Coulomb
SI derived unit · quantity: electric charge
01 · Definition
Coulomb hung a charged ball on a fine thread and measured the force of repulsion by the angle of twist. That is how the law was found that holds the whole of electrostatics together.
One coulomb is the charge that passes through a wire in one second at a current of one ampere. That is a great deal for static electricity and very little for the mains: lightning carries tens of coulombs, while the spark from a synthetic sweater carries microcoulombs. A phone battery holds about eleven thousand coulombs, though they are customarily counted in milliampere-hours. Since 2019 the chain has been turned round: the elementary charge is fixed as an exact number, and the coulomb is now precisely 6.241.509.074.460.762.607.776 elementary charges.
A comb charged by combing hair carries something like a tenth of a microcoulomb; a person who has walked across a carpet carries about a microcoulomb, and that is enough for a spark a centimetre long. The charge of a thundercloud reaches several tens of coulombs, and a single lightning stroke carries between five and thirty. Everything an electroscope shows lies in billionths of the unit: the force between charges falls off as the square of the distance and grows so fast that bodies push each other apart long before any appreciable amount has gathered.
02 · Conversion
Enter a charge and the passport will lay it out in every unit
The ampere-hour is the same charge with an hour in place of the second: the factor is exactly 3600. The faraday is the charge of a mole of electrons, the unit of electrochemistry.
The faraday ties electricity to chemistry: to release one mole of a monovalent substance at an electrode, 96.485 coulombs must be passed. The Faraday constant follows from multiplying the electron charge by the Avogadro number, and since 2019 both factors are exact — so the constant is exact as well. The whole of electroplating rests on this law: the thickness of a coating is reckoned from the charge passed, not from time or voltage.
| Unit | Name | Value | Where it is met |
|---|---|---|---|
| C | coulomb, the SI unit | 1 | physics, electrical engineering |
| mC | millicoulomb | 1000 | camera flashes, defibrillators |
| µC | microcoulomb | 1000000 | static electricity |
| nC | nanocoulomb | 1·10⁹ | electrostatics, dust specks |
| A·h | ampere-hour | 2.778·10⁻⁴ | accumulators, batteries |
| mA·h | milliampere-hour | 0.2778 | phones, laptops |
| statC | franklin, the CGSE system | 2.998·10⁹ | older theoretical physics |
| abC | abcoulomb, the CGSM system | 0.1 | electromagnetic CGS |
| faraday | the charge of a mole of electrons | 1.036·10⁻⁵ | electrochemistry, electroplating |
| e | elementary charge | 6.242·10¹⁸ | atomic and nuclear physics |
| A·h | ampere-hour | 2.778·10⁻⁴ | power engineering, batteries |
| C | coulomb | 1 | the unit of this sheet |
The ampere-hour is the same charge with an hour in place of the second: the factor is exactly 3600. The faraday is the charge of a mole of electrons, the unit of electrochemistry.
03 · Orders of magnitude
from the electron to a thundercloudOne coulomb: an ampere for a second
04 · Measuring instruments
What charge is measured with
Two gold leaves spread apart the further, the greater the charge on their common rod. The instrument shows potential, and the charge follows on multiplying by a known capacitance. It catches fractions of a picocoulomb and draws no current — which is why it has survived since the eighteenth century.
An electrolytic cell in which the charge that has passed turns into the mass of deposited metal. The electrode is weighed before and after, and Faraday’s law gives the charge. Slow, but absolute: the result depends on no electrical standard whatever.
Coulomb’s own instrument: a charged ball on a beam is repelled by a fixed one, the thread twists, and the angle of rotation gives the force. This is how the inverse-square law was established in 1785 — by measurement, not by guesswork.
A chip inside the battery continuously measures the current across a shunt and sums it over time, arriving at the charge spent. It is this quantity, not the voltage, that shows the battery percentage on a phone — though the error accumulates, and is reset at a full charge.
05 · Writing rules
Capital C — but not the degree Celsius
One and the same symbol is taken twice in the SI: without the degree sign it is charge, with it, temperature. The ampere-hour is not an SI unit but is accepted in practice; it must be written with a multiplication dot — A·h, not Ah and not A/h. The symbol for the quantity of charge is an italic Q, for the unit an upright C: in Q = 4.5 C the italic and the upright type tell the two apart. The Russian symbol is Кл. Charge can be negative, and the sign is part of the value: −1.6·10⁻¹⁹ C for the electron, +1.6·10⁻¹⁹ C for the proton. Their magnitudes agree exactly.
The symbol for the quantity of charge is an italic Q, for the unit an upright C: in Q = 4.5 C the italic and the upright type carry the distinction. The Russian symbol is Кл. The ampere-hour takes a mid-line dot or a space between the symbols, never a run-on: A·h, not Ah. A lowercase c on its own is the prefix centi- and the symbol for the speed of light, neither of which has anything to do with charge.
06 · Neighbouring units
The coulomb stands between current and voltage: current is charge per second, capacitance is charge per volt. Both relations fit on a single line.
Of the Simetrium passports sit next to the coulomb ampere, whose charge per second it is, farad and volt from the same formula, ampere-hour as the everyday measure of the same charge, and mole, through which charge is linked to amount of substance.
07 · Historical section
A charge people learned to count before they understood it
Charles Coulomb hung a beam on a fine silver thread and measured the force between charged balls by the angle of twist. The inverse-square dependence came out of the experiment, though guesses at it had been voiced before.
The International Congress of Electricians handed out names to several units at once: the volt, the ampere, the ohm, the coulomb and the farad all appeared in a single year. Charge was defined through current rather than the other way round — current was the easier thing to measure.
Robert Millikan balanced charged droplets of oil against an electric field and found that their charges were multiples of one quantity. This proved that charge is discrete and gave the value of the elementary one — with an error of half a per cent, owing to a wrong figure for the viscosity of air. The international coulomb was defined through a silver coulometer: the charge that deposits 1.118 milligrams of silver. It differed from the present one in the fifth digit.
The ampere was redefined through a fixed electron charge, and the coulomb gained a second, exact measure: a whole number of elementary charges. The old definition of the ampere by the force between conductors departed together with the magnetic constant, which ceased to be exact.
A unit with no standard, and none needed
Charge is not kept: any coulomb gathered leaks away through insulation, through the air and across its own surface within hours. That is why no coulomb standard as an object exists, or ever did — the unit is realised by measuring current over an interval of time, and since 2019 by counting electrons as well. Single-electron pumps drive one electron through a quantum dot per cycle: a billion cycles a second gives a current of about a hundred and sixty picoamperes, known to an accuracy beyond the reach of classical methods. Closing the volt–ampere–ohm triangle with quantum effects and obtaining the coulomb by a third independent route has so far eluded metrologists: the discrepancies lie at the level of parts per billion, and it is they that set the present limit on the accuracy of electrical measurement.
Catalogue · units of measurement
A passport for every quantity
Seven SI base units, twenty-two derived ones with names of their own, and the non-SI units that neither engineering nor daily life can do without. Each gets its own sheet: definition, conversion, instruments, writing rules. In 30 languages.
SI derived units with names of their own
the coulomb passport is openSI base units
in terracotta — the ampere and the second, of which the coulomb is madeCharge in other systems
Passport language
30 languages. The symbol C is international, but the everyday measure of charge differs: in some countries battery capacity is given in milliampere-hours, in others in watt-hours.