Coulomb

The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). It is defined to be equal to the electric charge delivered by a 1 ampere current in 1 second. It is used to define the elementary charge e.

Coulomb
Diagram showing 1 coulomb (electric charge at 1 ampere per 1 second) and the equivalent number of electrons
General information
Unit system	SI
Unit of	electric charge
Symbol	C
Named after	Charles-Augustin de Coulomb
Conversions
1 C in ...	... is equal to ...

SI base units	A⋅s
CGS units	≘ 2997924580 statC
Atomic units	≈6.241509×10¹⁸ e

Definition

The SI defines the coulomb as "the quantity of electricity carried in 1 second by a current of 1 ampere". Then the value of the elementary charge e is defined to be 1.602176634×10⁻¹⁹ C. Since the coulomb is the reciprocal of the elementary charge, $1~\mathrm {C} ={\frac {1}{1.602\,176\,634\times 10^{-19}}}~e.$ it is approximately 6241509074460762607.776 e and is thus not an integer multiple of the elementary charge.

The coulomb was previously defined in terms of the force between two wires. The coulomb was originally defined, using the latter definition of the ampere, as 1 A × 1 s. 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 that multiplies it by a power of 10.

SI multiples of coulomb (C)
Submultiples			Multiples
Value	SI symbol	Name	Value	SI symbol	Name
10⁻¹ C	dC	decicoulomb	10¹ C	daC	decacoulomb
10⁻² C	cC	centicoulomb	10² C	hC	hectocoulomb
10⁻³ C	mC	millicoulomb	10³ C	kC	kilocoulomb
10⁻⁶ C	μC	microcoulomb	10⁶ C	MC	megacoulomb
10⁻⁹ C	nC	nanocoulomb	10⁹ C	GC	gigacoulomb
10⁻¹² C	pC	picocoulomb	10¹² C	TC	teracoulomb
10⁻¹⁵ C	fC	femtocoulomb	10¹⁵ C	PC	petacoulomb
10⁻¹⁸ C	aC	attocoulomb	10¹⁸ C	EC	exacoulomb
10⁻²¹ C	zC	zeptocoulomb	10²¹ C	ZC	zettacoulomb
10⁻²⁴ C	yC	yoctocoulomb	10²⁴ C	YC	yottacoulomb
10⁻²⁷ C	rC	rontocoulomb	10²⁷ C	RC	ronnacoulomb
10⁻³⁰ C	qC	quectocoulomb	10³⁰ C	QC	quettacoulomb
Common multiples are in bold face.

Conversions

The magnitude of the electrical charge of one mole of elementary charges (approximately 6.022×10²³, the Avogadro number) is known as a faraday unit of charge (closely related to the Faraday constant). One faraday equals 9.648533212...×10⁴ coulombs. In terms of the Avogadro constant (N_A), one coulomb is equal to approximately 1.036×10⁻⁵ mol × N_A elementary charges.
Every farad of capacitance can hold one coulomb per volt across the capacitor.
One ampere hour equals 3600 C, hence 1 mA⋅h = 3.6 C.
One statcoulomb (statC), the obsolete CGS electrostatic unit of charge (esu), is approximately 3.3356×10⁻¹⁰ C or about one-third of a nanocoulomb.

In everyday terms

The charges in static electricity 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 AA battery from being fully charged to discharged is about 5 kC = 5000 C ≈ 1400 mA⋅h.
A typical smartphone battery can hold 10800 C ≈ 3000 mA⋅h.

Name and history

The coulomb is named after Charles-Augustin de Coulomb. As with every SI unit named for a person, its symbol starts with an upper case letter (C), but when written in full, it follows the rules for capitalisation of a common noun; i.e., coulomb becomes capitalised at the beginning of a sentence and in titles but is otherwise in lower case.

By 1878, the British Association for the Advancement of Science had defined the volt, ohm, and farad, but not the coulomb. In 1881, the International Electrical Congress, now the International Electrotechnical Commission (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 [i.e., what is nowadays called the "voltage (difference)"] across a conductor when a current of one ampere dissipates one watt of power. The coulomb (later "absolute coulomb" or "abcoulomb" for disambiguation) was part of the EMU 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.

Notes and references

"SI Brochure (2019)" (PDF). SI Brochure. BIPM. p. 127. Retrieved May 23, 2019.
BIPM (20 May 2019). "Mise en pratique for the definition of the ampere in the SI". BIPM. Retrieved 2022-02-18.
The International System of Units (PDF) (9th ed.), International Bureau of Weights and Measures, Dec 2022, ISBN 978-92-822-2272-0
"The NIST Reference on Units, Constants, and Uncertainty".
"2022 CODATA Value: Faraday constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 2024-05-18.
Martin Karl W. Pohl. "Physics: Principles with Applications" (PDF). DESY. Archived from the original (PDF) on 2011-07-18.
Hasbrouck, Richard. Mitigating Lightning Hazards Archived 2013-10-05 at the Wayback Machine, Science & Technology Review May 1996. Retrieved on 2009-04-26.
How to do everything with digital photography – David Huss, p. 23, at Google Books, "The capacity range of an AA battery is typically from 1100–2200 mAh."
"SI Brochure, Appendix 1" (PDF). BIPM. p. 144. Archived (PDF) from the original on 2006-06-18.
W. Thomson, et al. (1873) "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 10⁹ C.G.S. units of resistance; the 'volt' is approximately 10⁸ C.G.S. units of electromotive force; and the 'farad' is approximately 1/10⁹ of the C.G.S. unit of capacity."
(Anon.) (September 24, 1881) "The Electrical Congress", The Electrician, 7.
Donald Fenna, A Dictionary of Weights, Measures, and Units, OUP (2002), 51f.

[BIPM9-1] "SI Brochure (2019)" (PDF). SI Brochure. BIPM. p. 127. Retrieved May 23, 2019.

[MEP_for_amp-2] BIPM (20 May 2019). "Mise en pratique for the definition of the ampere in the SI". BIPM. Retrieved 2022-02-18.

[ampere-3] The International System of Units (PDF) (9th ed.), International Bureau of Weights and Measures, Dec 2022, ISBN 978-92-822-2272-0

[4] "The NIST Reference on Units, Constants, and Uncertainty".

[physconst-F-5] "2022 CODATA Value: Faraday constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 2024-05-18.

[6] Martin Karl W. Pohl. "Physics: Principles with Applications" (PDF). DESY. Archived from the original (PDF) on 2011-07-18.

[7] Hasbrouck, Richard. Mitigating Lightning Hazards Archived 2013-10-05 at the Wayback Machine, Science & Technology Review May 1996. Retrieved on 2009-04-26.

[8] How to do everything with digital photography – David Huss, p. 23, at Google Books, "The capacity range of an AA battery is typically from 1100–2200 mAh."

[9] "SI Brochure, Appendix 1" (PDF). BIPM. p. 144. Archived (PDF) from the original on 2006-06-18.

[10] W. Thomson, et al. (1873) "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 10⁹ C.G.S. units of resistance; the 'volt' is approximately 10⁸ C.G.S. units of electromotive force; and the 'farad' is approximately 1/10⁹ of the C.G.S. unit of capacity."

[11] (Anon.) (September 24, 1881) "The Electrical Congress", The Electrician, 7.

[12] Donald Fenna, A Dictionary of Weights, Measures, and Units, OUP (2002), 51f.