is measured in watts and time in hours
03 · Orders of magnitude
from the electronvolt to an earthquakeOne joule — an apple lifted by a metre
04 · Measuring instruments
What energy is measured with
Any energy is most easily turned into heat and measured by the warming of a known mass of water. That is exactly how Joule’s first experiment worked, and how heaters and fuels are certified today — only the thermometers and the insulation have changed.
It multiplies current by voltage and accumulates the result over time. The induction disc counted revolutions, the electronic one counts samples, but the quantity is the same — joules, merely shown as kilowatt-hours, of which three and a half million make one apiece.
A blackened plate absorbs radiation and warms by thousandths of a degree; the thermometer inside it gives the energy. This is how laser power is measured, and the solar flux at a weather station, and the faintest cosmic background radiation in cryogenic rigs.
A bullet lodges in a suspended block, and from the height the block rises one computes its kinetic energy. The method is older than the unit itself and still serves as the reference check in ballistics laboratories.
05 · Writing rules
Capital J, no full stop
The symbol comes from a surname and is therefore capital, while the name in running text is lowercase: joule, but J. The Russian symbol is Дж, three letters, and no full stop follows it. Prefixes are attached closed up: kJ, MJ, GJ.
Torque given in joules is a common and harmful error: the quantities differ although the dimension coincides. The calorie and the kilowatt-hour survive in particular fields by decision of the International Bureau of Weights and Measures, but scientific writing prefers the joule. Food labelling in the European Union must give kilojoules first, with kilocalories beside them, in brackets or on a second line.
06 · Neighbouring units
The joule sits in the middle of a chain: the newton multiplied by distance gives it, and it divided by time gives the watt.
In the neighbouring Simetrium passports: newton and watt on both sides of the chain, calorie and kilowatt-hour as non-SI units of the same quantity, electronvolt for particle physics, and erg from the CGS system.
07 · Historical section
How heat stopped being a substance
The reigning theory held that a weightless substance flowed from hot to cold. It explained heating and cooling well enough, but could not say where the heat of friction came from — and that heat came in any amount you liked.
Benjamin Thompson watched cannon barrels being bored in Munich and noticed that heat came out for as long as the drill turned, without any limit. A substance would have run out; work would not.
A brewer from Salford hung weights on a paddle stirrer in a tank of water and measured the warming to hundredths of a degree. The work of the descending weight yielded a strictly determined quantity of heat — the conversion factor between two worlds.
The name was proposed by Siemens at the British Association meeting of 1882, and the International Congress of Electricians settled it in 1889, still within the scientist’s lifetime. The General Conference on Weights and Measures made the joule the unit of energy, work and heat all at once, and the calorie was left to the kitchen and to old textbooks.
The unit where three scales met
Joule’s experiment was less a discovery than a measurement: he obtained the conversion factor between work and heat and pinned it to the third figure on instruments where the warming amounted to fractions of a degree. The precision came from insulation and patience — the series was repeated for years. After the conservation of energy was accepted, the calorie was defined no longer through water but through the joule, and its present value — four point one eight six eight — is assigned rather than measured. Since 2019 the joule has become an exact quantity by construction as well: the Planck constant is fixed as a number expressed in joule-seconds, and the kilogram is defined through it. The unit of energy has ceased to depend on any substance whatever, including the water on whose warming it all once began.
Catalogue · units of measurement
A passport for every quantity
Seven SI base units, twenty-two derived ones with names of their own, and the non-SI units that neither engineering nor daily life can do without. Each gets its own sheet: definition, conversion, instruments, writing rules. In 16 languages.
SI derived units with names of their own
the joule passport is openSI base units
in terracotta — the kilogram, metre and second, out of which the joule is assembledNon-SI units
in terracotta — energy units of other systemsPassport language
16 languages. The symbol J is international, but habits differ: the European label puts kilojoules first, the American one gives calories only.