According to the definition, magnetic permeability is a physical unit that has the formula symbol µ. It is similar to susceptibility and indicates how permeable a material is to the magnetic flux density. This is reinforced by a material with high permeability because it can be magnetized. The resistance of such a substance is accordingly low. Materials with high magnetic permeability are, for example, iron and other ferromagnetic materials. With the help of permeability, the connection between a magnetic field and the magnetic flux density is established.

Calculate with permeability

A magnetic field (magnetic field strength) (H) is described using magnetic permeability (µ) and magnetic flux density (B). It looks like this:

formel:beschreibung eines magnetfeldes (1)

The magnetic field constant is the scaling for the magnetic permeability. This has the formula symbol µ0 and is subject to the following regularity:

formel: magnetische feldkonstante(2)

The so-called magnetic permeability is calculated using this magnetic field constant and a material-specific relative magnetic permeability (also called absolute permeability):

formel: definition der magnetischen permeabilität(3)

In a vacuum, by definition:


With (4) and (1) the result is:

berechnung permeabilität(5)

From this regularity it follows that the magnetic flux density of a material is particularly high when the magnetic permeability is also very high. This confirms the fact that matter influences magnetic fields in such a way that a magnetic flux density depending on the material-specific permeability is formed in the matter.

Calculate the magnetic flux density

If you multiply the flux density in an airless space - i.e. a vacuum - by the relative magnetic permeability, you get the magnetic flux density. This is due to the influence of the material in the material. It also follows that the material strengthens the magnetic field when the permeability number is> 1. However, if the value is <1, the magnetic field is weakened again. In the literature, the relative permeability is often simply stated with the letter µ without an index.

Which substances have which magnetic permeability?

    1.Ferromagnetic materials

Ferromagnetic substances (e.g. iron) have a relative magnetic permeability> 1. This is due to the fact that they consist of individual atoms, which in turn have electron spins. They have the property of aligning themselves with an external magnetic field, which creates a new magnetic field in the exterior.. This can sometimes be many orders of magnitude stronger than the magnetic field required to align the electron spins. In ferromagnetic materials, the so-called exchange interaction stabilizes the alignment of the electron spins. This makes the relative magnetic permeability very large. In very special materials, such as amorphous substances (e.g. metallic glass), the permeability number is over 100,000. For iron, in turn, it amounts to around 10,000.


Paramagnets magnetize themselves in an external magnetic field in such a way that the magnetic field inside increases. They therefore also have alignable electron spins. However, these do not stabilize via the so-called exchange interaction. That is why paramagnetism only slightly strengthens a magnetic field. This is also the reason why the relative permeability is only a few thousandths to 100,000ths above the value 1.

    3.Diamagnetic materials

Diamagnetic materials are substances that are neither para nor ferromagnetic. They in turn have a relative magnetic permeability <1 and weaken the external magnetic field. Inside a diamagnet there are no electron spins that align. Instead, the penetration of the external magnetic field into the material induces an electrical current. True to the so-called Lenz rule, this is directed against the actual cause: The magnetic field of the induced current thus weakens the external magnetic field. Diamagnetism actually occurs in basically every matter, for example also in para and ferromagnets. However, the effect is clearly superimposed by the elementary magnets, since they can align.


The superconductors are a special permeable case: they have a permeability of 0, which completely eliminates the magnetic flux density in their interior. This means that a superconductor does not let a magnetic flux through. Therefore, the field lines run around a superconductor. For this reason, superconductors are often referred to as perfect diamagnets. There are interesting experiments in this connection: For example, superconductors float in a magnetic field.