Watt

This article is about the unit of power. For other uses, see Watt (disambiguation).

"MWT" redirects here. For the former Australian theatre company, see Melbourne Workers Theatre.

"Joules per second" redirects here, it should not be confused with Joule-second

The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m²⋅s⁻³.^[1][2][3] It is used to quantify the rate of energy transfer. The watt is named in honor of James Watt (1736–1819), an 18th-century Scottish inventor, mechanical engineer, and chemist who improved the Newcomen engine with his own steam engine in 1776. Watt's invention was fundamental for the Industrial Revolution.

watt
A 420-watt power supply
General information
Unit system	SI
Unit of	power
Symbol	W
Named after	James Watt
Conversions
1 W in ...	... is equal to ...
SI base units	1 kg⋅m2⋅s−3
CGS units	107 erg⋅s−1
English Engineering Units	0.7375621 ft⋅lbf/s = 0.001341022 hp

Overview

When an object's velocity is held constant at one meter per second against a constant opposing force of one newton, the rate at which work is done is one watt. $${\displaystyle \mathrm {1~W=1~J{/}s=1~N{\cdot }m{/}s=1~kg{\cdot }m^{2}{\cdot }s^{-3}} .}$$

In terms of electromagnetism, one watt is the rate at which electrical work is performed when a current of one ampere (A) flows across an electrical potential difference of one volt (V), meaning the watt is equivalent to the volt-ampere (the latter unit, however, is used for a different quantity from the real power of an electrical circuit). $${\displaystyle \mathrm {1~W=1~V{\cdot }A} .}$$

Two additional unit conversions for watt can be found using the above equation and Ohm's law. $${\displaystyle \mathrm {1~W=1~V^{2}/\Omega =1~A^{2}{\cdot }\Omega } ,}$$ where ohm (${\displaystyle \Omega }$) is the SI derived unit of electrical resistance.

Examples

• A person having a mass of 100 kg who climbs a 3-meter-high ladder in 5 seconds is doing work at a rate of about 600 watts. Mass times acceleration due to gravity times height divided by the time it takes to lift the object to the given height gives the rate of doing work or power.^{[lower-roman 1]}
• A laborer over the course of an eight-hour day can sustain an average output of about 75 watts; higher power levels can be achieved for short intervals and by athletes.^[4]

Origin and adoption as an SI unit

The watt is named after the Scottish inventor James Watt.^[5] The unit name was proposed by C. William Siemens in August 1882 in his President's Address to the Fifty-Second Congress of the British Association for the Advancement of Science.^[6] Noting that units in the practical system of units were named after leading physicists, Siemens proposed that watt might be an appropriate name for a unit of power.^[7] Siemens defined the unit within the existing system of practical units as "the power conveyed by a current of an Ampère through the difference of potential of a Volt".^[8]

In October 1908, at the International Conference on Electric Units and Standards in London,^[9] so-called international definitions were established for practical electrical units.^[10] Siemens' definition was adopted as the international watt. (Also used: 1 A² × 1 Ω.)^[5] The watt was defined as equal to 10⁷ units of power in the practical system of units.^[10] The "international units" were dominant from 1909 until 1948. After the 9th General Conference on Weights and Measures in 1948, the international watt was redefined from practical units to absolute units (i.e., using only length, mass, and time). Concretely, this meant that 1 watt was defined as the quantity of energy transferred in a unit of time, namely 1 J/s. In this new definition, 1 absolute watt = 1.00019 international watts. Texts written before 1948 are likely to be using the international watt, which implies caution when comparing numerical values from this period with the post-1948 watt.^[5] In 1960, the 11th General Conference on Weights and Measures adopted the absolute watt into the International System of Units (SI) as the unit of power.^[11]

Multiples

For additional examples of magnitude for multiples and submultiples of the watt, see Orders of magnitude (power).

