Apparent Permeability Calculator

Calculate μ_app and A_L from a measured inductor

Measured Values

Measured Inductance (mH)

Number of Turns

Core Geometry

Tongue (T) (inches)

Stack Height (inches)

Stacking Factor

Typical 0.90-0.95 for interleaved laminations

Apparent Permeability (μ_app)	—
Inductance Factor (A_L)	—
Core Area (A_c)	—
Magnetic Path (l_c)	—

Formulas Used

Inductance Factor: A_L = L / N²

Apparent Permeability: μ_app = (A_L × l_c) / (μ₀ × A_c)
where μ₀ = 4π × 10⁻⁷ H/m

Core Geometry:
A_c = T × Stack Height × Stacking Factor
l_c = 6 × T (where T = Tongue)

Apparent vs. Effective Permeability

Apparent Permeability (μ_app) is what you measure in practice. It represents the overall magnetic behavior of your assembled core, including all real-world effects: air gaps (intentional or not), lamination stacking imperfections, and the butt joints where E and I pieces meet.

Effective Permeability (μ_eff) is a calculated value that accounts for a known air gap in an otherwise ideal core. It's used in design equations when you're intentionally gapping a core:

μ_eff = μ_material / (1 + (l_gap/l_c) × μ_material)

Why they differ for EI cores:

Butt-joint gaps: Even without an intentional air gap, EI laminations have microscopic gaps where the E and I pieces meet. These small gaps significantly reduce permeability from the material's rated value.
Interleaving effects: Interleaved stacking (alternating E-I orientation) distributes butt joints across the stack, reducing their cumulative effect compared to non-interleaved stacking.
Stacking factor: The insulation between laminations and imperfect stacking reduce the effective magnetic cross-section.

Practical interpretation: If your measured μ_app is much lower than the lamination material's rated permeability (typically 4,000–10,000 for grain-oriented silicon steel), the difference is primarily due to butt-joint air gaps. For ungapped EI cores, μ_app values of 1,000–3,000 are common.