Watt
watt  

Unit system  SI derived unit 
Unit of  Power 
Symbol  W 
Named after  James Watt 
Conversions  
1 W in ...  ... is equal to ... 
SI base units  1 kg⋅m^{2}⋅s^{−3} 
CGS units  10^{7} erg⋅s^{−1} 
English Engineering Units  0.7375621 ft⋅lbf/s = 0.001341022 hp 
The watt (symbol: W) is a unit of power or radiant flux. In the International System of Units (SI), it is defined as a derived unit of (in SI base units)^{[1]}^{[2]} 1 kg⋅m^{2}⋅s^{−3} or, equivalently,^{[3]} 1 joule per second. It is used to quantify the rate of energy transfer. The watt is named after James Watt (1736–1819), an 18thcentury Scottish inventor.
Overview
When an object's velocity is held constant at one metre per second against a constant opposing force of one newton, the rate at which work is done is one watt.
 [math]\displaystyle{ \mathrm{1 ~ W = 1 ~ \frac{J}{s} = 1 ~ \frac{N {\cdot} m}{s} = 1 ~ \frac{kg {\cdot} m^2}{s^3}} }[/math]
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 voltampere (the latter unit, however, is used for a different quantity from the real power of an electrical circuit).
 [math]\displaystyle{ \mathrm{1 ~ W = 1 ~ V \cdot 1 ~ A} }[/math]
Two additional unit conversions for watt can be found using the above equation and Ohm's law.
 [math]\displaystyle{ \mathrm{1 ~ W = 1 ~ \frac{V^2}{\Omega} = 1 ~ A^2 {\cdot} \Omega} }[/math]
where ohm ([math]\displaystyle{ \Omega }[/math]) is the SI derived unit of electrical resistance.
Examples
 A person having a mass of 100 kg who climbs a 3metrehigh 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.^{[lowerroman 1]}
 A laborer over the course of an eighthour 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 initially by C. William Siemens in August 1882 in his President's Address to the FiftySecond 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 consistently within the thenexisting 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]} socalled "international" definitions were established for practical electrical units.^{[10]} Siemens' definition was adopted as the "international" watt. (Also used: 1 A^{2} × 1 Ω.)^{[5]} The watt was defined as equal to 10^{7} 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 now 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 post1948 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

Yoctowatt
The yoctowatt (yW) is equal to one septillionth of a watt (10^{−24} W).
Zeptowatt
The zeptowatt (zW) is equal to one sextillionth of a watt (10^{−21} W).
Attowatt
The attowatt (aW) is equal to one quintillionth of a watt (10^{−18} W). The sound intensity in water corresponding to the international standard reference sound pressure of 1 μPa is approximately 0.65 aW/m^{2}.^{[12]}
Femtowatt
The femtowatt (fW) is equal to one quadrillionth of a watt (10^{−15} W). Technologically important powers that are measured in femtowatts are typically found in references to radio and radar receivers. For example, meaningful FM tuner performance figures for sensitivity, quieting and signaltonoise 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 75ohm load or 0.5477 microvolt across a 300ohm load; the specification takes into account the RF input impedance of the tuner.
Picowatt
The picowatt (pW), not to be confused with the much larger petawatt (PW), is equal to one trillionth of a watt (10^{−12} W). Technologically important powers that are 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 as a level in decibels.^{[13]}
Nanowatt
The nanowatt (nW) is equal to one billionth of a watt (10^{−9} W). Important powers that are measured in nanowatts are also typically used in reference to radio and radar receivers.
Microwatt
The microwatt (µW) is equal to one millionth of a watt (10^{−6} W). Important powers that are 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
The milliwatt (mW) is equal to one thousandth of a watt (0.001 W or 10^{−3} W). A typical laser pointer outputs about 5 milliwatts of light power, whereas a typical hearing aid uses less than 1 milliwatt.^{[15]} Audio signals and other electronic signal levels are often measured in dBm, referenced to 1 milliwatt.
