Elementary charge, e

The size of the charge on a proton, and on an electron with the sign reversed. Every particle ever observed on its own carries a whole-number multiple of it, and since 2019 its value has been exact.

e = 1.602176634 × 10⁻¹⁹ C

Exact by definition, so it has no uncertainty at all.

In other units

Values marked … are exact, but their decimals run on, so they stop at ten significant figures instead of being rounded.

Elementary charge in SI units and in other units
Quantity	Value
e	1.602176634 × 10⁻¹⁹ C
1 C	6.241509074… × 10¹⁸ elementary charges
1 eV	1.602176634 × 10⁻¹⁹ J

1 C in elementary charges

1 C ÷ (1.602176634 × 10⁻¹⁹ C)
= 6.241509074… × 10¹⁸ elementary charges

The number of electrons that carry one coulomb.

1 eV in J

1 eV = e × 1 V
= 1.602176634 × 10⁻¹⁹ C × 1 V
= 1.602176634 × 10⁻¹⁹ J

The same digits as e, because an electronvolt is the energy one elementary charge gains across one volt.

Where the value comes from

Robert Millikan’s oil-drop experiments, from 1909, first showed charge arriving in whole multiples of a single value. By the 2010s the best value no longer came from charged drops: CODATA worked e out from the fine-structure constant and the Planck constant, each known far more precisely than any direct measurement of a charge.

In 2019 e was fixed at exactly 1.602176634 × 10⁻¹⁹ C, and that is now the definition of the ampere: the current that carries 1/(1.602176634 × 10⁻¹⁹) elementary charges past a point each second. The Josephson and von Klitzing constants became exact with it, so electrical standards no longer need the conventional values they had used since 1990.

Two constants made exact with e

Josephson constant, 2e/h = 4.835978484… × 10¹⁴ Hz/V
von Klitzing constant, h/e² = 25,812.80745… Ω

Which form to use

Use e in coulombs for charge, and the same digits in joules for the electronvolt: 1 eV = 1.602176634 × 10⁻¹⁹ J exactly.

For a mole of charges, multiply by the Avogadro constant rather than counting charge by charge: N_A e is the Faraday constant, 96,485.3 C/mol.

At the scale of single charges e is the natural unit: a sodium ion carries +e and a sulfate ion −2e, and a microcoulomb is about 6.24 × 10¹² elementary charges.

Common mistakes

Giving the electron a charge of +e. e is positive by definition; the electron carries −e and the proton +e.
Converting electronvolts the wrong way round. Joules to electronvolts divides by e; electronvolts to joules multiplies by it.
Confusing e, the charge, with e, the base of natural logarithms. The Boltzmann factor for a charge crossing a voltage, exp(−eV/kT), contains both, which is why the exponential is safer written as exp.

Tools that use it

Photon Energy Calculator gives photon energies in electronvolts with it.
Coulomb’s Law Calculator shows each charge as a multiple of e.
Unit Converter offers it as a unit of charge, and in the electronvolt.
Electromagnetic Spectrum Explorer converts every photon energy on the spectrum between joules and electronvolts with it.
Rutherford Scattering Simulator gives the alpha its charge of 2e and the nucleus Ze, and turns MeV into joules with it.
Photoelectric Effect Simulator turns the maximum kinetic energy in electronvolts into the stopping potential in volts, V₀ = K_max/e.
Charged Particle in a Magnetic Field Simulator gives each particle and ion its charge in r = mv/(qB) and the energy qV an ion gains from the accelerating voltage.

Related constants

Faraday constant, F = 96,485.33212… C/mol
Avogadro constant, N_A = 6.02214076 × 10²³ mol⁻¹
Planck constant, h = 6.62607015 × 10⁻³⁴ J·s
Coulomb’s constant, kₑ = 8.9875517862(14) × 10⁹ N·m²/C²