The coulomb (symbol: C) is the unit of

electric charge Electric charge (symbol ''q'', sometimes ''Q'') is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative''. Like charges repel each other and ...

in the

International System of Units The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official s ...

(SI). It is defined to be equal to the electric charge delivered by a 1

ampere The ampere ( , ; symbol: A), often shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One ampere is equal to 1 c ...

current in 1

second The second (symbol: s) is a unit of time derived from the division of the day first into 24 hours, then to 60 minutes, and finally to 60 seconds each (24 × 60 × 60 = 86400). The current and formal definition in the International System of U ...

, with the

elementary charge The elementary charge, usually denoted by , is a fundamental physical constant, defined as the electric charge carried by a single proton (+1 ''e'') or, equivalently, the magnitude of the negative electric charge carried by a single electron, ...

''e'' as a defining constant in the SI.

Definition

The SI defines the coulomb as "the quantity of electricity carried in 1 second by a current of 1 ampere" by fixing the value of the

, . Inverting the relationship, the coulomb can be expressed in terms of the elementary charge:

1 ~ \mathrm = \frac = \frac ~ e.

It is approximately and is thus not an integer multiple of the elementary charge. The coulomb was previously defined in terms of the

based on the force between two wires, as . The 2019 redefinition of the ampere and other SI base units fixed the numerical value of the elementary charge when expressed in coulombs and therefore fixed the value of the coulomb when expressed as a multiple of the fundamental charge.

SI prefixes

Like other SI units, the coulomb can be modified by adding a

prefix A prefix is an affix which is placed before the stem of a word. Particularly in the study of languages, a prefix is also called a preformative, because it alters the form of the word to which it is affixed. Prefixes, like other affixes, can b ...

that multiplies it by a

power of 10 In mathematics, a power of 10 is any of the integer powers of the number ten; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer). By definition, the number one is a power (the zeroth power ...

Conversions

* The magnitude of the electrical charge of one

mole Mole (or Molé) may refer to: Animals * Mole (animal) or "true mole" * Golden mole, southern African mammals * Marsupial mole Marsupial moles, the Notoryctidae family, are two species of highly specialized marsupial mammals that are found i ...

s (approximately , the Avogadro number) is known as a faraday unit of charge (closely related to the

Faraday constant In physical chemistry, the Faraday constant (symbol , sometimes stylized as ℱ) is a physical constant defined as the quotient of the total electric charge () by the amount () of elementary charge carriers in any given sample of matter: it ...

). One faraday equals In terms of the

Avogadro constant The Avogadro constant, commonly denoted or , is an SI defining constant with an exact value of when expressed in reciprocal moles. It defines the ratio of the number of constituent particles to the amount of substance in a sample, where th ...

(''N''_A), one coulomb is equal to approximately × ''N''_A elementary charges. * Every

farad 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). It is named afte ...

capacitance Capacitance is the ability of an object to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are two closely related ...

can hold one coulomb per

volt The volt (symbol: V) is the unit of electric potential, Voltage#Galvani potential vs. electrochemical potential, electric potential difference (voltage), and electromotive force in the International System of Units, International System of Uni ...

across the

capacitor In electrical engineering, a capacitor is a device that stores electrical energy by accumulating electric charges on two closely spaced surfaces that are insulated from each other. The capacitor was originally known as the condenser, a term st ...

. * One

ampere hour An ampere-hour or amp-hour (symbol: A⋅h or A h; often simplified as Ah) is a unit of electric charge, having dimensions of electric current multiplied by time, equal to the charge transferred by a steady current of one ampere flowing for ...

equals , hence = . * One

statcoulomb The statcoulomb (statC), franklin (Fr), or electrostatic unit of charge (esu) is the unit of measurement for electrical charge used in the centimetre–gram–second electrostatic units variant (CGS-ESU) and Gaussian systems of units. In term ...

(statC), the obsolete CGS electrostatic unit of charge (esu), is approximately or about one-third of a nanocoulomb.

In everyday terms

* The charges in

static electricity Static electricity is an imbalance of electric charges within or on the surface of a material. The charge remains until it can move away by an electric current or electrical discharge. The word "static" is used to differentiate it from electric ...

from rubbing materials together are typically a few microcoulombs. * The amount of charge that travels through a lightning bolt is typically around 15 C, although for large bolts this can be up to 350 C. * The amount of charge that travels through a typical

alkaline In chemistry, an alkali (; from the Arabic word , ) is a basic salt of an alkali metal or an alkaline earth metal. An alkali can also be defined as a base that dissolves in water. A solution of a soluble base has a pH greater than 7.0. The ...

AA battery The AA battery (or double-A battery) is a standard size single cell cylindrical Dry cell, dry battery. ANSI and IEC battery nomenclature gives several designations for cells in this size, depending on cell features and chemistry. The Battery nom ...

from being fully charged to discharged is about = ≈ . * A typical smartphone battery can hold ≈ .

Name and history

By 1878, the

British Association for the Advancement of Science The British Science Association (BSA) is a Charitable organization, charity and learned society founded in 1831 to aid in the promotion and development of science. Until 2009 it was known as the British Association for the Advancement of Scienc ...

had defined the volt, ohm, and farad, but not the coulomb. In 1881, the

International Electrical Congress The International Electrical Congress was a series of international meetings, from 1881 to 1904, in the then new field of applied electricity. The first meeting was initiated by the French government, including official national representatives, le ...

, now the

International Electrotechnical Commission The International Electrotechnical Commission (IEC; ) is an international standards organization that prepares and publishes international standards for all electrical, electronics, electronic and related technologies. IEC standards cover a va ...

(IEC), approved the volt as the unit for electromotive force, the ampere as the unit for electric current, and the coulomb as the unit of electric charge. At that time, the volt was defined as the potential difference .e., what is nowadays called the "voltage (difference)"across a conductor when a current of one ampere dissipates one

watt The watt (symbol: W) is the unit of Power (physics), power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantification (science), quantify the rate of Work ...

of power. The coulomb (later "absolute coulomb" or "

abcoulomb The abcoulomb (abC or aC) or electromagnetic unit of charge (emu of charge) is the derived physical unit of electric charge in the cgs-emu system of units. One abcoulomb is equal to ten coulombs. The name "abcoulomb" was introduced by Kennell ...

" for disambiguation) was part of the

EMU The emu (; ''Dromaius novaehollandiae'') is a species of flightless bird endemism, endemic to Australia, where it is the Tallest extant birds, tallest native bird. It is the only extant taxon, extant member of the genus ''Dromaius'' and the ...

system of units. The "international coulomb" based on laboratory specifications for its measurement was introduced by the IEC in 1908. The entire set of "reproducible units" was abandoned in 1948 and the "international coulomb" became the modern coulomb.Donald Fenna, ''A Dictionary of Weights, Measures, and Units'', OUP (2002), 51f.

Notes and references