Joule (J)
Definition, derivation and practical energy measurement in the International System of Units
Energy unites mechanics, thermodynamics, electricity and chemistry: one unit describes the work of a crane, the heat in a saucepan and the energy content of a food. The joule, symbol J, is the SI unit of energy, work and heat, and one of the most central derived SI units. It is built from the base units kilogram, meter and second.
As with the base units, definition, realization and practical energy measurement must be kept apart. One particular source of confusion, mixing up energy (joules) with power (watts), has its own section below.
The definition of the joule in the SI system
Within the International System of Units (SI) the joule is defined as:
the work done when the point of application of a force of 1 newton is displaced 1 meter in the direction of the force.
In base units, 1 J = 1 N·m = 1 kg·m²·s⁻². The same unit can be written in several equivalent ways:
- 1 J = 1 W·s (power times time),
- 1 J = 1 C·V (charge times voltage),
- 1 J = 1 Pa·m³ (pressure times volume).
That one unit covers mechanical work, electrical energy and heat is no coincidence: it expresses the conservation of energy. The SI revision of 2019 left the definition unchanged, but with the kilogram now defined through the Planck constant, the joule rests entirely on constants of nature.
Fact box: History of the joule
| Year | Event |
| 1843-1850 | James Prescott Joule determines the mechanical equivalent of heat with the paddle-wheel experiment: about 4.15 J per calorie. |
| 1882 | The name joule is proposed for the practical unit of energy. |
| 1889 | The second International Electrical Congress adopts the joule, defined as 10⁷ erg. |
| 1946 | The CGPM defines the joule in the MKS system as the work of 1 newton over 1 meter. |
| 1960 | The joule becomes a derived unit of the newly established SI. |
| 2019 | The kilogram is redefined through the Planck constant; the joule now rests entirely on constants of nature. |
The unit is named after the English physicist James Prescott Joule (1818-1889), whose measurements showed that heat and work are the same quantity.
How much is one joule?
One joule is a small amount of energy: the work needed to lift 100 grams one meter straight up. Some reference values:
- an AA battery: around 10 kJ,
- a slice of bread: around 300 kJ (about 70 kcal),
- one kilowatt-hour: exactly 3.6 MJ,
- a lightning strike: of the order of 1 GJ.
The calorie survives as a unit of food energy. The thermochemical calorie is defined as exactly 4.184 J, so 1 kcal = 4.184 kJ. Atomic physics uses the electronvolt, since 2019 exactly 1.602 176 634 × 10⁻¹⁹ J, because the elementary charge is now fixed.
Joules, watts and kilowatt-hours
The question “how many watts is a joule” has no answer, because the joule measures energy and the watt measures power, that is, energy per unit of time: 1 W = 1 J/s. A 1 W device converts 1 J every second, and a 1 kW device 3.6 MJ in one hour. This is why the kilowatt-hour (kWh) is a unit of energy, not of power.
The relation between joule and kilowatt-hour is exact: 1 kWh = 1,000 W × 3,600 s = 3,600,000 J. Meters, bills and battery capacities use kWh because joules give impractically large numbers, but the quantity is the same.
Definition, realization and use
The three levels must be kept apart:
- The definition states what a joule is in principle: force times distance.
- The realization covers the methods by which a known energy is produced and measured traceably to the base units.
- The use covers energy measurement in grids, industry, buildings, food and research.
How the joule is realized
The joule has no primary standard of its own; it is realized through its component quantities, and the most accurate route is electrical: energy = voltage × current × time. Voltage is realized with Josephson standards, current through resistance from quantum Hall standards, and time through the caesium transition frequency that defines the second. All three are quantum based, which gives a very low uncertainty.
Mechanically, the joule is realized as force times distance, traceable to the newton and the meter, and thermally through calorimetry, where a known electrical energy calibrates the heat measurement. The Kibble balance, which realizes the kilogram, rests on exactly this comparison and ties the two routes together.
Practical energy measurement and error sources
In practice, energy is almost always measured as power integrated over time: electricity meters sum voltage times current, heat meters sum flow times temperature difference, and fuels carry a heating value per kilogram or cubic meter.
The main error sources are the time base, phase errors between voltage and current in AC systems, sensor temperature dependence and, in calorimetry, heat losses. Food energy is calculated from composition with standard factors, not measured directly.
The joule and other derived units
The joule is tied to several other derived SI units and to common units outside the SI:
| Unit | Quantity | Relation to the joule |
| newton (N) | Force | 1 J = 1 N·m |
| watt (W) | Power | 1 W = 1 J/s |
| pascal (Pa) | Pressure | 1 Pa = 1 J/m³ |
| volt (V) | Electric potential | 1 V = 1 J/C |
| electronvolt (eV) | Energy (atomic physics) | 1 eV = 1.602 176 634 × 10⁻¹⁹ J |
| calorie (cal) | Energy (food) | 1 cal = 4.184 J |
| kilowatt-hour (kWh) | Energy (electricity) | 1 kWh = 3.6 MJ |
Multiples and common conversions
Common multiples are millijoule (1 mJ = 10⁻³ J), kilojoule (1 kJ = 10³ J), megajoule (1 MJ = 10⁶ J) and gigajoule (1 GJ = 10⁹ J). Food is labelled in kJ, fuels in MJ or GJ, and electrical energy in kWh.
All conversions between units of energy are exact multiplications by a constant. The joule page and the energy category convert between joules, calories, kilowatt-hours and electronvolts. Converting between energy and power always requires a time and is not a pure unit conversion.
Summary
The joule is the SI unit of energy, work and heat, defined as kg·m²·s⁻² and equal to the newton-meter, the watt-second and the coulomb-volt. That a single unit suffices for every form of energy is an expression of the conservation of energy.
It has no standard of its own and is realized through electrical quantum standards, mechanical work or calorimetry, all traceable to the kilogram, meter and second. The distinction between joules and watts is the most important one for anyone calculating with energy.