Magnetic Permeability Calculator
Enter magnetic flux density B and field strength H to compute permeability μ = B/H, relative permeability and susceptibility.
Input Data
Results
At a glance:Magnetic permeability μ = B/H is the proportionality between magnetic flux density B and magnetic field strength H in a material (from B = μH). The vacuum permeability μ₀ = 4π×10⁻⁷ T·m/A. Relative permeability μ_r = μ/μ₀: μ_r ≈ 1 for non-magnetic materials (air, copper), μ_r ≫ 1 for ferromagnets (iron up to 10⁵), μ_r slightly <1 for diamagnets, slightly >1 for paramagnets. Magnetic susceptibility χ = μ_r − 1 relates magnetization M to H (M = χH). This tool computes μ, μ_r, χ from B and H (and reports μ₀).
Formula
μ = B/H
μ_r = μ/μ₀
χ = μ_r − 1
μ₀ = 4π×10⁻⁷ H/m
$$\mu = \frac{B}{H}, \quad \mu_r = \frac{\mu}{\mu_0}, \quad \chi_m = \mu_r - 1, \quad \mu_0 = 4\pi \times 10^{-7}\ \mathrm{H/m}$$How to Use
- Enter flux density B (T).
- Enter field strength H (A/m).
- The calculator returns μ, μ_r, χ and μ₀.
Case Studies
Iron core
B = 1.5 T, H = 200 A/m.
μ = 1.5/200 = 7.5×10⁻³ H/m.
μ_r = 7.5e-3/1.257e-6 ≈ 5967, χ ≈ 5966.
FAQ
What does μ_r > 1 mean?
The material amplifies the magnetic field inside it (ferromagnets, like iron cores in transformers) by aligning microscopic domains.
What is susceptibility χ?
χ = μ_r − 1 measures how easily a material magnetizes in response to H. Diamagnetic χ<0, paramagnetic χ>0 small, ferromagnetic χ very large (and history-dependent).
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.