The electron volt calculator above converts between an accelerating voltage and the energy a charged particle gains from it, in electron-volts and in joules. The electron-volt is not an SI unit, but it is the unit atomic, nuclear and particle physics actually use, because the joule is absurdly large for anything happening to a single particle.
Arb Digital publishes free physics calculators that keep adjacent conversions separate rather than lumping them together. The live energy converter rescales bulk energy between joules, calories, kilowatt-hours and the rest, and it has no concept of a charge state at all. This page is about the specific relationship between a potential difference and the energy a charge of a given state gains from crossing it, which is what the electron-volt is defined by.
What This Electron Volt Calculator Does
Given a voltage and a charge state, it returns the energy per particle in electron-volts and in joules. Given an energy, it returns the voltage that would produce it for that charge state. It also gives the molar equivalent, which is how the same energy appears in chemistry, and the total energy carried by however many particles you specify.
The conversion is exact. Since the 2019 redefinition of the SI, the elementary charge is a defined constant with no uncertainty, so the electron-volt to joule relationship is exact too. There is no approximation anywhere on this page, which is not something you can say about most physics calculators.
How to Use It
- Choose the direction — voltage to energy, or energy to the voltage that would produce it.
- Enter the value in whichever unit you have, from volts to gigavolts, or from electron-volts to gigaelectron-volts.
- Set the charge state. This is the step that catches people. It is 1 for an electron or a proton, and higher for a multiply charged ion.
- Set the particle count if you want a total rather than a per-particle figure.
- Read the joule figure when you need to combine this energy with anything measured in SI units.
The Formula: What an Electron-Volt Actually Is
One electron-volt is defined as the kinetic energy gained by a single electron accelerated from rest through a potential difference of one volt in a vacuum. Since work done equals charge multiplied by potential difference, that energy is W = qV, and for one elementary charge crossing one volt it comes to exactly 1.602176634 × 10−19 joules — the value NIST publishes as the CODATA electron volt to joule relationship, marked exact.
For a particle of charge state z crossing a potential difference V, the energy in electron-volts is E(eV) = z × V, and in joules it is E(J) = z × e × V. The reason those two expressions look so similar is that the electron-volt was constructed to make them so.
It is exact because the elementary charge is exact. Since the 2019 revision of the SI, the elementary charge is one of the defining constants of the system, fixed at 1.602176634 × 10−19 coulombs with zero uncertainty — see the NIST CODATA value for the elementary charge and the background on NIST's page on SI units. The electron-volt is therefore an exactly known quantity in joules, unlike most non-SI units, which are defined by measurement.
The molar figure comes from multiplying by the Avogadro constant. One electron-volt per particle corresponds to 96.485 kJ per mole, which is the Faraday constant expressed as an energy, and it is the bridge between the units a spectroscopist uses and the units a chemist uses.
Work the default through by hand. A singly charged particle accelerated through 1 kV gains 1 × 1,000 = 1,000 eV, which is 1 keV. In joules that is 1,000 × 1.602176634 × 10−19 = 1.602176634 × 10−16 J. Per mole it is 1,000 × 96.485 = 96,485 kJ/mol, which is an enormous chemical energy — a reminder that a kilovolt beam is doing something far more violent than chemistry.
Why Charge State Is the Input Everyone Forgets
Because the electron-volt is defined for one elementary charge, and because most people meet it in the context of electrons, it is easy to treat "volts" and "electron-volts" as the same number with different labels. For an electron they are. For anything else they are not.
A doubly charged ion crossing 1,000 volts gains 2,000 electron-volts, because twice the charge does twice the work over the same potential drop. A triply charged ion gains 3,000. This matters constantly in mass spectrometry and ion implantation, where multiply charged species are routine and the beam energy depends on the charge state as much as on the supply setting. The same source at the same voltage produces ions of several different energies if it produces several charge states.
Where the Electron-Volt Turns Up, and at What Scale
The unit is convenient because so much of physics falls into recognisable bands. Chemical bond energies and the energies of visible photons sit at a few electron-volts. Removing a core electron from a light atom takes hundreds to thousands. Medical and industrial X-ray tubes run at tens to hundreds of kiloelectron-volts, which is where electron speeds become relativistic. Nuclear binding energies per nucleon are around eight megaelectron-volts, and particle accelerators reach gigaelectron-volts and beyond.
