When an object'svelocity is held constant at onemeter per second against a constant opposing force of onenewton, the rate at whichwork is done is one watt.
In terms ofelectromagnetism, one watt is the rate at whichelectrical work is performed when a current of oneampere (A) flows across an electricalpotential difference of onevolt (V), meaning the watt is equivalent to thevolt-ampere (the latter unit, however, is used for a different quantity from thereal power of an electrical circuit).
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 togravity times height divided by the time it takes to lift the object to the given height gives therate of doing work orpower.[i]
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]
The watt is named after the Scottish inventorJames Watt.[5] The unit name was proposed byC. William Siemens in August 1882 in his President's Address to the Fifty-Second Congress of theBritish Association for the Advancement of Science.[6] Noting that units in thepractical system of units were named after leading physicists, Siemens proposed thatwatt 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 anAmpère 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-calledinternational definitions were established for practical electrical units.[10] Siemens' definition was adopted as theinternational watt. (Also used:1 A2 × 1 Ω.)[5] The watt was defined as equal to 107 units of power in thepractical system of units.[10] The"international units" were dominant from 1909 until 1948. After the 9thGeneral Conference on Weights and Measures in 1948, theinternational 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, 1absolute watt = 1.00019international watts. Texts written before 1948 are likely to be using theinternational 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 theabsolute watt into theInternational System of Units (SI) as the unit of power.[11]
For additional examples of magnitude for multiples and submultiples of the watt, seeOrders 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 inbold face
Attowatt
The sound intensity in water corresponding to the international standard referencesound pressure of 1 μPa is approximately 0.65 aW/m2.[12]
Femtowatt
Powers measured in femtowatts are typically found in references toradio andradar receivers. For example, meaningfulFM tuner performance figures for sensitivity, quieting andsignal-to-noise require that theRF 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 RFinput impedance of the tuner.
Picowatt
Powers measured in picowatts are typically used in reference to radio and radar receivers,acoustics and in the science ofradio astronomy. One picowatt is the international standard reference value ofsound 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.
A typicallaser pointer outputs about five milliwatts of light power, whereas a typicalhearing aid uses less than one milliwatt.[15]Audio signals and other electronic signal levels are often measured indBm, referenced to one milliwatt.
Kilowatt
"Kilowatt" and "Kilowatts" redirect here. For the musician James Watts, seeKiloWatts (musician).
The kilowatt is typically used to express the output power ofengines and the power ofelectric motors, tools, machines, and heaters. It is also a common unit used to express theelectromagnetic power output of broadcast radio and televisiontransmitters. One kilowatt is approximately equal to 1.34horsepower. A small electric heater with oneheating element can use 1 kilowatt. The averageelectric power consumption of a household in the United States is about 1 kilowatt.[ii] A surface area of 1 square meter on Earth receives typically about one kilowatt of sunlight from the Sun (thesolar 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; largeserver farms ordata centers; and some scientific research equipment, such assupercolliders, 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-poweredelectric locomotives typically have a peak power output of5 or 6 MW, while some produce much more. TheEurostar e300, for example, uses more than12 MW, while heavydiesel-electric locomotives typically produce and use3 and 5 MW. U.S.nuclear power plants have net summer capacities between about500 and 1300 MW.[18]: 84–101 The earliest citing of the megawatt in theOxford English Dictionary (OED) is a reference in the 1900Webster's International Dictionary of the English Language. TheOED also states thatmegawatt appeared in a November 28, 1947, article in the journalScience (506:2).
A gigawatt is typical average power for an industrial city of one million habitants, and is the output of a large power station. The GW unit is thus used for large power plants andpower 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 BelgianDoel 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
Theprimary 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 fornanosecond intervals. The average lightning strike peaks at 1 TW, but these strikes only last for 30microseconds.
A petawatt can be produced by the current generation of lasers for time scales on the order of picoseconds. One such laser isLawrence Livermore'sNova laser, which achieved a power output of 1.25 PW by a process calledchirped 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 asEarth'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]
In theelectric power industry,megawatt electrical (MWe[31] or MWe)[32] refers by convention to theelectric power produced by a generator, whilemegawatt thermal orthermal megawatt[33] (MWt, MWt, or MWth, MWth) refers tothermal power produced by the plant. For example, theEmbalse nuclear power plant in Argentina uses afission reactor to generate 2,109 MWt (i.e. heat), which creates steam to drive a turbine, which generates 648 MWe (i.e. electricity). OtherSI prefixes are sometimes used, for examplegigawatt electrical (GWe). TheInternational 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.,Pth = 270 W rather thanP = 270 Wth) and so these unit symbols are non-SI.[34] In compliance with SI, the energy companyØrsted A/S uses the unit megawatt for produced electrical power and the equivalent unitmegajoule per second for delivered heating power in acombined heat and power station such asAvedøre Power Station.[35]
The termspower andenergy 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 energyper unit time.
For example, when alight bulb with apower rating of100W is turned on for one hour, the energy used is 100watt 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, theThree 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 asterawatt 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.
Thewatt-second is a unit of energy, equal to thejoule. 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,[iii] it is not correct to refer to a watt (or watt-hour) as a watt per hour.[36]
^The energy in climbing the stairs is given bymgh. Settingm = 100 kg,g = 9.8 m/s2 andh = 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 refers to therate 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 thepower plants on an electric grid to compensate for loss of output from other sources, such as whensolar power generation drops to zero as the sun sets. Seeduck curve.
^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.ISBN9780128149256.
^Avallone, Eugene A; et al., eds. (2007),Marks' Standard Handbook for Mechanical Engineers (11th ed.), New York: Mc-Graw Hill, pp. 9–4,ISBN978-0-07-142867-5.
^abcKlein, Herbert Arthur (1988) [1974].The Science of measurement: A historical survey. New York: Dover. p. 239.ISBN9780486144979.
^"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.
^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"
^Ainslie, M. A. (2015). A century of sonar: Planetary oceanography, underwater noise monitoring, and the terminology of underwater sound. Acoustics Today.
