Volt to Electron Volt Calculator

Background.

An X-ray tube running at 70 kilovolts cannot emit a photon carrying more than 70 keV. Every electron crossing the tube picks up one electron volt of energy for each volt it falls through, and the most any single photon can take away is everything one electron brought. That bookkeeping, energy in electron volts equals charge number times voltage, is all this conversion does, and it is used constantly in labs, accelerators and electrochemistry.

The electron volt is a unit of energy: the energy one elementary charge gains or loses across a potential difference of one volt. Since the 2019 revision of the SI fixed the elementary charge, 1 eV is exactly 1.602176634 × 10⁻¹⁹ joules. A volt on its own is a joule per coulomb, so a voltage never tells you an energy until you say how much charge moved. Count that charge in elementary charges and the energy in eV is simply z × V.

The charge number is where mistakes creep in. An electron or a proton has z = 1, an alpha particle 2, a fully stripped carbon nucleus 6, and an Al³⁺ ion 3, so across the same gap the alpha gains twice what the proton does. Mass plays no part. A proton and an electron gain identical energy from the same voltage, even though they end up at very different speeds.

The unit suits the atomic scale. Thermal energy at room temperature is about 0.025 eV, visible photons run from about 1.8 to 3.1 eV, ionising hydrogen takes 13.6 eV, and the Large Hadron Collider brings each proton to 6.8 TeV.

What is volt to electron volt calculator?

One electron volt is the change in energy of a particle carrying one elementary charge, e, when it moves through a potential difference of one volt. Because the 2019 SI defines e as exactly 1.602176634 × 10⁻¹⁹ coulombs, the conversion to joules is exact. For a particle of z elementary charges crossing V volts, the energy change is zV electron volts. The result says how much energy the field exchanged with the particle, not whether it was gained or spent, and nothing about the particle's speed.

How to use this calculator.

1. 01Enter the potential difference the particle actually crosses, in volts. In a multi-stage device, add up the stages it passes through; only the start and end potentials count, not the route between them.
2. 02Enter the charge-number magnitude z: 1 for an electron, proton or singly charged ion, 2 for an alpha particle or Ca²⁺, 3 for Al³⁺. Ignore the sign; enter the size of the charge only.
3. 03Read the energy in eV. Divide by 1,000 for keV or by 1,000,000 for MeV when the voltages are large.
4. 04Decide the direction separately: a positive charge moving toward lower potential gains the energy, while moving it the other way costs that much work. The same holds for an electron with the potentials reversed.

The formula.

The work an electric field does on a charge q moving through a potential difference V is W = qV, which is what defines a volt as one joule per coulomb. Writing the charge as z elementary charges, q = z·e, gives W = z·e·V joules. Dividing by e, the size of one electron volt in joules, leaves E = z × V in electron volts. The elementary charge cancels completely, so the conversion needs no constant at all. Multiply by 1.602176634 × 10⁻¹⁹ only when you want joules.

Because an electrostatic field is conservative, the energy depends only on the potentials at the two ends, not on the path, the shape of the electrodes or how long the trip takes. It holds at any speed, including when the particle is relativistic, since it is an energy statement. What it leaves out is anything that takes energy away along the way: collisions with gas, radiation, or a particle that never reaches the far electrode.

The charge number may be entered as a non-integer, which is useful for quark charges of one-third or two-thirds, or for a beam's average charge state.

A worked example.

Frequently asked questions.

References& sources.

1. [1]BIPM, SI Brochure, 9th ed., table of non-SI units accepted for use with SI.
2. [2]NIST, Guide for the Use of the International System of Units, SP 811.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.