Electric charge

Prof. Dr. Thorsten Jungmann (last updated 2026-05-04)

Electric charge (German: elektrische Ladung) is a fundamental property of matter: it determines how strongly particles and bodies interact electrically with one another. There is positive and negative electric charge, and the total electric charge is conserved in closed systems.

1 Quantity symbol and unit

The quantity symbol of electric charge is the capital letter $Q$.
The unit of electric charge $Q$ is the coulomb, named after Charles-Augustin de Coulomb, abbreviated with the letter C as its unit symbol.

$$[Q]=\mathrm{C}$$

In the International System of Units (SI), the coulomb (C) is defined via the elementary charge $e$.

$$e=1.602176634\cdot 10^{-19}\mathrm{C}$$

The electric charge of the proton is $+e$, that of the electron $-e$.

$1\mathrm{C}$ is the electric charge (the amount of charge carriers) that is transported within one second through the cross-section of a conductor in which a current of $1\mathrm{A}$ flows. The electric charge can therefore also be given in ampere-seconds ($\mathrm{As}$).

$$[Q]=\mathrm{C}=\mathrm{A}\cdot \mathrm{s}=\mathrm{A}\mathrm{s}$$

The electric charge $Q$ corresponds to a number of $n$ elementary charges. This can be expressed by the following equation:

$$Q=n\cdot e$$

where:

• $Q$: the electric charge in coulombs ($\mathrm{C}$)
• $n$: the number of elementary charges
• $e$: the elementary charge $e\approx 1.602\cdot 10^{-19}\mathrm{C}$

2 Practical and worked examples

2.1 Relationship between current and time

If the current $I$ flows over the period $t$, the amount of charge $Q$ is transported:

$$Q=I\cdot t$$

2.2 Electric charge in a capacitor

A capacitor with the capacitance $C$ that is charged at the voltage $U$ holds the electric charge $Q$.

$$Q=C\cdot U$$

2.3 Car battery

The electric charge $Q$ of a battery corresponds to the number $n$ of negative elementary charges $e$.

$$Q=n\cdot e$$

The battery capacity is usually given not in $\mathrm{As}$ but in ampere-hours ($\mathrm{Ah}$).

$$1\mathrm{Ah}=1\mathrm{Ah}\cdot \frac{3600\mathrm{s}}{1\mathrm{h}}=3600\mathrm{As}$$

How many electrons are there in a fully charged 60Ah car battery?

$$n=\frac{Q}{e}=\frac{60\mathrm{Ah}}{1.602\cdot 10^{-19}\mathrm{As}}=\frac{60\cdot 3600\mathrm{As}}{1.602\cdot 10^{-19}\mathrm{As}}=\frac{216000\mathrm{C}}{1.602\cdot 10^{-19}\mathrm{C}}=\underline{1.348\cdot 10^{24}}$$

When charged, a 60 Ah starter battery in a car holds $n=1.348\cdot 10^{24}$, i.e. just over a septillion electrons ready to send them through the entire vehicle electrical system and to make their energy available to the systems in the car. They set the starter motor in motion, for example, make the lights shine, the air conditioning cool and the ventilation ventilate.

3 Typical orders of magnitude

• ESD/static electricity:
  $Q=10^{-10}\dots 10^{-6}\mathrm{C}(\mathrm{pC}\dots \mu \mathrm{C})$
• Electronics/capacitors:
  $Q=10^{-9}\dots 10^{-3}\mathrm{C}(\mathrm{nC}\dots \mathrm{mC})$
• Rechargeable batteries:
  $Q=10^3\dots 10^6\mathrm{C}(\mathrm{kC}\dots \mathrm{MC})$

4 Example phrasings

• ‘The electric charge is $2.0\mu \mathrm{C}$ (microcoulombs)’.
• ‘At $5\mathrm{V}$, the capacitor takes up the electric charge $Q=C\cdot U=0.5\mu \mathrm{C}$.’
• ‘With $I=500\mathrm{mA}$ in $t=10\mathrm{ms}$, $5\mathrm{mC}$ (millicoulombs) flow.’
• ‘One coulomb corresponds to approximately $6.242\cdot 10^{18}\text{elementary charges}$.’

5 Related quantities

• Connection to current and time:
  $Q=\int i(t)\mathrm{d}t\text{(general)}\text{or}Q=I\cdot t\text{(constant)}$
• Capacitance and voltage:
  $Q=C\cdot U$
• Force in an electric field (uniform):
  $F=q\cdot E$
• Gauss’s law (free charge) with electric flux density:
  $\oint \vec{D}\cdot \mathrm{d}\vec{A}=Q$

6 Related components

• Capacitor (stores electric charge)
• Battery / rechargeable battery (provides charge carriers)
• Multimeter (determination via current/time)