Magnetic Permeability Calculator

This magnetic permeability calculator (or simply permeability calculator) can obtain a material's permeability, relative permeability, and susceptibility from the relation between these parameters.

We paired this calculator with a short text describing:

• Differences between diamagnetic, paramagnetic, and ferromagnetic materials;
• The magnetic permeability formula;
• The relative permeability formula; and
• How to calculate magnetic permeability.

You can also use this tool as a magnetic susceptibility calculator! Keep reading to understand the relationship between the parameters used in this tool.

Permeability, or magnetic permeability (not to be confused with a fluid's permeability), is a material's capacity to be affected by an applied magnetic field.

Its SI, International System of Units, unit is the henry per meter (H/m), and we refer to permeability by the letter $\mu$.

According to this value, we can classify materials into three categories in relation to the permeability of free space $\mu_{0}$:

• Paramagnetic. In the presence of an external magnetic field, these materials are magnetized and are attracted to the external magnetic field. $\mu > \mu_{0}$
• Diamagnetic. Diamagnetic materials, in contrast, produce a magnetic field in opposition to the external magnetic field. Thus, they are repelled. $\mu < \mu_{0}$
• Ferromagnetic. These materials can retain the magnetic field after the external magnetic field is removed and become permanent magnets. $\mu >> \mu_{0}$

Permeability expresses the ratio between the magnetic flux density and magnetic field strength:

where:

• $B$ is the magnetic flux density; and
• $H$ is the magnetic field stregth.

We can also write permeability in terms of $\mu_{0}$:

where:

• $\mu_{r}$ is called relative permeability;
• $\mu_{0}$ is the permeability of free space; and
• $\mu$ is the material's permeability.

You can also input magnetic susceptibility $\chi$ in this magnetic permeability calculator. Both expressions are related by: