Watt

watt
Unit system	SI derived unit
Unit of	Power
Symbol	W
Named after	James Watt
Unit conversions
1 W in ...	... is equal to ...
SI base units	kg⋅m^2⋅s^−3
CGS units	1×10^7 erg s^−1

The watt (symbol: W) is a derived unit of power in the International System of Units (SI), named after the Scottish engineer James Watt (1736–1819). The unit is defined as joule per second^[1] and can be used to express the rate of energy conversion or transfer with respect to time. It has dimensions of Mass·Length²·Time⁻³.

Examples

When an object's velocity is held constant at one meter per second against constant opposing force of one newton the rate at which work is done is 1 watt.

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

In terms of electromagnetism, one watt is the rate at which work is done when one ampere (A) of current flows through an electrical potential difference of one volt (V).

$\mathrm{W = V \cdot A}$

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

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

Where ohm ($\Omega$) is the SI derived unit of electrical resistance.

• A person having a mass of 100 kilograms 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.^{[notes 1]}
• A laborer over the course of an 8-hour day can sustain an average output of about 75 watts; higher power levels can be achieved for short intervals and by athletes.^[2]

Origin and adoption as an SI unit

The watt is named after the Scottish scientist James Watt for his contributions to the development of the steam engine. The measurement unit was recognized by the Second Congress of the British Association for the Advancement of Science in 1882, concurrent with the start of commercial power production from both water and steam. In 1960 the 11th General Conference on Weights and Measures adopted it for the measurement of power into the International System of Units (SI).

Multiples

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

SI multiples for watt (W) Submultiples Multiples Value SI symbol Name Value SI symbol Name 10^−1 W dW deciwatt 10^1 W daW decawatt 10^−2 W cW centiwatt 10^2 W hW hectowatt 10^−3 W mW milliwatt 10^3 W kW kilowatt 10^−6 W µW microwatt 10^6 W MW megawatt 10^−9 W nW nanowatt 10^9 W GW gigawatt 10^−12 W pW picowatt 10^12 W TW terawatt 10^−15 W fW femtowatt 10^15 W PW petawatt 10^−18 W aW attowatt 10^18 W EW exawatt 10^−21 W zW zeptowatt 10^21 W ZW zettawatt 10^−24 W yW yoctowatt 10^24 W YW yottawatt Common multiples are in bold face

Femtowatt

The femtowatt is equal to one quadrillionth (10⁻¹⁵) of a watt. Technologically important powers that are measured in femtowatts are typically found in reference(s) 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 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.

Nanowatt

The nanowatt 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 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.^[3]

Milliwatt

The milliwatt 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.^[4] Audio signals and other electronic signal levels are often measured in dBm, referenced to one milliwatt.

Kilowatt

The kilowatt is equal to one thousand (10³) watts, or one sthène-metre per second. 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.^{[notes 2][5]}

Also, kilowatts of light power can be measured in the output pulses of some lasers.

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).^[6]

Megawatt

The megawatt 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, although 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.^[7]

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 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^[8] and the installed capacity of wind power in Germany was 25.8 GW.^[9] The largest unit (out of four) of the Belgian Doel Nuclear Power Station has a peak output of 1.04 GW.^[10] HVDC converters have been built with power ratings of up to 2 GW.^[11]

Terawatt

The terawatt is equal to one trillion (10¹²) watts. The total power used by humans worldwide is commonly measured in terawatts (see primary energy). The most powerful lasers from the mid-1960s to the mid-1990s produced power in terawatts, but only for nanosecond time frames. The average lightning strike peaks at 1 terawatt, but these strikes only last for 30 microseconds.

Petawatt

The petawatt 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 (10⁻¹² 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, or enough energy to power a 100 W light bulb for six seconds.^[12] 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 (2×10¹⁵ W) for a duration of approximately 1 ps.^[13][14]

Based on the average total solar irradiance^[15] of 1.366 kW/m², the total power of sunlight striking Earth's atmosphere is estimated at 174 PW (see: solar constant).

Electrical and thermal watts

In the electric power industry, megawatt electrical (MWe^[16] or MW_e^[17]) is electric power, while megawatt thermal or thermal megawatt^[18] (MWt, MW_t, or MWth, MW_th) refers to thermal power produced. Other SI prefixes are sometimes used, for example gigawatt electrical (GW_e). "watt electrical" and "watt thermal" are not SI units,^[19] The International Bureau of Weights and Measures 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 regards these symbols as incorrect.^[20]

For example, the Embalse nuclear power plant in Argentina uses a fission reactor to generate 2109 MW_t of heat, which creates steam to drive a turbine, which generates 648 MW_e of electricity (a numerical energy conversion efficiency of 648/2109 = 0.307, or 30.7%). The difference is due to the inefficiency of steam-turbine generators and the limitations of the theoretical Rankine cycle.