Centiwatt
The centiwatt (cW) is equal to one hundredth of a watt (0.01 W or 10^{−2} W).
Deciwatt
The deciwatt (dW) is equal to one tenth of a watt (0.1 W or 10^{−1} W).
Decawatt
The decawatt (daW) is equal to ten watts (10 W or 10^{1} W).
Hectowatt
The hectowatt (hW) is equal to one hundred watts (100 W or 10^{2} W).
Kilowatt
The kilowatt (kW) is equal to one thousand watts (1000 W or 10^{3} W). This unit 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.^{[lowerroman 2]}
A surface area of 1 square meter on Earth receives typically about 1 kilowatt of sunlight from the Sun (the solar irradiance) (on a clear day at midday, close to the equator).^{[17]}
Megawatt
The megawatt (MW) is equal to one million watts (10^{6} W). 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 highpowered electric locomotives typically have a peak power output of 5 or 6 MW, while some produce much more. The Eurostar, for example, uses more than 12 MW, while heavy dieselelectric locomotives typically produce/use 3 and 5 MW. U.S. nuclear power plants have net summer capacities between about 500 and 1300 MW.^{[18]}^{:{{{1}}}}
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 28 November 1947 article in the journal Science (506:2). File:Office of Nuclear Energy video explaining gigawatts.ogv
Gigawatt
The gigawatt (GW) is equal to one billion watts (10^{9} W) or 1 gigawatt = 1000 megawatts. This unit is often used for large power plants or 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 installed 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 terawatt (TW) is equal to one trillion watts (10^{12} W). The primary energy used by humans worldwide was about 160,000 terawatthours in 2019, corresponding to an average continuous power consumption of 18 TW that year.^{[23]} The most powerful lasers from the mid1960s to the mid1990s 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
The petawatt (PW) is equal to one quadrillion watts (10^{15} W) and can be produced by the current generation of lasers for time scales on the order of picoseconds (10^{−12} s). One such laser is the Lawrence Livermore's Nova laser, which achieved a power output of 1.25 PW (1.25×10^{15} W) by a process called chirped pulse amplification. The duration of the pulse was roughly 0.5 ps (5×10^{−13} s), giving a total energy of 600 J.^{[24]} 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.^{[25]}^{[26]}
Based on the average total solar irradiance^{[27]} of 1.366 kW/m^{2}, 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.^{[28]}
Exawatt
The exawatt (EW) is equal to one quintillion watts (10^{18} W).
Zettawatt
The zettawatt (ZW) is equal to one sextillion watts (10^{21} W).
Yottawatt
The yottawatt (YW) is equal to one septillion watts (10^{24} W). The power output of the Sun is 382.8 YW.^{[29]}
Conventions in the electric power industry
In the electric power industry, megawatt electrical (MWe^{[30]} or MW_{e}^{[31]}) refers by convention to the electric power produced by a generator, while megawatt thermal or thermal megawatt^{[32]} (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 2109 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 SIstandard, states that further information about a quantity should not be attached to the unit symbol but instead to the quantity symbol (i.e., P_{thermal} = 270 W rather than P = 270 W_{th}) and so these units are nonSI.^{[33]} 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.^{[34]}
When describing alternating current (AC) electricity, another distinction is made between the watt and the voltampere. While these units are equivalent for simple resistive circuits, they differ when loads exhibit electrical reactance.
Radio transmission
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 halfwave dipole antenna would need to radiate to match the intensity of the transmitter's main lobe.
Distinction between watts and watthours
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 40watt bulb for 2.5 hours, or a 50watt 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 = 1×10^{12} 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 exists in principle (as a unit of rate of change of power with time^{[lowerroman 3]}), it is not correct to refer to a watt (or watt hour) as a "watt per hour".^{[35]}
See also
 Kibble balance (formerly known as a watt balance)
 Nominal power (photovoltaic)
 Power factor
 Solar constant
 Voltampere
 Wattage conversion factors
 Wattmeter
 Primary energy
Explanatory notes
 ↑ The energy in climbing the stairs is given by mgh. Setting m = 100 kg, g = 9.8 m/s^{2} and h = 3 m gives 2940 J. Dividing this by the time taken (5 s) gives a power of 588 W.
