## How to convert energy in electron-volts (eV) to electrical voltage in volts (V)

Electron-volts (eV) and Volts (V) are SI units used to express different quantities. Electron-volt is the amount of energy, equivalent to the work done while accelerating an electron across a potential difference of a Volt. Therefore, you can derive the electrical voltage, in volts (V), from electron volts (eV) and elementary charge, in Coulombs (C). However, you cannot convert electron volts into electrical voltage.

### Using eV and elementary charge e to Calculate Voltage *V*

Given the energy E (eV) and the electric charge Q (e), you can calculate the voltage* V *(V). In this case, you should divide the electron-volts by the elementary charge, also referred to as the electron or proton charge, as follows:

*V*_{(V)} = *E*_{(eV)} /* Q*_{(e)}

The symbol e is used to represent the elementary charge, which is the electric charge contained in one electron.

Therefore,

Volt = electron volt / elementary charge

Alternatively,

V = eV / e

**Example**

Work out the voltage supply of an electrical circuit, in volts, given that the energy consumption by the circuit is 900 electron-volts, if the charge flow through the circuit is 30 electron charges.

*Solution*

*V* = 900eV / 30e = 30V

### Using eV and Elementary charge Q to calculate Voltage *V*

It is also possible to calculate the voltage *V*, in volts (V), across two points using the electrical charge Q, in coulombs C and energy E, in electron-volts (eV). In this case, you should multiply the energy E by 1.602176565×10-19 and then divide the result by the electrical charge Q, as follows:

*V*_{(V)} = 1.602176565×10^{-19} × *E*_{(eV)} /* Q*_{(C)}

Therefore,

volt = 1.602176565×10^{-19} × electronvolt / coulomb

Alternatively,

V = 1.602176565×10^{-19} × eV / C

**Example**

If the consumption of an electrical circuit is 800 electron-volts, calculate the voltage supply, in volts across the circuit, given that it has a charge flow of 3C.

*Solution*

*V* = 1.602176565×10^{-19} × 800eV / 3C = 4.2724×10^{-17}V