Material Permeability Converter

Magnetic permeability (μ) is a measure of how a material responds to an applied magnetic field, essentially indicating how easily a material can be magnetized. It’s defined as the ratio of magnetic flux density (B) to the magnetizing field strength (H) within the material, expressed as μ = B/H. Permeability is fundamental in electromagnetics because it determines how materials interact with magnetic fields—whether they concentrate magnetic flux (ferromagnetic materials with high μ), slightly repel it (diamagnetic materials with μ slightly less than μ₀), or have minimal effect (paramagnetic materials with μ slightly greater than μ₀). This property is crucial for designing transformers, inductors, magnetic shielding, magnetic recording media, and essentially any device or system involving electromagnetic fields.

Microhenry per meter (μH/m) and nanohenry per meter (nH/m) are submultiples of henry per meter (H/m) used for expressing smaller permeability values more conveniently. The relationships are: 1 H/m = 1,000,000 μH/m = 1,000,000,000 nH/m. These smaller units are often more practical in real-world applications since many materials have permeability values much smaller than 1 H/m. For example, the permeability of free space (μ₀) is approximately 1.257 μH/m, and most non-ferromagnetic materials have permeabilities close to this value. Using these smaller units helps avoid working with very small decimal numbers and reduces the risk of calculation errors in practical engineering and scientific work.

Different equivalent units for permeability (H/m, T·m/A, Wb/(A·m)) exist because of the various ways magnetic phenomena can be described and measured in electromagnetic theory. These equivalences arise from the relationships between different electromagnetic quantities in SI units: Henry (H) is the unit of inductance, Tesla (T) is the unit of magnetic flux density, Weber (Wb) is the unit of magnetic flux, and Ampere (A) is the unit of electric current. The relationships can be derived from Maxwell’s equations and the definitions of electromagnetic quantities. For example, since B = μH, where B is in Tesla and H is in A/m, permeability μ must have units of T/(A/m) = T·m/A. Similarly, since magnetic flux Φ = B·A (area), the Weber (unit of flux) is related by Wb = T·m², giving μ units of Wb/(A·m). These equivalent expressions are useful in different contexts depending on which electromagnetic quantities are being directly measured or calculated.

The permeability of free space (μ₀), also known as the magnetic constant or vacuum permeability, is a fundamental physical constant with the exact value of 4π × 10⁻⁷ H/m (approximately 1.256637 × 10⁻⁶ H/m). It represents the magnetic permeability in a classical vacuum and serves as a baseline against which the permeability of all other materials is compared. The importance of μ₀ extends beyond being just a reference value—it appears in many electromagnetic equations, including Maxwell’s equations, and is essential for calculating magnetic fields, inductance, and electromagnetic wave propagation in vacuum. In materials science and engineering, the relative permeability (μᵣ = μ/μ₀) is often used to describe how much more or less permeable a material is compared to vacuum. Additionally, μ₀ is part of the definition of other important constants, like the speed of light in vacuum (c = 1/√(ε₀μ₀), where ε₀ is the permittivity of free space).

Permeability values vary widely across materials:
• Vacuum (by definition): μ₀ = 4π × 10⁻⁷ H/m ≈ 1.257 μH/m
• Air: Approximately μ₀ (very slightly paramagnetic)
• Diamagnetic materials (slightly repel magnetic fields):
  – Bismuth: μᵣ ≈ 0.9999833 (relative to μ₀)
  – Copper: μᵣ ≈ 0.999991
  – Water: μᵣ ≈ 0.9999912
• Paramagnetic materials (slightly attract magnetic fields):
  – Aluminum: μᵣ ≈ 1.00002
  – Platinum: μᵣ ≈ 1.0003
  – Oxygen (gas): μᵣ ≈ 1.0000019
• Ferromagnetic materials (strongly attract and concentrate magnetic fields):
  – Pure iron: μᵣ ≈ 200,000 (varies with field strength)
  – Electrical steel (silicon steel): μᵣ ≈ 4,000-10,000
  – Permalloy (Ni-Fe alloy): μᵣ ≈ 100,000
  – Mu-metal (for magnetic shielding): μᵣ ≈ 80,000-100,000
  – Ferrites: μᵣ ≈ 50-15,000 (depending on composition)
Note that for ferromagnetic materials, permeability is not constant but varies with magnetic field strength and follows a hysteresis curve, which is why ranges are given.