Watt (W)

Definition, derivation and practical power measurement in the International System of Units

Power states how fast energy is converted: how much work is done or heat given off per unit of time. We meet it daily on lamps, electricity bills, engines and power stations. In the International System of Units (SI), power is measured in watts, symbol W. The watt is a derived SI unit, defined entirely through the base units kilogram, metre and second, with no definition of its own beside them.

The watt is often confused with energy units such as the kilowatt-hour, and horsepower lives on in the motoring world. To sort this out it is necessary, as with the base units, to distinguish between definition, realization and practical power measurement.

The definition of the watt in the SI system

The watt is defined within the SI as:

one watt is the power corresponding to an energy conversion of one joule per second.

In other SI units, 1 W = 1 J/s = 1 N·m/s = 1 V·A, and in base units 1 W = 1 kg·m²·s⁻³. The definition rests on:

the joule, the SI unit of energy and work,
the second, defined via the hyperfine transition of the caesium-133 atom,
indirectly the kilogram and the metre, on which the joule in turn is built.

The relation 1 W = 1 V·A also ties the watt to the volt and the ampere, which decides how the unit is realized.

Fact box: the history of the watt

Year	Event
1782	James Watt (1736-1819) introduces the horsepower as a measure of the output of his steam engines.
1882	The British Association adopts the name watt, proposed by C. W. Siemens, for the unit joule per second.
1889	The International Electrical Congress includes the watt among the practical electrical units.
1948	The 9th CGPM establishes the watt as an absolute unit in the MKS system.
1960	The watt becomes part of the newly created International System of Units, the SI.
2019	The SI revision fixes h and e, so that electrical power can be realized exactly via the Josephson and quantum Hall effects.

How much is one watt?

One watt is a modest power: roughly the heat from a small LED lamp, or the power needed to lift 100 grams by one metre every second. Some reference values:

LED lamp: 5-10 W,
human basal metabolism: 80-100 W,
electric kettle: about 2 kW,
passenger car at full throttle: around 100 kW,
wind turbine: several MW,
nuclear reactor: around 1 GW,
Sweden’s electricity demand: 15-25 GW depending on the season.

Definition, realization and use

Power metrology keeps three levels apart:

The definition states what the watt is in principle: one joule per second.
The realization refers to the experiments that produce a power of known value, traceable to the base units.
The use refers to power measurement in electricity grids, industry, laboratories and households.

The watt has no primary standard of its own. Power is realized through combinations of other units’ standards, and the electrical route gives the lowest uncertainty.

How the watt is realized

Electrical power is the product of voltage and current, P = U·I. The voltage is realized with Josephson standards and the current via the voltage across a quantum Hall resistance. Since the SI revision of 2019 gave the Planck constant h and the elementary charge e exact values, these realizations are exact within the SI, and the electrical watt is traceable to h, e and the atomic second.

Mechanical power is realized as force times velocity or torque times angular velocity. The best-known link between the two is the Kibble balance, formerly the watt balance, where mechanical power m·g·v is balanced against electrical power U·I. That equality is what has realized the kilogram since 2019, so the watt and the kilogram are bound together at the foundation of the SI.

Practical power measurement and sources of error

In alternating-current circuits, power must be calculated from RMS values and the phase shift between voltage and current. The active power in watts is then smaller than the apparent power in volt-amperes (VA); the ratio is the power factor. A device rated at 1 000 VA does not necessarily deliver 1 000 W.

Other sources of error are the instruments’ own consumption, the temperature dependence of shunts and transducers and, in thermal measurement, heat losses to the surroundings. In electricity grids, the phase errors of instrument transformers affect the measured value directly.

The watt and other derived units

The watt connects the units of mechanics and of electricity with each other:

Unit	Quantity	Relation to the watt
joule (J)	Energy	1 W = 1 J/s
volt (V)	Electric potential	1 W = 1 V·A
newton (N)	Force	1 W = 1 N·m/s
pascal (Pa)	Pressure	1 W = 1 Pa·m³/s
kilowatt-hour (kWh)	Energy (outside the SI)	1 kWh = 3 600 000 J = 3.6 MJ

Watt, kilowatt-hour and horsepower: multiples and common conversions

The common multiples are the milliwatt (1 mW = 0.001 W), the kilowatt (1 kW = 1 000 W), the megawatt (1 MW = 10⁶ W), the gigawatt (1 GW = 10⁹ W) and the terawatt (1 TW = 10¹² W). The kilowatt-hour is not a unit of power but of energy: what 1 kW converts in one hour, exactly 3.6 MJ. How many kWh 100 W corresponds to can only be answered with a time: 100 W for 10 hours gives 1 kWh.

Horsepower lives on in the context of engines. The metric horsepower is 735.498 75 W and the imperial horsepower about 745.7 W, so 100 metric horsepower corresponds to about 73.5 kW.

Conversions are done directly in the power converter on Konvertera.nu. The unit watt and all power units are collected there, and energy units such as the kilowatt-hour and the joule in the energy converter.

Summary

The watt is the SI unit of power, one joule per second, or kg·m²·s⁻³ in base units. The relation 1 W = 1 V·A makes it as much at home in electrical engineering as in mechanics, and the electrical route gives its most accurate realization.

Distinguishing power from energy, watts from kilowatt-hours, and knowing what horsepower and volt-amperes actually state is the key to using the unit correctly. Through Josephson and quantum Hall standards and the Kibble balance, the watt is today realized with traceability to the constants of nature.