SI multiples of watt (W)

Submultiples			Multiples
Value	SI symbol	Name	Value	SI symbol	Name
10−1 W	dW	deciwatt	101 W	daW	decawatt
10−2 W	cW	centiwatt	102 W	hW	hectowatt
10−3 W	mW	milliwatt	103 W	kW	kilowatt
10−6 W	μW	microwatt	106 W	MW	megawatt
10−9 W	nW	nanowatt	109 W	GW	gigawatt
10−12 W	pW	picowatt	1012 W	TW	terawatt
10−15 W	fW	femtowatt	1015 W	PW	petawatt
10−18 W	aW	attowatt	1018 W	EW	exawatt
10−21 W	zW	zeptowatt	1021 W	ZW	zettawatt
10−24 W	yW	yoctowatt	1024 W	YW	yottawatt
10−27 W	rW	rontowatt	1027 W	RW	ronnawatt
10−30 W	qW	quectowatt	1030 W	QW	quettawatt
Common multiples are in bold face

Attowatt

The sound intensity in water corresponding to the international standard reference sound pressure of 1 μPa is approximately 0.65 aW/m².^[12]

Femtowatt

Powers measured in femtowatts are typically found in references to radio and radar receivers. For example, meaningful FM tuner performance figures for sensitivity, quieting and signal-to-noise require that the RF energy applied to the antenna input be specified. These input levels are often stated in dBf (decibels referenced to 1 femtowatt). This is 0.2739 microvolts across a 75-ohm load or 0.5477 microvolt across a 300-ohm load; the specification takes into account the RF input impedance of the tuner.

Picowatt

Powers measured in picowatts are typically used in reference to radio and radar receivers, acoustics and in the science of radio astronomy. One picowatt is the international standard reference value of sound power when this quantity is expressed in decibels.^[13]

Nanowatt

Powers measured in nanowatts are also typically used in reference to radio and radar receivers.

Microwatt

Powers measured in microwatts are typically stated in medical instrumentation systems such as the electroencephalograph (EEG) and the electrocardiograph (ECG), in a wide variety of scientific and engineering instruments and also in reference to radio and radar receivers. Compact solar cells for devices such as calculators and watches are typically measured in microwatts.^[14]

Milliwatt

A typical laser pointer outputs about five milliwatts of light power, whereas a typical hearing aid uses less than one milliwatt.^[15] Audio signals and other electronic signal levels are often measured in dBm, referenced to one milliwatt.

Kilowatt

"Kilowatt" and "Kilowatts" redirect here. For the musician James Watts, see KiloWatts (musician).

"kW" redirects here. For other uses, see kW (disambiguation).

The kilowatt is typically used to express the output power of engines and the power of electric motors, tools, machines, and heaters. It is also a common unit used to express the electromagnetic power output of broadcast radio and television transmitters.

One kilowatt is approximately equal to 1.34 horsepower. A small electric heater with one heating element can use 1 kilowatt. The average electric power consumption of a household in the United States is about 1 kilowatt.^{[lower-roman 2]}

A surface area of 1 square meter on Earth receives typically about one kilowatt of sunlight from the Sun (the solar irradiance) (on a clear day at midday, close to the equator).^[17]

Megawatt

Many events or machines produce or sustain the conversion of energy on this scale, including large electric motors; large warships such as aircraft carriers, cruisers, and submarines; large server farms or data centers; and some scientific research equipment, such as supercolliders, and the output pulses of very large lasers. A large residential or commercial building may use several megawatts in electric power and heat. On railways, modern high-powered electric locomotives typically have a peak power output of 5 or 6 MW, while some produce much more. The Eurostar e300, for example, uses more than 12 MW, while heavy diesel-electric locomotives typically produce and use 3 and 5 MW. U.S. nuclear power plants have net summer capacities between about 500 and 1300 MW.^{[18]: 84–101}

The earliest citing of the megawatt in the Oxford English Dictionary (OED) is a reference in the 1900 Webster's International Dictionary of the English Language. The OED also states that megawatt appeared in a November 28, 1947, article in the journal Science (506:2).

A United States Department of Energy video explaining gigawatts

Gigawatt

A gigawatt is typical average power for an industrial city of one million habitants and also the output of a large power station. The GW unit is thus used for large power plants and power grids. For example, by the end of 2010, power shortages in China's Shanxi province were expected to increase to 5–6 GW^[19] and the installation capacity of wind power in Germany was 25.8 GW.^[20] The largest unit (out of four) of the Belgian Doel Nuclear Power Station has a peak output of 1.04 GW.^[21] HVDC converters have been built with power ratings of up to 2 GW.^[22]

Terawatt

The primary energy used by humans worldwide was about 160,000 terawatt-hours in 2019, corresponding to an average continuous power consumption of 18 TW that year.^[23] Earth itself emits 47±2 TW,^[24] far less than the energy received from solar radiation. The most powerful lasers from the mid-1960s to the mid-1990s produced power in terawatts, but only for nanosecond intervals. The average lightning strike peaks at 1 TW, but these strikes only last for 30 microseconds.