That range spans about ten orders of magnitude, and the electron-volt covers all of it with familiar prefixes rather than negative powers of ten. Practitioners also use it for mass, via the mass-energy relation: the electron's rest mass is usually quoted as 511 keV rather than 9.1 × 10−31 kg, and that habit is what makes the relativistic arithmetic on the neighbouring speed page tractable in the head.
Where This Sits Next to the Other Energy Tools
The boundary with the energy converter is worth being explicit about. That page rescales a bulk quantity of energy between units — joules, calories, BTU, kilowatt-hours — and it neither knows nor needs a charge state. This page converts a potential difference into a per-particle energy, and the charge state is central to it. If you have a quantity of energy and want it in different units, use the converter. If you have a voltage and want to know what a particle gains from it, use this.
The other close neighbour is the electron speed calculator, and the split is equally clean. The conversion here is definitional and stays exact at any energy. Turning that energy into a speed is a dynamics problem, and above a few tens of kilovolts it needs the relativistic treatment, because the simple half-m-v-squared relation breaks down. Energy scales linearly with voltage indefinitely; speed does not.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Assuming electron-volts always equal volts — that holds only at charge state 1, and multiply charged ions gain proportionally more.
- Treating the electron-volt as a unit of charge or of voltage — it is a unit of energy, and the name misleads almost everyone once.
- Mixing eV with keV or MeV in the same expression — the prefixes span many orders of magnitude and a slip is never small.
- Using this to get a speed directly — converting energy to speed needs the relativistic relation for electrons above a few kilovolts.
- Forgetting the particle count when comparing with a bulk energy — a single particle's energy in joules is vanishingly small next to anything macroscopic.
Related Free Tools From Arb Digital
Pair this with the electron speed calculator to turn the energy into a speed, and the energy converter when you need the joule figure in other bulk units. The relativistic kinetic energy calculator and the kinetic energy calculator cover the mechanics, the photoelectric effect calculator and the de Broglie wavelength calculator the quantum side, and the electric charge converter and the excess electrons calculator the charge side. Everything Arb Digital publishes is on the free online tools hub.
Frequently Asked Questions
Energy, despite the name. It is the kinetic energy gained by one elementary charge accelerated through one volt, and it equals 1.602176634 times ten to the minus nineteen joules exactly. The word volt appears because the definition refers to a potential difference, not because the unit measures one.
Only when the charge state is one. The electron-volt was defined so that a single elementary charge crossing one volt gains exactly one electron-volt, which makes the two numbers coincide for electrons and singly charged ions. For a doubly charged ion the energy is twice the voltage in electron-volts.
Multiply by 1.602176634 times ten to the minus nineteen. That factor is exact, because since the 2019 revision of the SI the elementary charge is a defining constant with no uncertainty, which makes the electron-volt an exactly known quantity in joules rather than a measured one.
A general converter rescales a quantity of energy between units and has no notion of a charge state. This page converts a potential difference into the energy a particle of a given charge state gains from crossing it, which is what the electron-volt is defined by. Use the converter for bulk energy, this for per-particle energy from a voltage.
Yes, but not with the simple half-m-v-squared relation once the energy is an appreciable fraction of the particle's rest energy. For an electron, whose rest energy is 511 keV, that means the relativistic treatment is needed above a few tens of kilovolts. The dedicated speed page handles that properly.
Because of the mass-energy relation. Dividing a rest energy by the speed of light squared gives a mass, so masses are quoted as energies divided by c squared and the c squared is usually left implicit. The electron's rest mass as 511 keV is far easier to work with than 9.1 times ten to the minus thirty-one kilograms.
It bridges to chemistry. One electron-volt per particle is about 96.485 kilojoules per mole, which is the Faraday constant expressed as an energy. Chemists quote bond and reaction energies per mole, spectroscopists quote them per photon in electron-volts, and this factor moves between the two conventions.
No. The conversion assumes the particle crosses the full potential difference without collisions, which is the case in a vacuum. A particle travelling through gas loses energy continuously to collisions and arrives with less than the calculation gives, and that loss depends on the gas, the pressure and the path length.
This tool is provided for educational use. It performs the exact definitional conversion between potential difference and particle energy in a vacuum, and does not model collisional losses, initial thermal energy or space-charge effects.
