View source for Farad

{{short description|SI unit of electric capacitance}}
{{Other uses}}

{{Infobox unit
| name = farad
| image = [[File:OneFarad5.5Velectrolyticcapacitor.jpg|300px]]
| caption = A 1-farad [[supercapacitor]]. The scale behind is in inches (top) and centimetres (bottom).
| standard = [[SI]]
| quantity = [[capacitance]]
| symbol = F
| namedafter = [[Michael Faraday]]
| units1 = [[SI base unit]]s
| inunits1 = [[kilogram|kg]]<sup>−1</sup>⋅[[meter|m]]<sup>−2</sup>⋅[[second|s]]<sup>4</sup>⋅[[ampere|A]]<sup>2</sup>
}}

The '''farad''' (symbol: '''F''') is the unit of electrical [[capacitance]], the ability of a body to store an [[electrical charge]], in the [[International System of Units|International System of Units (SI)]], equivalent to 1 [[coulomb]] per [[volt]] (C/V).<ref name=":0" /> It is named after the English physicist [[Michael Faraday]] (1791–1867). In [[SI base units]] 1&nbsp;F = 1&nbsp;[[kilogram|kg]]<sup>−1</sup>⋅[[meter|m]]<sup>−2</sup>⋅[[second|s]]<sup>4</sup>⋅[[ampere|A]]<sup>2</sup>.

==Definition==
The [[capacitance]] of a capacitor is one farad when one [[coulomb]] of charge changes the potential between the plates by one [[volt]].<ref name=":0">{{cite book|title=The International System of Units (SI)|date=2006|publisher=Bureau International des Poids et Mesures (International Committee for Weights and Measures)|page=144|url=https://www.bipm.org/en/publications/si-brochure/|edition=8th}}</ref><ref>{{Cite web |title=farad {{!}} Definition, Symbol, & Facts {{!}} Britannica |url=https://www.britannica.com/science/farad |access-date=2022-07-25 |website=www.britannica.com |language=en}}</ref> Equally, one farad can be described as the capacitance which stores a one-coulomb charge across a potential difference of one volt.<ref>{{cite book|title=Dictionary of Science and Technology|date=1995|publisher=Larousse|isbn=0752300105|editor=Peter M B Walker}}</ref>

The relationship between capacitance, charge, and potential difference is linear. For example, if the potential difference across a [[capacitor]] is halved, the quantity of charge stored by that capacitor will also be halved.<!--Sub-units are not defined yet so stick to the main units-->

For most applications, the farad is an impractically large unit of capacitance. Most electrical and electronic applications are covered by the following [[SI prefix]]es:

*1&nbsp;mF (millifarad, one thousandth ({{10^|−3}}) of a farad) = 0.001&nbsp;F = {{gaps|1|000}}&nbsp;μF = {{gaps|1|000|000|000}}&nbsp;pF
*1&nbsp;μF (microfarad, one millionth ({{10^|−6}}) of a farad) = 0.000&nbsp;001&nbsp;F = {{gaps|1|000}}&nbsp;nF = {{gaps|1|000|000}}&nbsp;pF
*1&nbsp;nF (nanofarad, one billionth ({{10^|−9}}) of a farad) = 0.000&nbsp;000&nbsp;001&nbsp;F = 0.001&nbsp;μF = {{gaps|1|000}}&nbsp;pF
*1&nbsp;pF (picofarad, one trillionth ({{10^|−12}}) of a farad) = 0.000&nbsp;000&nbsp;000&nbsp;001&nbsp;F = 0.001&nbsp;nF

===Equalities===
A farad is a [[SI derived unit|derived unit]] based on four of the seven base units of the [[International System of Units]]: [[kilogram]] (kg), [[metre]] (m), [[second]] (s), and [[ampere]] (A).

