Capacitance

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

Capacitance (German: Kapazität) describes the ability of a capacitor to store electric charge. The greater the capacitance, the more charge can be stored at the same voltage. Capacitance is therefore a measure of the ‘holding capacity’ of a capacitor for electric charge.

1 Quantity symbol and unit

The quantity symbol of capacitance is $C$. It is given in the unit farad, named after Michael Faraday, with the unit symbol F.

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

(read: ‘The unit of capacitance $C$ is the farad.’)

The farad is a derived SI unit. 1 farad is very large – in practice, much smaller units are usually used.

Capacitance is defined as the ratio of the stored electric charge $Q$ to the applied voltage $U$:

$$C=\frac{Q}{U}$$

This formula shows that a capacitor with a large capacitance can store more charge at the same voltage than a capacitor with a small capacitance.

Water analogy: Imagine a capacitor as a water tank. The capacitance corresponds to the base area of the tank. A tank with a large base area (large capacitance) can hold more water (corresponds to the charge) at the same water level (corresponds to the voltage) than a narrow tank.

Capacitance is constant over time. In time-dependent circuits (e.g. during charging and discharging), the capacitance stays the same; only the charge, voltage and current at the capacitor change over time.

2 Practical and worked examples

2.1 Capacitor in a DC circuit

When a capacitor is charged via a resistor, the voltage rises exponentially:

$$u_C(t)=U_0\cdot \left(1-e^{-\frac{t}{\tau }}\right)$$

where:

• $u_C(t)$ the voltage across the capacitor as a function of time
• $U_0$ the operating voltage (final voltage)
• $e$ Euler’s number ($e\approx 2.7183$)
• $t$ the time
• $R$ the resistance
• $C$ the capacitance
• $\tau$ the time constant $\tau =\mathrm{R}\cdot \mathrm{C}$

2.2 Energy in a capacitor

The energy stored in a capacitor is calculated as follows:

$$W=\frac{1}{2}\cdot C\cdot U^2$$

where:

• $W$ the stored energy
• $C$ the capacitance
• $U$ the voltage

2.3 Capacitance of a parallel-plate capacitor

For an ideal parallel-plate capacitor, the following applies:

$$C=\epsilon \cdot \frac{A}{d}={\epsilon }_0\cdot {\epsilon }_r\cdot \frac{A}{d}$$

where:

• $\epsilon$ the permittivity
• ${\epsilon }_0$ the electric field constant (${\epsilon }_0\approx 8.8542\cdot 10^{-12}F/m$)
• ${\epsilon }_r$ the relative permittivity of the dielectric (dimensionless)
• $A$ the plate area in ${\mathrm{m}}^2$
• $d$ the plate separation in $\mathrm{m}$

This formula shows that larger plates and a smaller separation result in a larger capacitance.

3 Typical orders of magnitude

Capacitance values in practice span many orders of magnitude:

• Picofarad ($\mathrm{pF}=10^{-12},\mathrm{F}$): small ceramic capacitors, cable capacitances
• Nanofarad ($\mathrm{nF}=10^{-9},\mathrm{F}$): film capacitors in electronics
• Microfarad ($\mu \mathrm{F}=10^{-6}\mathrm{F}$): electrolytic capacitors, motor capacitors
• Millifarad ($\mathrm{mF}=10^{-3},\mathrm{F}$): large electrolytic capacitors
• Farad ($\mathrm{F}$): supercapacitors (Goldcaps)

Example: While the capacitance between two traces on a circuit board is only a few picofarads, supercapacitors used as energy storage devices can reach several farads.

4 Example phrasings

• ‘The electrolytic capacitor has a capacitance of 470 µF.’
• ‘For interference suppression, a 100 nF capacitor is connected in parallel.’
• ‘The cable capacitance of the cable is 150 pF per metre.’
• ‘The motor capacitor for the washing machine is rated at 8 µF.’
• ‘Supercapacitors reach capacitances of several farads.’

5 Related quantities

• The electric charge in a capacitor is calculated from:

$$Q=C\cdot U$$

• The stored energy in a capacitor:

$$W=\frac{1}{2}\cdot C\cdot U^2=\frac{1}{2}\cdot \frac{Q^2}{C}$$

• The capacitive reactance with alternating current:

$$X_C=\frac{1}{\omega \cdot C}=\frac{1}{2\pi f\cdot C}$$

• The time constant during charging/discharging:

$$\tau =R\cdot C$$

6 Relevant components

Capacitance is the characteristic property of the capacitor.