Electronvolts are a handy measurement unit, but how do we calculate electronvolts from volts? And what is the difference between these two quantities?

Learn:

  • What is an electronvolt: volt vs. electronvolt (an electrifying comparison);
  • How to find electronvolts from volts, an easy conversion; and
  • An application of the electronvolt formula.

In the time required by an electron to circle a particle accelerator, you'll be an expert in the matter. And maybe in the antimatter too!

Volt vs electronvolt: what is an electronvolt?

While you may know what a volt is — but we will see it again later, just for safety — you may not know why many things change if we glue an "electron" in front of it.

Let's see the two concepts separately.

What is a volt?

The volt is the measurement unit for an electric potential difference, the difference in the electric field between two points. This quantity corresponds to the work required to move a test charge between these two points. And which charge is a perfect test charge if not the electron?

🙋 Electrons are subatomic particles, elementary components of atoms, with unitary negative electric charge, ee. The electron's charge is the smallest charge that can exist: there can be fractional charges (quarks, for example), but they can't live "independently".

What is an electronvolt?

Even though it resembles the volt in name, the electronvolt (eV) is an entirely different kettle of fish. The electronvolt is a measure of the kinetic energy acquired by an electron moving in a 1 V1\ \text{V} electric potential difference.

The electronvolt is a fundamental measurement unit in particle physics: with a direct connection with the potential a particle travels in, calculations in terms of eV are a shortcut in many fields.

Calculate volt to electronvolt: conversion between ev and volt

We can't convert volt to electronvolt formally: the two units measure different quantities. We can, however, quickly calculate the electronvolts involved in a problem if we know the charge and the potential difference.

To calculate volt to electronvolt, the formula you need to use is more than straightforward:

eV=qV\text{eV} = q \cdot V

Where:

  • eV\text{eV}Energy in electronvolts;
  • qqCharge of the analyzed particle; and
  • VVPotential difference in volts.

A quantity equal to 1 eV1\ \text{eV} corresponds to many possible situations but more easily to the one we illustrated above. Now that you know the conversion to electronvolt from volt, you can see that:

1 eV=1 e1 V1\ \text{eV} = 1\ \text{e}\cdot1\ \text{V}

Where ee is the elementary charge, the charge of an electron, ee is a universal constant with value:

e=1.602176634×1019 Ce = 1.602176634\times10^{−19}\ \text{C}

Measured in coulombs (yup, the same guy you may have met on our Coulomb's law calculator).

An electronvolt is then numerically equivalent to the charge of an electron: talk about convenience.

How to find electronvolts in some experimental situations

The electronvolt is an incredibly minute quantity. Dragging around that negative exponent causes it to appear often in multiples as the teraelectronvolt or gigaelectronvolt.

Since eVs are a measure of kinetic energy, we can directly relate the velocity to the electronvolt: the conversion is advantageous. The large hadron collider in Geneva (LHC) is currently rated for energies of 14 TeV14\ \text{TeV}. We don't even have to calculate the volts from the electronvolts: the potential difference corresponding to this energy is 14 TV14\ \text{TV}: your standard high-voltage powerline tops at (at most) 50 kV50\ \text{kV}. The calculated electron speed is... too high! Relativistic effects would come easily into play since the kinetic energy calculations in a classical framework return v>cv>c, an impossible statement.

Davide Borchia
Voltage
V
Electric charge
e
Energy (electron volts)
eV
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