Petawatt

See also: List of petawatt lasers

A petawatt can be produced by the current generation of lasers for time scales on the order of picoseconds. One such laser is Lawrence Livermore's Nova laser, which achieved a power output of 1.25 PW by a process called chirped pulse amplification. The duration of the pulse was roughly 0.5 ps, giving a total energy of 600 J.^[25] Another example is the Laser for Fast Ignition Experiments (LFEX) at the Institute of Laser Engineering (ILE), Osaka University, which achieved a power output of 2 PW for a duration of approximately 1 ps.^[26][27]

Based on the average total solar irradiance of 1.361 kW/m²,^[28] the total power of sunlight striking Earth's atmosphere is estimated at 174 PW. The planet's average rate of global warming, measured as Earth's energy imbalance, reached about 0.5 PW (0.3% of incident solar power) by 2019.^[29]

Yottawatt

The power output of the Sun is 382.8 YW, about 2 billion times the power estimated to reach Earth's atmosphere.^[30]

Conventions in the electric power industry

In the electric power industry, megawatt electrical (MWe^[31] or MW_e)^[32] refers by convention to the electric power produced by a generator, while megawatt thermal or thermal megawatt^[33] (MWt, MW_t, or MWth, MW_th) refers to thermal power produced by the plant. For example, the Embalse nuclear power plant in Argentina uses a fission reactor to generate 2,109 MW_t (i.e. heat), which creates steam to drive a turbine, which generates 648 MW_e (i.e. electricity). Other SI prefixes are sometimes used, for example gigawatt electrical (GW_e). The International Bureau of Weights and Measures, which maintains the SI-standard, states that further information about a quantity should not be attached to the unit symbol but instead to the quantity symbol (e.g., P_th = 270 W rather than P = 270 W_th) and so these unit symbols are non-SI.^[34] In compliance with SI, the energy company Ørsted A/S uses the unit megawatt for produced electrical power and the equivalent unit megajoule per second for delivered heating power in a combined heat and power station such as Avedøre Power Station.^[35]

When describing alternating current (AC) electricity, another distinction is made between the watt and the volt-ampere. While these units are equivalent for simple resistive circuits, they differ when loads exhibit electrical reactance.

Radio transmission

Main article: Effective radiated power

Radio stations usually report the power of their transmitters in units of watts, referring to the effective radiated power. This refers to the power that a half-wave dipole antenna would need to radiate to match the intensity of the transmitter's main lobe.

Distinction between watts and watt-hours

The terms power and energy are closely related but distinct physical quantities. Power is the rate at which energy is generated or consumed and hence is measured in units (e.g. watts) that represent energy per unit time.

For example, when a light bulb with a power rating of 100W is turned on for one hour, the energy used is 100 watt hours (W·h), 0.1 kilowatt hour, or 360 kJ. This same amount of energy would light a 40-watt bulb for 2.5 hours, or a 50-watt bulb for 2 hours.

Power stations are rated using units of power, typically megawatts or gigawatts (for example, the Three Gorges Dam in China is rated at approximately 22 gigawatts). This reflects the maximum power output it can achieve at any point in time. A power station's annual energy output, however, would be recorded using units of energy (not power), typically gigawatt hours. Major energy production or consumption is often expressed as terawatt hours for a given period; often a calendar year or financial year. One terawatt hour of energy is equal to a sustained power delivery of one terawatt for one hour, or approximately 114 megawatts for a period of one year:

Power output = energy / time

1 terawatt hour per year = 1×10¹² W·h / (365 days × 24 hours per day) ≈ 114 million watts,

equivalent to approximately 114 megawatts of constant power output.

The watt-second is a unit of energy, equal to the joule. One kilowatt hour is 3,600,000 watt seconds.

