Magnetic Permeability Calculator

Created by Dominik Czernia, PhD
Reviewed by Bogna Szyk and Steven Wooding
Last updated: Feb 07, 2024

This magnetic permeability calculator is a tool that will help you determine the dependency between magnetic permeability and susceptibility. In the following text, we will explain what permeability is and present how you can calculate it using the permeability definition. Read on if you want to find out why some materials are magnetic while others are not.

Did you know that there are substances called superconductors that have an unusual property that allows them to levitate in a magnetic field? Isn't it fascinating? That's why we have also answered the question of what a superconductor is.

What is permeability?

According to the permeability definition, it describes a magnetic field produced by the material that arises in response to an applied magnetic field. We divide materials into three main types based on the magnetic permeability µ:

  • In diamagnetic materials, an externally applied magnetic field creates an internal magnetic field with an opposite direction, causing a repulsive effect. Their magnetic permeability is less than the magnetic permeability of free space µ₀.

  • Paramagnetic materials have a magnetic permeability greater than µ₀, but their internal magnetic field arises only in the presence of an external magnetic field. The magnetic field attracts them.

  • Ferromagnetic materials have magnetic permeability much greater than µ₀, and they can retain their internal magnetic field even in the absence of an external magnetic field. Ferromagnetism is the mechanism that forms permanent magnets in specific materials, e.g., one of the strongest – a neodymium magnet.

Do you know what is the microscopic origin of the magnetism of matter? Check out our magnetic moment calculator to learn how you can compute an elementary magnetic moment of an atom.

Magnetic permeability and susceptibility

In magnetism, we use three fields:

  • Magnetization M\bold M, which is the magnetic field created by the material;
  • Magnetic field H\bold H, which is the magnetic field from outside of the material; and
  • Magnetic field B\bold B, which is the total magnetic field inside the material.

And these fields are closely related to each other:

  • B=μH\bold B = \mu \bold H, where μ\mu is the permeability;

  • M=χH\bold M = \chi \bold H, where χ\chi is the magnetic susceptibility (check Curie's law calculator); and

  • B=μ0(H+M)\bold B = \mu_0 (\bold H + \bold M), where μ0=4π107 H/m\mu_0 = 4 \pi 10^{-7}\ \rm H/m is the magnetic permeability of free space. The unit H\rm H is called "henry," and it is a unit of inductance (see the solenoid inductance calculator).

Our magnetic permeability calculator provides a conversion between μ\mu and χ\chi, which results from the above equations:

χ=μμ01=μr1\chi = \frac{\mu}{\mu_0} - 1 = \mu_r - 1

We usually use so-called relative permeability μr=μ/μ0\mu_r = \mu / \mu_0 to simplify the notation. Try our magnetic permeability calculator and see how it works!

What is a superconductor?

The physical properties of some materials sharply change when cooled below a characteristic critical temperature. Their electrical resistance and permeability become exactly zero, and therefore they are called superconductors.

A material with zero permeability behaves like an ideal diamagnetic which completely ejects a magnetic field from the interior of the superconductor, and we can observe the levitation phenomenon. Perhaps the dreams of levitating cars will soon come true.

Dominik Czernia, PhD
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Relative permeability
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