 ↑ 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]}
 ↑ Watts per hour would properly refer to a rate of change of power being used (or generated). Watts per hour might be useful to characterize the rampup behavior of power plants, or slowreacting plant where their power could only change slowly. For example, a power plant that changes its power output from 1 MW to 2 MW in 15 minutes would have a rampup rate of 4 MW/h.
References
 ↑ Bureau international des poids et mesures, Le Système international d’unités (SI) / The International System of Units (SI), 9th ed. (Sèvres: 2019), ISBN 978‑92‑822‑2272‑0, §2.3.4, Table 4.
 ↑ Yildiz, I.; Liu, Y. (2018). "Energy units, conversions, and dimensional analysis". in Dincer, I.. Comprehensive energy systems. Vol 1: Energy fundamentals. Elsevier. pp. 12–13. ISBN 9780128149256.
 ↑ International Bureau of Weights and Measures (2006), The International System of Units (SI) (8th ed.), pp. 118, 144, ISBN 9282222136, http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf
 ↑ Avallone, Eugene A, ed. (2007), Marks' Standard Handbook for Mechanical Engineers (11th ed.), New York: McGraw Hill, pp. 9–4, ISBN 9780071428675.
 ↑ ^{5.0} ^{5.1} ^{5.2} Klein, Herbert Arthur (1988). The Science of measurement: A historical survey. New York: Dover. p. 239. ISBN 9780486144979.
 ↑ "Address by C. William Siemens". Report of the FiftySecond meeting of the British Association for the Advancement of Science. 52. London: John Murray. 1883. pp. 1–33. https://www.biodiversitylibrary.org/item/95237#page/85/mode/1up.
 ↑ 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"
 ↑ "Siemens", 1883, p. 5"
 ↑ Tunbridge, P. (1992). Lord Kelvin: His Influence on Electrical Measurements and Units. Peter Peregrinus: London. p. 51. ISBN 0863412378.
 ↑ ^{10.0} ^{10.1} Fleming, John Ambrose (1911). "Units, Physical". in Chisholm, Hugh. Encyclopædia Britannica. 27 (11th ed.). Cambridge University Press. pp. 738–745; see page 742.
 ↑ "Resolution 12 of the 11th CGPM (1960)". Bureau International des Poids et Mesures (BIPM). https://www.bipm.org/en/CGPM/db/11/12/.
 ↑ Ainslie, M. A. (2015). A century of sonar: Planetary oceanography, underwater noise monitoring, and the terminology of underwater sound. Acoustics Today.
 ↑ Morfey, C.L. (2001). Dictionary of Acoustics.
 ↑ "ByeBye Batteries: Radio Waves as a LowPower Source", The New York Times, Jul 18, 2010, https://www.nytimes.com/2010/07/18/business/18novel.html.
 ↑ Stetzler, Trudy; Magotra, Neeraj; Gelabert, Pedro; Kasthuri, Preethi; Bangalore, Sridevi. "LowPower RealTime Programmable DSP Development Platform for Digital Hearing Aids". Datasheet Archive. http://www.datasheetarchive.com/datasheetpdf/019/DSA00333218.html.
 ↑ Nakagami, Hidetoshi; Murakoshi, Chiharu; Iwafune, Yumiko (2008). "International Comparison of Household Energy Consumption and Its Indicator". ACEEE Summer Study on Energy Efficiency in Buildings. Pacific Grove, California: American Council for an EnergyEfficient Economy. Figure 3. Energy Consumption per Household by Fuel Type. 8:214–8:224. http://www.aceee.org/files/proceedings/2008/data/papers/8_24.pdf. Retrieved 14 February 2013.
 ↑ Elena Papadopoulou, Photovoltaic Industrial Systems: An Environmental Approach Springer 2011 ISBN:3642163017, p.153
 ↑ (in enus) 2007–2008 Information Digest (Report). 19. United States Nuclear Regulatory Commission. 20070801. pp. 84101. https://www.nrc.gov/readingrm/doccollections/nuregs/staff/sr1350/v19/sr1350v19.pdf. Retrieved 20211227.
 ↑ Bai, Jim; Chen, Aizhu (11 November 2010). "China's Shanxi to face 5–6 GW power shortage by yrend – paper". in Lewis, Chris. Reuters. http://in.reuters.com/article/idINTOE6AA0AD20101111.
 ↑ "Not on my beach, please". The Economist. 19 August 2010. http://www.economist.com/node/16846774.
 ↑ "Chiffres clés" (in fr). Electrabel. 2011. http://www.electrabel.com/whoarewe/nuclear/keyfigures_doel.aspx.
 ↑ Davidson, CC; Preedy, RM; Cao, J; Zhou, C; Fu, J (October 2010), "UltraHighPower Thyristor Valves for HVDC in Developing Countries", 9th International Conference on AC/DC Power Transmission, London: IET.
 ↑ Hannah Ritchie and Max Roser (2020). "Global Direct Primary Energy Consumption". Our World in Data (Published online at OurWorldInData.org.). https://ourworldindata.org/grapher/globalprimaryenergy?country=~OWID_WRL. Retrieved 20200209.
 ↑ "Crossing the Petawatt threshold". Livermore, California: Lawrence Livermore National Laboratory. https://www.llnl.gov/str/Petawatt.html.
 ↑ World's most powerful laser: 2 000 trillion watts. What's it?, IFL Science, http://www.iflscience.com/technology/worldsmostpowerfullaser2000trillionwattswhatsit.
 ↑ Eureka alert, Aug 2015, http://www.eurekalert.org/pub_releases/201508/ouwpl080615.php.
 ↑ "Construction of a Composite Total Solar Irradiance (TSI) Time Series from 1978 to present". PMODWRC. http://www.pmodwrc.ch/pmod.php?topic=tsi/composite/SolarConstant.
 ↑ Loeb, Norman G.; Johnson, Gregory C.; Thorsen, Tyler J.; Lyman, John M. et al. (15 June 2021). "Satellite and Ocean Data Reveal Marked Increase in Earth's Heating Rate". Geophysical Research Letters 48 (13). doi:10.1029/2021GL093047. Bibcode: 2021GeoRL..4893047L.
 ↑ Williams, Dr. David R.. "Sun Fact Sheet". NASA. https://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html.
 ↑ Rowlett, Russ. "How Many? A Dictionary of Units of Measurement. M". University of North Carolina at Chapel Hill. http://www.unc.edu/~rowlett/units/dictM.html.
 ↑ Cleveland, CJ (2007). "Watt". Encyclopedia of Earth. http://editors.eol.org/eoearth/wiki/Watt_(Energy).
 ↑ "Solar Energy Grew at a Record Pace in 2008 (excerpt from EERE Network News". Department of Energy). 25 March 2009. http://apps1.eere.energy.gov/news/news_detail.cfm/news_id=12362.
 ↑ International Bureau of Weights and Measures (2006), The International System of Units (SI) (8th ed.), p. 132, ISBN 9282222136, http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf
 ↑ "Avedøre Power Station (Avedøre værket)". DONG Energy. http://www.dongenergy.com/en/business%20activities/generation/activities/central_power_stations/pages/avedoere_power_station.aspx.
 ↑ "Inverter Selection". Northern Arizona Wind and Sun. http://www.windsun.com/Inverters/Inverter_selection.htm.
External links
 Borvon, Gérard. "History of the electrical units". http://seaus.free.fr/spip.php?article964.
 Nelson, Robert A. (February 2000). The International System of Units: Its History and Use in Science and Industry. Via Satellite. ATI courses. http://www.aticourses.com/international_system_units.htm.
Original source: https://en.wikipedia.org/wiki/Watt.
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