Enter the number of electrons per unit volume into the calculator to determine the Fermi Energy.

- All Energy Calculators
- Ionization Energy Calculator
- Energy Level Calculator
- Photon Energy Calculator

## Fermi Energy Formula

The following equation is used to calculate the Fermi Energy.

Ef = (h^2/2me) * (3*pi^2*n)^2/3

Variables:

- Where Ef is the Fermi Energy (Joules)
- n is the number of electrons per unit volume
- h is Planck’s Constant 6.62606957e-34
- me is the electron mass 9.10938188e-31

## How to Calculate Fermi Energy?

The following two example problems outline the steps and information needed in order to calculate Fermi Energy.

**Example Problem #1:**

- First, determine the number of electrons per unit volume. In this example, the number of electrons per unit volume is measured to be 9.
- Finally, calculate the Fermi Energy using the formula above:

Ef = (h^2/2me) * (3*pi^2*n)^2/3 =

Inserting the values from above and solving the equation with the imputed values gives:

Ef = (6.62606957e-34^2/(2*9.10938188e-31)) * (3*3.14159^2*9)^2/3 = 5.704e-33 joules

**Example Problem #2: **

Using the same process as example problem 1, we first define the needed variables outlined by the formula. In this case, the values are provided as follows:

Number of electrons per unit volume = 3

Entering these values into the formula or calculator above gives us the following:

**Ef = (h^2/2me) * (3*pi^2*n)^2/3 = 6.338e-34 **(Joules)