Radio transmission

Radio stations usually report the power of their transmitters in units of watts, referring to the effective radiated power. It refers to the relative power of the transmission when it it is directed towards the horizon for maximum geographic coverage, rather than uniformly broadcast in all directions.

Confusion of watts, watt-hours and watts per hour

The terms power and energy are frequently confused. 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. A power station would be rated in multiples of watts (for example, the Three Gorges Dam is rated at approximately 22 gigawatts), but its annual energy sales or output would be in multiples of watt hours. Major energy production or consumption is often expressed as terawatt hours for a given period that is often a calendar year or financial year. One terawatt hour is equal to a sustained power of approximately 114 megawatts for a period of one year.

The watt second is a unit of energy, equal to the joule. One kilowatt hour is 3,600,000 watt seconds. The watt second is used, for example, to rate the energy storage of flash lamps used in photography, although the term joule is generally employed.

Terms such as watts per hour (W/h) are often misused when watts would be correct.^[21] Watts per hour properly refers to a change of power per hour. Watts per hour might be useful to characterize the ramp-up behavior of power plants. For example, a power plant that reaches a power output of 1 MW from 0 MW in 15 minutes has a ramp-up rate of 4 MW/h. Hydroelectric power plants have a very high ramp-up rate, which makes them particularly useful in peak load and emergency situations.

See also

• Conversion of units
• Declared net capacity (power plants)
• Metre–tonne–second system of units
• Orders of magnitude (power)
• Power factor
• Root mean square (RMS)
• Volt-ampere
• Watt balance
• Watt-peak
• Wattmeter

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.

References

1. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), pp. 118, 144, ISBN 92-822-2213-6
2. Avallone, Eugene A; et. al, eds. (2007), Marks' Standard Handbook for Mechanical Engineers (11th ed.), New York: Mc-Graw Hill, pp. 9–4, ISBN 0-07-142867-4.
3. "Bye-Bye Batteries: Radio Waves as a Low-Power Source", The New York Times, Jul 18, 2010.
4. Stetzler, Trudy; Magotra, Neeraj; Gelabert, Pedro; Kasthuri, Preethi; Bangalore, Sridevi. "Low-Power Real-Time Programmable DSP Development Platform for Digital Hearing Aids". Datasheet Archive. Retrieved 8 February 2010.
5. 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. Retrieved 14 February 2013.
6. Elena Papadopoulou, Photovoltaic Industrial Systems: An Environmental Approach Springer 2011 ISBN 3642163017, p.153
7. "2007–2008 Information Digest, Appendix A" (PDF). Nuclear Regulatory Commission. 2007. Retrieved 27 January 2008.
8. Bai, Jim; Chen, Aizhu (11 November 2010). Lewis, Chris, ed. "China's Shanxi to face 5–6 GW power shortage by yr-end – paper". Peking: Reuters.
9. "Not on my beach, please". The Economist. 19 August 2010.
10. "Chiffres clés" [Key numbers]. Electrabel. Who are we: Nuclear (in French). 2011.
11. Davidson, CC; Preedy, RM; Cao, J; Zhou, C; Fu, J (October 2010), "Ultra-High-Power Thyristor Valves for HVDC in Developing Countries", 9th International Conference on AC/DC Power Transmission, London: IET.
12. "Crossing the Petawatt threshold". Livermore, CA: Lawrence Livermore National Laboratory. Retrieved 19 June 2012.
13. World’s most powerful laser: 2 000 trillion watts. What’s it?, IFL Science.
14. Eureka alert (publicity release), Aug 2015.
15. "Construction of a Composite Total Solar Irradiance (TSI) Time Series from 1978 to present". CH: PMODWRC. Retrieved 2005-10-05.
16. "M". How Many? A Dictionary of Units of Measurement. UNC.
17. Cleveland, CJ (2007). "Watt". Encyclopedia of Earth.
18. "Solar Energy Grew at a Record Pace in 2008 (excerpt from EERE Network News". US: Department of Energy). 25 March 2009.
19. Thompson; Taylor. "Guide for the Use of the International System of Units (SI)" (PDF). Special Publication. NIST. SP811.
20. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 138, ISBN 92-822-2213-6
21. "Inverter Selection". Northern Arizona Wind and Sun. Retrieved 27 March 2009.

External links

• Borvon, Gérard, History of the electrical units, FR: Free.
• Nelson, Robert A (February 2000), The International System of Units: Its History and Use in Science and Industry, Via Satellite, ATI courses.