Magnetic Permeability Calculator

Calculate magnetic permeability, relative permeability, and magnetic susceptibility relationships

Calculate Magnetic Properties

Absolute magnetic permeability of the material

Magnetic Properties Results

Absolute Permeability

μ: 0.000e+0 H/m

μ: 0.000e+0 μH/m

μ: 0.000e+0 nH/m

Relative Properties

μᵣ: 0.000000

χ: 0.000e+0

Type:

Relationships

μ = μᵣ × μ₀: 0.000e+0 = 0.000000 × 1.257e-6

χ = μᵣ - 1: 0.000e+0 = 0.000000 - 1

μ₀ (free space): 1.257e-6 H/m

Common Material Examples

Diamagnetic Materials

Water: μᵣ ≈ 0.999991

Copper: μᵣ ≈ 0.999994

Gold: μᵣ ≈ 0.999996

Bismuth: μᵣ ≈ 0.999834

χ < 0, weakly repelled

Paramagnetic Materials

Aluminum: μᵣ ≈ 1.000022

Magnesium: μᵣ ≈ 1.000012

Titanium: μᵣ ≈ 1.00018

Oxygen: μᵣ ≈ 1.000002

χ > 0 (small), weakly attracted

Ferromagnetic Materials

Iron: μᵣ ≈ 200-5000

Nickel: μᵣ ≈ 100-600

Cobalt: μᵣ ≈ 250

Mu-metal: μᵣ ≈ 80,000

χ ≫ 0, strongly attracted

Key Formulas

Permeability Relationship

μ = μᵣ × μ₀

Absolute = Relative × Free space

Susceptibility

χ = μᵣ - 1

Susceptibility from relative permeability

Magnetic Fields

B = μH

Magnetic flux density

Free Space Constant

μ₀ = 4π × 10⁻⁷ H/m

Permeability of vacuum

Unit Conversions

1 H/m10⁶ μH/m
1 H/m10³ mH/m
1 H/m10⁹ nH/m
μ₀1.257 μH/m
Henry (H)Unit of inductance

Understanding Magnetic Permeability

What is Magnetic Permeability?

Magnetic permeability (μ) is a measure of how easily a magnetic field can pass through a material. It describes the material's ability to support the formation of a magnetic field within itself. Materials with high permeability are easily magnetized and enhance magnetic fields.

Types of Magnetic Materials

  • Diamagnetic: μᵣ < 1, weakly repelled by magnets
  • Paramagnetic: μᵣ > 1 (slightly), weakly attracted
  • Ferromagnetic: μᵣ ≫ 1, strongly magnetic

Mathematical Relationships

B = μH (Magnetic flux density)

μ = μᵣ × μ₀ (Absolute permeability)

χ = μᵣ - 1 (Magnetic susceptibility)

M = χH (Magnetization)

Applications

  • Transformer core design
  • Magnetic shielding
  • Inductor design
  • MRI machine engineering

Superconductors and Perfect Diamagnetism

What are Superconductors?

Superconductors are materials that, when cooled below a critical temperature, exhibit zero electrical resistance and perfect diamagnetism (μᵣ = 0). They completely expel magnetic fields from their interior, a phenomenon known as the Meissner effect.

Levitation Effect

The perfect diamagnetism of superconductors allows for magnetic levitation. A magnet placed above a superconductor will float due to the complete expulsion of magnetic field lines.

Common Superconductors

Mercury: Tc = 4.2 K (-269°C)

First discovered superconductor

YBCO: Tc = 93 K (-180°C)

High-temperature superconductor

Niobium: Tc = 9.3 K (-264°C)

Used in MRI machines