# Brillouin Function Calculator

Brillouin function is a special function that can be seen when studying an idealized paramagnetic material in statistical measurements. The special function is well known during the calculation of the magnetization of an ideal paramagnet. It shows the dependency of the magnetization over an applied magnetic field and total angular momentum of the microscopic magnetic moments of a material. Enter the J and X value in this online Brillouin function calculator to find the result.

Brillouin function is a special function that can be seen when studying an idealized paramagnetic material in statistical measurements. The special function is well known during the calculation of the magnetization of an ideal paramagnet. It shows the dependency of the magnetization over an applied magnetic field and total angular momentum of the microscopic magnetic moments of a material. Enter the J and X value in this online Brillouin function calculator to find the result.

Code to add this calci to your website  #### Formula:

B = ((((2 * j) + 1) / (2 * j)) *coth((((2 * j) + 1) * x) / (2 * j))) - ((1 / (2 * j)) * coth(1 / (2 * j))) Where, j = J x = X B = Brillouin Function

### Example:

Find the Brillouin function for J and X value as 2 and 3.

#### Solution:

B = ((((2 × 2) + 1) / (2 × 2)) × coth((((2 × 2) + 1) × 3) / (2 × 2))) - ((1 / (2 × 2)) × coth(1 / (2 × 2)))
= 0.8578