Magnetic Permeability Calculator
Free calculate absolute and relative magnetic permeability from b and h fields. Get instant, accurate results with our easy-to-use calculator.
Input Parameters
H-field (magnetizing field)
Results
Enter parameters to calculate
What is Magnetic Permeability?
Magnetic permeability (μ) is a material property that quantifies how easily a material can be magnetized - how well it supports the formation of a magnetic field within itself. It relates the magnetic flux density (B) to the magnetic field strength (H).
Absolute permeability (μ) = B/H. Relative permeability (μ_r) = μ/μ₀, where μ₀ = 4π×10⁻⁷ H/m is the permeability of free space. Relative permeability is dimensionless and indicates how much more (or less) permeable a material is compared to vacuum.
Materials are classified by permeability: Diamagnetic (μ_r < 1), Paramagnetic (μ_r > 1, slightly), Ferromagnetic (μ_r >> 1, very large). Iron has μ_r ≈ 200-5000, making it highly permeable.
Magnetic Permeability Formulas
Where:
- • μ = Absolute permeability (H/m)
- • B = Magnetic flux density (T)
- • H = Magnetic field strength (A/m)
Relative permeability:
μ_r = μ / μ₀ = B / (μ₀H)
Permeability of free space: μ₀ = 4π×10⁻⁷ H/m
How to Calculate
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1
Convert units to SI
Convert B to Tesla (1 G = 10⁻⁴ T), ensure H is in A/m.
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2
Calculate absolute permeability
μ = B / H. This gives permeability in H/m.
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3
Calculate relative permeability
μ_r = μ / μ₀. This dimensionless ratio compares to vacuum.
Practical Examples
Example 1: Vacuum/Air
B = 0.1 T, H = 79,577 A/m (typical for air).
Solution:
μ = 0.1 / 79,577 = 1.257×10⁻⁶ H/m
μ_r = (1.257×10⁻⁶) / (4π×10⁻⁷) ≈ 1.0
Air is essentially non-magnetic (μ_r ≈ 1)
Example 2: Iron
B = 1.0 T, H = 500 A/m (in iron).
Solution:
μ = 1.0 / 500 = 0.002 H/m
μ_r = 0.002 / (4π×10⁻⁷) ≈ 1,591
Iron is highly permeable (μ_r >> 1)
Applications
Electromagnets
Designing electromagnets, selecting core materials, and optimizing magnetic field strength using high-permeability materials.
Transformers
Designing transformer cores, selecting materials for efficient energy transfer, and minimizing magnetic losses.
Magnetic Materials
Characterizing materials, understanding ferromagnetism, and analyzing magnetic properties for material selection.
Education
Teaching electromagnetism, understanding B-H relationships, and learning about magnetic material properties.
Frequently Asked Questions
What is the difference between B and H?
H (magnetic field strength) is the "driving" field from currents. B (magnetic flux density) is the total field including material response. B = μH, where μ accounts for material magnetization.
Why is relative permeability useful?
Relative permeability (μ_r) is dimensionless and directly compares materials. μ_r = 1 for vacuum/air, μ_r >> 1 for ferromagnets. It's easier to work with than absolute permeability values.
Can permeability be negative?
For normal materials, no. However, some metamaterials can have negative permeability (and negative permittivity), leading to negative refractive index and unusual electromagnetic properties.
How does temperature affect permeability?
For ferromagnetic materials, permeability decreases with temperature. Above the Curie temperature, ferromagnets become paramagnetic (μ_r ≈ 1). Temperature effects are significant in material design.
What are typical permeability values?
Vacuum/air: μ_r = 1. Paramagnetic: 1.00001-1.01. Ferromagnetic: 100-100,000+ (iron: 200-5000, mu-metal: up to 100,000). Diamagnetic: 0.9999-1.0 (slightly less than 1).