While a watt per hour is a unit of rate of change of power with time,^{[lower-roman 3]} it is not correct to refer to a watt (or watt-hour) as a watt per hour.^[36]

See also

• Energy portal
• Engineering portal
• Physics portal

• Kibble balance (formerly known as a watt balance)
• Nominal power (photovoltaic)
• One Watt Initiative
• Power factor
• Solar constant
• Wattage conversion factors
• Wattmeter

Explanatory notes

1. The energy in climbing the stairs is given by mgh. Setting m = 100 kg, g = 9.8 m/s² and h = 3 m gives 2940 J. Dividing this by the time taken (5 s) gives a power of 588 W.
2. Average household electric power consumption is 1.19 kW in the US, 0.53 kW in the UK. In India it is 0.13 kW (urban) and 0.03 kW (rural) – computed from GJ figures quoted by Nakagami, Murakoshi and Iwafune.^[16]
3. Watts per hour refers to the rate of change of power being used (or generated). For example, a power plant that changes its power output from 100 MW to 200 MW in 15 minutes would have a ramp-up rate of 400 MW/h. Gigawatts per hour are used to characterize the ramp-up required of the power plants on an electric grid to compensate for loss of output from other sources, such as when solar power generation drops to zero as the sun sets. See duck curve.

References

1. Newell, David B; Tiesinga, Eite (2019). The international system of units (SI) (PDF) (Report). Gaithersburg, MD: National Institute of Standards and Technology. doi:10.6028/nist.sp.330-2019. §2.3.4, Table 4.
2. Yildiz, I.; Liu, Y. (2018). "Energy units, conversions, and dimensional analysis". In Dincer, I. (ed.). Comprehensive energy systems. Vol 1: Energy fundamentals. Elsevier. pp. 12–13. ISBN 9780128149256.
3. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), pp. 118, 144, ISBN 92-822-2213-6, archived (PDF) from the original on June 4, 2021, retrieved December 16, 2021
4. Avallone, Eugene A; et al., eds. (2007), Marks' Standard Handbook for Mechanical Engineers (11th ed.), New York: Mc-Graw Hill, pp. 9–4, ISBN 978-0-07-142867-5.
5. Klein, Herbert Arthur (1988) [1974]. The Science of measurement: A historical survey. New York: Dover. p. 239. ISBN 9780486144979.
6. "Address by C. William Siemens". Report of the Fifty-Second meeting of the British Association for the Advancement of Science. Vol. 52. London: John Murray. 1883. pp. 1–33.
7. Siemens supported his proposal by asserting that Watt was the first who "had a clear physical conception of power, and gave a rational method for measuring it". "Siemens, 1883, p. 6"
8. Report of the British Association for the Advancement of Science. Vol. 52nd Meeting (1882). April 3, 1883.
9. Tunbridge, P. (1992). Lord Kelvin: His Influence on Electrical Measurements and Units. Peter Peregrinus: London. p. 51. ISBN 0-86341-237-8.
10. Fleming, John Ambrose (1911). "Units, Physical" . In Chisholm, Hugh (ed.). Encyclopædia Britannica. Vol. 27 (11th ed.). Cambridge University Press. pp. 738–745, see page 742.
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13. Morfey, C.L. (2001). Dictionary of Acoustics.
14. "Bye-Bye Batteries: Radio Waves as a Low-Power Source", The New York Times, July 18, 2010, archived from the original on March 21, 2017.
15. Stetzler, Trudy; Magotra, Neeraj; Gelabert, Pedro; Kasthuri, Preethi; Bangalore, Sridevi. "Low-Power Real-Time Programmable DSP Development Platform for Digital Hearing Aids". Datasheet Archive. Archived from the original on March 3, 2011. Retrieved February 8, 2010.
16. Nakagami, Hidetoshi; Murakoshi, Chiharu; Iwafune, Yumiko (2008). International Comparison of Household Energy Consumption and Its Indicator (PDF). ACEEE Summer Study on Energy Efficiency in Buildings. Pacific Grove, California: American Council for an Energy-Efficient Economy. Figure 3. Energy Consumption per Household by Fuel Type. 8:214–8:224. Archived (PDF) from the original on January 9, 2015. Retrieved February 14, 2013.
17. Elena Papadopoulou, Photovoltaic Industrial Systems: An Environmental Approach, Springer 2011 ISBN 3642163017, p.153
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19. Bai, Jim; Chen, Aizhu (November 11, 2010). Lewis, Chris (ed.). "China's Shanxi to face 5–6 GW power shortage by yr-end – paper". Peking: Reuters. Archived from the original on November 21, 2020.
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35. "Avedøre Power Station (Avedøre værket)". DONG Energy. Archived from the original on March 17, 2014. Retrieved March 17, 2014.
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• Media related to Watt at Wikimedia Commons
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• Borvon, Gérard. "History of the electrical units".
• Nelson, Robert A. (February 2000). The International System of Units: Its History and Use in Science and Industry. Via Satellite. ATI courses.