Atomic, molecular, semiconductor, nuclear, and particle energies are often far smaller than one joule. A convenient unit for these scales is the electron-volt.

One electron-volt is the energy corresponding to one elementary charge multiplied by one volt:

$$\boxed{1,\mathrm{eV}=e,(1,\mathrm V)}.$$

Since

$$e=1.602176634\times10^{-19},\mathrm C$$

and

$$1,\mathrm V=1,\mathrm{J/C},$$

$$\boxed{1,\mathrm{eV}=1.602176634\times10^{-19},\mathrm J}.$$

This conversion is exact in the modern SI.

Electron-volts measure energy, not voltage

Despite its name, the electron-volt is a unit of energy. The volt is a different quantity: one volt is one joule per coulomb.

The name comes from electrostatics: a particle with charge magnitude $e$ changes its electric potential energy by one electron-volt when it moves through a potential difference of one volt in the appropriate direction. But once defined, the electron-volt can be used for any kind of energy, including photon energies, binding energies, band gaps, and particle rest energies.

Converting between electron-volts and joules

To convert electron-volts to joules, multiply by

$$1.602176634\times10^{-19},\mathrm{J/eV}.$$

For example,

$$500,\mathrm{eV} =(500)(1.602176634\times10^{-19}),\mathrm J \approx8.01\times10^{-17},\mathrm J.$$

To convert joules to electron-volts, divide by the same factor. For example,

$$3.204\times10^{-19},\mathrm J \approx2.00,\mathrm{eV}.$$

Common multiples

Useful multiples include

$$1,\mathrm{keV}=10^3,\mathrm{eV},$$

$$1,\mathrm{MeV}=10^6,\mathrm{eV},$$

$$1,\mathrm{GeV}=10^9,\mathrm{eV}.$$

Thus

$$1,\mathrm{MeV}=1.602176634\times10^{-13},\mathrm J.$$

Electron-volts do not introduce a new kind of energy. They simply provide a convenient unit for microscopic energy scales.