# Volt to Electronvolt Calculator

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**, $e$. 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 $1\ \text{V}$ 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:

Where:

- $\text{eV}$ —
**Energy**in electronvolts; - $q$ —
**Charge**of the analyzed particle; and - $V$ —
**Potential difference**in volts.

A quantity equal to $1\ \text{eV}$ 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:

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

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 $14\ \text{TeV}$. We don't even have to calculate the volts from the electronvolts: the potential difference corresponding to this energy is $14\ \text{TV}$: your standard high-voltage powerline tops at (at most) $50\ \text{kV}$. The calculated electron speed is... too high! Relativistic effects would come easily into play since the kinetic energy calculations in a classical framework return $v>c$, an impossible statement.