# Magnetic Permeability Calculator

URL: https://speedycalculator.com/calculators/physics/magnetic-permeability/
Last updated: 2026-10-30

> The magnetic permeability calculator converts between absolute permeability, relative permeability and magnetic susceptibility, with typical values for common materials.

## Inputs

- Input
- Material
- Relative permeability μ_r
- Permeability μ (H/m)
- Susceptibility χ

## Results

- Relative permeability μ_r
- Permeability μ
- Susceptibility χ
- Magnetic behaviour

## Formula

```
μ = μ_r·μ₀,  χ = μ_r − 1,  μ₀ = 1.25664 × 10⁻⁶ H/m
```

## Explanation

Permeability describes how easily a material supports a magnetic field. Iron cores multiply the field of a coil thousands of times; copper and water are very slightly diamagnetic and weaken it.

### How to use the Magnetic Permeability Calculator

- **Input**
- **Material**
- **Relative permeability μ_r**
- **Permeability μ (H/m)**
- **Susceptibility χ**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose a material or enter one of the three quantities.

### Inputs explained

FieldWhat to enterInputChoose one: Material preset, Relative permeability μ_r, Permeability μ, Susceptibility χMaterialChoose one: Vacuum, Air, Water, Copper …Relative permeability μ_rA numberPermeability μ (H/m)A numberSusceptibility χA number

### What each result means

- **Permeability μ** = [Relative permeability μ_r]×1.25663706212e-06
- **Susceptibility χ** = [Relative permeability μ_r] - 1

### Example values

How the main result changes when **Relative permeability μ_r** changes and everything else stays at the example values above:

Relative permeability μ_rRelative permeability μ_r5005,0007505,0001,0005,0001,2505,0001,5005,0002,0005,000

## Worked example

Inputs — Input: Material preset; Material: Iron (99.8%).

Results — **Relative permeability μ_r = 5,000**; Permeability μ = 0.006283 H/m; Susceptibility χ = 4,999; Magnetic behaviour = Ferromagnetic / ferrimagnetic.

## Key terms

- **Susceptibility**: Magnetisation per unit applied field.

## FAQ

**What is μ₀?**
The vacuum permeability, about 1.2566 × 10⁻⁶ H/m.

**What is diamagnetism?**
Weak repulsion from magnetic fields (χ < 0).

**Is μ_r constant for iron?**
No – it depends on field strength and saturates.

**Why use mu-metal?**
Its very high permeability makes excellent magnetic shields.


## Sources

- [OpenStax – University Physics Volume 2](https://openstax.org/details/books/university-physics-volume-2)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)