# Watt

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⋅m2⋅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 18th-century Scottish inventor.

watt
Unit systemSI derived unit
Unit ofPower
SymbolW
Named afterJames Watt
Conversions
1 W in ...... is equal to ...
SI base units   kgm2s−3
CGS units   107 ergs−1
English Engineering Units   0.7375621 ft⋅lbf/s = 0.001341022 hp

## 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.

${\displaystyle \mathrm {1~W=1~{\frac {J}{s}}=1~{\frac {N{\cdot }m}{s}}=1~{\frac {kg{\cdot }m^{2}}{s^{3}}}} }$

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).

${\displaystyle \mathrm {1~W=1~V\cdot 1~A} }$

Two additional unit conversions for watt can be found using the above equation and Ohm's law.

${\displaystyle \mathrm {1~W=1~{\frac {V^{2}}{\Omega }}=1~A^{2}{\cdot }\Omega } }$

where ohm (${\displaystyle \Omega }$) is the SI derived unit of electrical resistance.

#### Examples

• A person having a mass of 100 kilograms who climbs a three-metre-high ladder in five 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] This unit name was proposed initially 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 consistently within the then-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 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 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

Submultiples Multiples Value SI symbol Name Value 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 Common multiples are in bold face

#### Yoctowatt

The yoctowatt (yW) is equal to one septillionth (10−24) of a watt.

#### Zeptowatt

The zeptowatt (zW) is equal to one sextillionth (10−21) of a watt.

#### Attowatt

The attowatt (aW) is equal to one quintillionth (10−18) of a watt. The sound intensity in water corresponding to the international standard reference sound pressure of 1 μPa is approximately 0.65 aW/m2.[12]

#### Femtowatt

The femtowatt (fW) is equal to one quadrillionth (10−15) of a watt. 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 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 microvolt 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

The picowatt (pW), not to be confused with the much larger petawatt (PW), is equal to one trillionth (10−12) of a watt. 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 (10−9) of a watt. 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 (10−6) of a watt. Important powers that are measured in microwatts are typically stated in medical instrumentation systems such as the EEG and the 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 (10−3) of a watt. A typical laser pointer outputs about five milliwatts of light power, whereas a typical hearing aid for people uses less than one milliwatt.[15] Audio signals and other electronic signal levels are often measured in dBm, referenced to one milliwatt.

#### Kilowatt

The kilowatt (kW) is equal to one thousand (103) watts. 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 1.0 kilowatt. The average electric power consumption of a household in the United States is about one kilowatt.[lower-roman 2]

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

#### Megawatt

The megawatt (MW) is equal to one million (106) watts. 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, for example, uses more than 12 MW, while heavy diesel-electric locomotives typically produce/use 3 to 5 MW. U.S. nuclear power plants have net summer capacities between about 500 and 1300 MW.[18]

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

#### Gigawatt

The gigawatt (GW) is equal to one billion (109) watts 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 (1012) watts. The total power used by humans worldwide is commonly measured in terawatts. 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 terawatt, but these strikes only last for 30 microseconds.

#### Petawatt

The petawatt (PW) is equal to one quadrillion (1015) watts and can be produced by the current generation of lasers for time scales on the order of picoseconds (1012 s). One such laser is the Lawrence Livermore's Nova laser, which achieved a power output of 1.25 PW (1.25×1015 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.[23] 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.[24][25]

Based on the average total solar irradiance[26] of 1.366 kW/m2, the total power of sunlight striking Earth's atmosphere is estimated at 174 PW.

## Conventions in the electric power industry

In the electric power industry, megawatt electrical (MWe[27] or MWe[28]) refers by convention to the electric power produced by a generator, while megawatt thermal or thermal megawatt[29] (MWt, MWt, or MWth, MWth) refers to thermal power produced by the plant. For example, the Embalse nuclear power plant in Argentina uses a fission reactor to generate 2109 MWt (i.e. heat), which creates steam to drive a turbine, which generates 648 MWe (i.e. electricity). Other SI prefixes are sometimes used, for example gigawatt electrical (GWe). 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 (i.e., Pthermal = 270 W rather than P = 270 Wth) and so these units are non-SI.[30] 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.[31] Megawatt mechanical (MWm)[clarification needed] is rarely used.[32]

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 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 Wh / (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[lower-roman 3]), it is not correct to refer to a watt (or watt hour) as a "watt per hour".[33]

## 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 would properly refer to a rate of change of power being used (or generated). Watts per hour might be useful to characterize the ramp-up behavior of power plants, or slow-reacting 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 ramp-up rate of 4 MW/h.

## References

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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. "Siemens", 1883, p. 5"
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