Expressed in combinations of SI units, the farad is:
<math display="block">\text{F}
= \dfrac{\text{s}^4 {\cdot} \text{A}^2}{\text{m}^{2} {\cdot} \text{kg}}
= \dfrac{\text{s}^2 {\cdot} \text{C}^2}{\text{m}^{2} {\cdot} \text{kg}}
= \dfrac{\text{C}}{\text{V}}
= \dfrac{\text{A} {\cdot} \text{s}}{\text{V}}
= \dfrac{\text{W} {\cdot} \text{s}} {{\text{V}^2} }
= \dfrac{\text{J}}{{\text{V}^2} }
= \dfrac{\text{N} {\cdot} \text{m}} {{\text{V}^2} }
= \dfrac{\text{C}^2}{\text{J}}
= \dfrac{\text{C}^2}{\text{N} {\cdot} \text{m}}
= \dfrac{\text{s}}{\Omega}
= \dfrac{1}{\Omega {\cdot} \text{Hz}}
= \dfrac{\text{S}}{\text{Hz}}
= \dfrac{\text{s}^{2}}{\text{H}},
</math>

where {{nowrap|1=F = farad}}, {{nowrap|1=s = [[second]]}}, {{nowrap|1=C = [[coulomb]]}}, {{nowrap|1=V = [[volt]]}}, {{nowrap|1=W = [[watt]]}}, {{nowrap|1=J = [[joule]]}}, {{nowrap|1=N = [[newton (unit)|newton]]}}, {{nowrap|1=Ω = [[ohm]]}}, Hz = [[hertz]], {{nowrap|1=S = [[siemens (unit)|siemens]]}}, {{nowrap|1=H = [[henry (unit)|henry]]}}, {{nowrap|1=A = [[ampere (unit)|ampere]]}}.<ref>{{Cite book |url=https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf/2d2b50bf-f2b4-9661-f402-5f9d66e4b507 |title=The International System of Units (SI) |publisher=Bureau International des Poids et Mesures |year=2019 |edition=9th |pages=138}}</ref>

==History==
The term "farad" was originally coined by [[Latimer Clark]] and [[Charles Tilston Bright|Charles Bright]] in 1861,<ref>
As names for units of various electrical quantities, Bright and Clark suggested "ohma" for voltage, "farad" for charge, "galvat" for current, and "volt" for resistance. See:
* Latimer Clark and Sir Charles Bright (1861) [https://www.biodiversitylibrary.org/item/93052#page/483/mode/1up "On the formation of standards of electrical quantity and resistance,"] ''Report of the Thirty-first Meeting of the British Association for the Advancement of Science'' (Manchester, England: September 1861), section: Mathematics and Physics, pp. 37-38.
* Latimer Clark and Sir Charles Bright (November 9, 1861) [https://babel.hathitrust.org/cgi/pt?id=nyp.33433090837166;view=1up;seq=15 "Measurement of electrical quantities and resistance,"] ''The Electrician'', '''1''' (1): 3–4.</ref> in honor of [[Michael Faraday]], for a unit of quantity of charge, and by 1873, the farad had become a unit of capacitance.<ref>Sir W. Thomson, etc. (1873) [https://www.biodiversitylibrary.org/page/29853513#page/324/mode/1up "First report of the Committee for the Selection and Nomenclature of Dynamical and Electrical Units,"] ''Report of the 43rd Meeting of the British Association for the Advancement of Science'' (Bradford, September 1873), pp. 222-225. From p. 223: "The "ohm," as represented by the original standard coil, is approximately 10<sup>9</sup> C.G.S. units of resistance: the "volt" is approximately 10<sup>8</sup> C.G.S. units of electromotive force: and the "farad" is approximately 1/10<sup>9</sup> of the C.G.S. unit of capacity."</ref> In 1881, at the International Congress of Electricians in Paris, the name farad was officially used for the unit of electrical capacitance.<ref>(Anon.) (September 24, 1881) [https://babel.hathitrust.org/cgi/pt?id=nyp.33433090837489;view=1up;seq=309 "The Electrical Congress,"] ''The Electrician'', '''7''': 297. From p. 297: "7. The name farad will be given to the capacity defined by the condition that a coulomb in a farad gives a volt."</ref><ref>{{cite book|last1=Tunbridge|first1=Paul|title=Lord Kelvin: his influence on electrical measurements and units|date=1992|publisher=Peregrinus|location=London|isbn=9780863412370|pages=26, 39–40|url=https://books.google.com/books?id=bZUK624LZBMC|access-date=5 May 2015}}</ref>

==Explanation==
[[File:Capacitors Various.jpg|thumb|Examples of different types of capacitors]]
A [[capacitor]] generally consists of two conducting surfaces, frequently referred to as plates, separated by an insulating layer usually referred to as a [[dielectric]]. The original capacitor was the [[Leyden jar]] developed in the 18th century. It is the accumulation of electric charge on the plates that results in [[capacitance]]. Modern capacitors are constructed using a range of manufacturing techniques and materials to provide the extraordinarily wide range of capacitance values used in [[electronics]] applications from femtofarads to farads, with maximum-voltage ratings ranging from a few [[volt]]s to several kilovolts.

Values of capacitors are usually specified in terms of [[SI prefix#List of SI prefixes|SI prefixes]] of farads (F), <!--'''millifarads''' (mF),--> '''microfarads''' ('''μF'''), '''nanofarads''' ('''nF''') and '''picofarads''' ('''pF''').<ref name="Braga">{{cite book |title=Robotics, Mechatronics, and Artificial Intelligence |last=Braga |first=Newton C. |year=2002 |access-date=2008-09-17 |publisher=Newnes |page=21 |url=https://books.google.com/books?id=yqb-f-HKem0C&q=microfarad+common+measurement&pg=PA21 |isbn=0-7506-7389-3 |quote=Common measurement units are the microfarad (μF), representing 0.000,001 F; the nanofarad (nF), representing 0.000,000,001 F; and the picofarad (pF), representing 0.000,000,000,001 F.}}</ref> The '''millifarad''' ('''mF''') is rarely used in practice; a capacitance of 4.7&nbsp;mF (0.0047&nbsp;F), for example, is instead written as {{gaps|4|700|u=μF}}. The '''nanofarad''' ('''nF''') is used more often in Europe than in the United States.<ref>{{cite book |title=Make: Electronics: Learning Through Discovery |last=Platt |first=Charles |year=2009 |access-date=2014-07-22 |publisher=O'Reilly Media |page=61 |url=https://books.google.com/books?id=PQzYdC3BtQkC&q=nanofarad&pg=PA61 |isbn=9781449388799 |quote=Nanofarads are also used, more often in Europe than in the United States.}}</ref> The size of commercially available capacitors ranges from around 0.1&nbsp;pF to {{gaps|5|000|F}} (5&nbsp;kF) [[supercapacitor]]s. [[Parasitic capacitance]] in high-performance [[integrated circuit]]s can be measured in femtofarads (1 fF = 0.001&nbsp;pF = {{10^|-15}}&nbsp;F), while high-performance test equipment can detect changes in capacitance on the order of tens of attofarads (1&nbsp;aF = {{10^|−18}}&nbsp;F).<ref>{{cite book |title=Analog MOS Integrated Circuits for Signal Processing |last=Gregorian |first=Roubik |year=1976 |publisher=John Wiley & Sons |page=78}}</ref>

A value of 0.1&nbsp;pF is about the smallest available in capacitors for general use in electronic design, since smaller ones would be dominated by the [[parasitic capacitance]]s of other components, wiring or [[printed circuit board]]s. Capacitance values of 1&nbsp;pF or lower can be achieved by twisting two short lengths of insulated wire together.<ref>{{cite web |title=What's All This Femtoampere Stuff, Anyhow? |url=https://www.electronicdesign.com/technologies/test-measurement/article/21766108/whats-all-this-femtoampere-stuff-anyhow |last=Pease |first=Bob |author-link=Bob Pease |publisher=Electronic Design |date=2 September 1993 |access-date=2013-03-09}}</ref><ref>{{cite web |title=What's All This Best Stuff, Anyhow? |url=https://www.electronicdesign.com/analog/whats-all-best-stuff-anyhow |last=Pease |first=Bob |publisher=Electronic Design |date=1 December 2006 |access-date=2013-03-09}}</ref>

The capacitance of the Earth's [[ionosphere]] with respect to the ground is calculated to be about 1&nbsp;F.<ref>{{cite web |url=http://konfluence.org/efield.pdf |title=Electrical Properties of the Fair-Weather Atmosphere and the Possibility of Observable Discharge on Moving Objects |last=Williams |first=L. L. |date=January 1999 |access-date=2012-08-13 |archive-url=https://web.archive.org/web/20161221015744/http://konfluence.org/efield.pdf |archive-date=2016-12-21 |url-status=dead }}</ref>

===Informal and deprecated terminology===
The picofarad (pF) is sometimes colloquially pronounced as "puff" or "pic", as in "a ten-puff capacitor".<ref>{{cite web |title=Puff |url=http://scienceworld.wolfram.com/physics/Puff.html |publisher=Wolfram Research |access-date=2009-06-09}}</ref> Similarly, "mic" (pronounced "mike") is sometimes used informally to signify microfarads.

Nonstandard abbreviations were and are often used. Farad has been abbreviated "f", "fd", and "Fd". For the prefix "micro-", when [[mu (letter)|the Greek small letter "μ"]] or the legacy micro sign "μ" is not available (as on typewriters) or inconvenient to enter, it is often substituted with the similar-appearing "u" or "U", with little risk of confusion. It was also substituted with the similar-sounding "M" or "m"{{CN|date = July 2025}}, which can be confusing because M officially stands for 1,000,000, and m preferably stands for 1/1000. In texts prior to 1960, and on capacitor packages until more recently, "microfarad(s)" was abbreviated "mf"{{CN|date = July 2025}} or "MFD" rather than the modern "μF". A 1940 [[Radio Shack]] catalog listed every capacitor's rating in "Mfd.", from 0.000005 Mfd. (5 pF) to 50 Mfd. (50 μF).<ref>{{cite web |title=1940 Radio Shack Catalog - Page 54 - Condensers |url=http://www.radioshackcatalogs.com/html/1940/hr054.html |website=radioshackcatalogs.com |access-date=11 July 2017 |archive-url=https://web.archive.org/web/20170711160428/http://www.radioshackcatalogs.com/html/1940/hr054.html |archive-date=11 July 2017}}</ref>

"Micromicrofarad" or "micro-microfarad" is an obsolete unit found in some older texts and labels, contains a nonstandard [[metric double prefix]]. It is exactly equivalent to a picofarad (pF). It is abbreviated μμF, uuF, or (confusingly) "mmf"{{CN|date = July 2025}}, "MMF", or "MMFD".

Summary of obsolete or deprecated capacitance units or abbreviations: (upper/lower case variations are not shown)
* μF (microfarad) = mf, mfd, uf
* pF (picofarad) = mmf, mmfd, pfd, μμF

{{unichar|3332}} is a square version of {{lang|ja|ファラッド}} ({{Transliteration|ja|faraddo}}, the Japanese word for "farad") intended for Japanese [[vertical text]]. 
It is included in Unicode for [[CJK Compatibility|compatibility with earlier character sets]].

===Related concepts===
The reciprocal of capacitance is called [[elastance|electrical elastance]], the (non-standard, non-SI) unit of which is the [[daraf]].<ref>{{cite web|title=Daraf |url=http://www.websters-dictionary-online.com/definitions/daraf |publisher=Webster's Online Dictionary |access-date=2009-06-19 |url-status=dead |archive-url=https://web.archive.org/web/20111004054525/http://www.websters-dictionary-online.com/definitions/daraf |archive-date=2011-10-04 }}</ref>

==CGS units==
The '''abfarad''' (abbreviated abF) is an obsolete [[centimetre–gram–second system of units#Electromagnetic units in various CGS systems|CGS unit of capacitance]], which corresponds to {{10^|9}} farads (1 gigafarad, GF).<ref>{{cite book |title=Modern Dictionary of Electronics |last=Graf |first=Rudolf F. |year=1999 |publisher=Newnes |page=1 |url=https://books.google.com/books?id=AYEKAQAAQBAJ |isbn=9780080511986 |access-date=2016-04-15}}</ref>

The '''statfarad''' (abbreviated statF) is a rarely used CGS unit equivalent to the capacitance of a capacitor with a charge of 1 [[statcoulomb]] across a potential difference of 1 [[statvolt]]. It is 1/(10<sup>−5</sup>&nbsp;''c''<sup>2</sup>)&nbsp;farad, approximately 1.1126 picofarads. More commonly, the centimeter (cm) is used, which is equal to the statfarad.

==Notes==
{{Reflist|33em}}

==External links==
*[https://www.translatorscafe.com/unit-converter/electrostatic-capacitance/ Farad unit conversion tool]

{{SI units}}
{{Michael Faraday}}

[[Category:SI derived units]]
[[Category:Units of electrical capacitance]]
[[Category:Michael Faraday]]