Magnetic Permeability Calculator

Enter magnetic flux density (B) and magnetic field strength (H) to calculate absolute permeability (μ = B/H) and relative permeability (μr = μ/μ0).

Quick Facts

Absolute permeability
μ = B / H
Ratio of magnetic flux density to magnetic field strength, in henries per meter (H/m).
Permeability of free space
μ0 = 4π × 10⁻⁷ H/m
The reference value against which every material's permeability is compared.
Relative permeability
μr = μ / μ0
Dimensionless; μr ≈ 1 for vacuum/air, 100-10,000+ for ferromagnetic materials like iron.

Your Results

Calculated
Absolute Permeability
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μ = B ÷ H, in henries per meter
Relative Permeability
-
μr = μ ÷ μ0 (dimensionless)
Magnetic Susceptibility
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χm = μr − 1
Material Behavior
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Approximate classification from μr

Ready

Enter B and H, then press Calculate.

Formula and Method for Magnetic Permeability

Magnetic permeability describes how easily a material supports the formation of a magnetic field within itself. It is defined as the ratio of magnetic flux density B (in tesla) to magnetic field strength H (in amperes per meter): μ = B / H, measured in henries per meter (H/m). Dividing μ by the permeability of free space, μ0 = 4π × 10⁻⁷ H/m, gives the dimensionless relative permeability, μr = μ / μ0, which tells you how many times more (or less) magnetic a material is than a vacuum.

Understanding the formula

B (magnetic flux density) and H (magnetic field strength) are related by B = μH, so measuring both at the same point in a material lets you solve directly for μ = B/H. The relative permeability μr = μ/μ0 strips out the vacuum baseline, and the closely related magnetic susceptibility, χm = μr − 1, measures how strongly a material magnetizes in response to an applied field: χm is negative (though tiny) for diamagnetic materials, slightly positive for paramagnetic materials, and large and positive for ferromagnetic materials like iron, nickel, and cobalt.

Working with units

  • Magnetic flux density (B) is measured in tesla (T) in SI, or gauss (G) in the older CGS system, where 1 G = 10⁻⁴ T
  • Magnetic field strength (H) is measured in amperes per meter (A/m) in SI, or oersted (Oe) in CGS, where 1 Oe = 1000/(4π) A/m ≈ 79.577 A/m
  • Mixing SI and CGS units without converting is the most common source of order-of-magnitude errors in permeability calculations — always convert both B and H to consistent units before dividing

Knowing the limits

For linear materials (vacuum, air, most diamagnetic and paramagnetic substances), permeability is essentially constant regardless of field strength. For ferromagnetic materials, however, μ = B/H is not a fixed material constant — it varies with H, rises to a peak, and then falls as the material saturates at high field strengths, and it also depends on magnetic history (hysteresis). Treat any ferromagnetic permeability result as valid only at the specific B-H operating point you measured, and consult the manufacturer's B-H curve for design work.

Frequently Asked Questions

What is the difference between absolute and relative permeability?
Absolute permeability μ (in henries per meter, H/m) is the ratio of magnetic flux density to magnetic field strength, μ = B/H. Relative permeability μr = μ/μ0 is a dimensionless ratio comparing a material's permeability to that of free space (μ0 = 4π×10⁻⁷ H/m), so μr = 1 means the material behaves like a vacuum.
What are typical relative permeability values?
Vacuum and air have μr ≈ 1. Diamagnetic materials like copper and bismuth have μr slightly below 1. Paramagnetic materials like aluminum and platinum have μr slightly above 1. Ferromagnetic materials like iron, nickel, and cobalt range from about 100 to several thousand, and specialty alloys such as mu-metal can exceed 50,000.
Why does permeability change with field strength for materials like iron?
Ferromagnetic materials are nonlinear: their internal magnetic domains align more easily at low-to-moderate field strengths, then saturate at high field strengths where further increases in H produce little additional B. Because of this, μ = B/H is only accurate at one specific operating point on the material's B-H curve, not a fixed constant as it is for linear (diamagnetic or paramagnetic) materials.
How do I convert oersted to A/m?
1 oersted (Oe) equals 1000/(4π) A/m, or about 79.577 A/m. This comes from the CGS-to-SI relationship between magnetic field strength units and is built into this calculator's unit selector.

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