Volts to electron-volts calculator

Understanding the relationship between volts, electron-volts, and joules is essential when working with energy conversion, especially in physics and electronics. This article explains these terms, their differences, and how to convert between them.

What Are Volts, Electron-Volts, and Joules?

• Volt (V): A unit of electric potential or voltage. It measures the energy per unit charge. One volt means one joule of energy is transferred per coulomb of charge:
  \[
  1 \, \text{V} = 1 \, \text{J/C}
  \]
• Electron-Volt (eV): A unit of energy commonly used in atomic and particle physics. It represents the energy gained or lost by an electron when it moves through a potential difference of one volt:
  \[
  1 \, \text{eV} = 1.602 \times 10^{-19} \, \text{J}
  \]
• Joule (J): A unit of energy in the International System of Units (SI). It is used for a wide range of energy measurements.

How Are These Units Related?

The relationships between these units are based on the charge of a single electron:

• \[
  1 \, \text{eV} = 1.602 \times 10^{-19} \, \text{J}
  \]
• To convert from volts to electron-volts, multiply the voltage by the charge in coulombs. For a single electron:
  \[
  \text{Energy (eV)} = \text{Voltage (V)} \times 1.602 \times 10^{-19} \, \text{C}
  \]

Conversion Formulas

1. Volts to Electron-Volts: Multiply the voltage by the electron charge:
   \[
   \text{Energy (eV)} = \text{Voltage (V)} \times 1.602 \times 10^{-19}
   \]
2. Electron-Volts to Joules: Use the fixed conversion factor:
   \[
   \text{Energy (J)} = \text{Energy (eV)} \times 1.602 \times 10^{-19}
   \]
3. Volts to Joules for One Electron: Combine the relationships to get:
   \[
   \text{Energy (J)} = \text{Voltage (V)} \times 1.602 \times 10^{-19}
   \]

Practical Example

Problem: Convert 5 volts to electron-volts and then to joules.

1. Step 1: Volts to Electron-Volts
   Multiply the voltage by the electron charge:
   \[
   \text{Energy (eV)} = 5 \, \text{V} \times 1 \, \text{e} = 5 \, \text{eV}
   \]
2. Step 2: Electron-Volts to Joules
   Use the conversion factor:
   \[
   \text{Energy (J)} = 5 \, \text{eV} \times 1.602 \times 10^{-19} = 8.01 \times 10^{-19} \, \text{J}
   \]