Calculate magnetic permeance and reluctance of magnetic circuits. Supports series/parallel paths, air gaps, and common core geometries for transformer and inductor design.
The Magnetic Permeance Calculator computes permeance (Λ) and reluctance (ℛ) for magnetic circuits — the magnetic analogs of electrical conductance and resistance. Permeance measures how easily magnetic flux flows through a path, and is fundamental to transformer, inductor, and electromagnetic actuator design. It is especially useful when an air gap or core geometry is dominating the result.
In magnetic circuit analysis, the magnetomotive force (MMF = NI) drives flux (Φ) through reluctance: Φ = MMF / ℛ. Reluctance depends on the path's length, cross-sectional area, and material permeability: ℛ = l / (μA). Permeance is simply the inverse: Λ = 1/ℛ = μA/l.
Enter the core geometry, material permeability, and air gap dimensions to calculate total circuit reluctance, permeance, inductance, and flux for a given excitation. Compare different core materials and geometries in the reference tables. It gives a fast read on whether the gap or the core is dominating the result.
Use this calculator when you need to estimate magnetic circuit reluctance, permeance, or inductance for a core and air-gap layout. It is useful for transformer, inductor, and actuator design where geometry and permeability drive the result, especially when a small gap changes the answer a lot. That helps you spot how strongly an air gap affects the magnetic path.
Reluctance: ℛ = l / (μ₀μᵣA). Permeance: Λ = μ₀μᵣA / l = 1/ℛ. Inductance: L = N²Λ = N²/(ℛ_total). Flux: Φ = NI/ℛ = MMF/ℛ. Air Gap Reluctance: ℛ_gap = l_gap / (μ₀A_gap).
Result: ℛ_total = 2.07 × 10⁶ A-turns/Wb, L = 19.3 mH
Core reluctance = 0.2/(4π×10⁻⁷×5000×0.0004) = 79,577 A-t/Wb. Air gap reluctance = 0.001/(4π×10⁻⁷×0.0004) = 1,989,436 A-t/Wb. Total = 2,069,013. L = 200²/2,069,013 = 19.3 mH. The air gap dominates reluctance despite being only 0.5% of path length.
Magnetic circuit analysis uses the electrical circuit analogy to solve for flux, MMF, and reluctance in magnetic paths. Just as Kirchhoff's voltage law applies to electrical circuits, the sum of MMF drops around a magnetic loop equals the total applied MMF. This makes complex geometries tractable using familiar circuit techniques.
For a simple magnetic circuit with a core and air gap in series, the total reluctance is the sum of core and gap reluctances. The gap typically dominates because air's permeability is 1000-10000× lower than the core material.
Intentional air gaps serve several purposes in inductor and transformer design. They linearize the inductance (making it less dependent on core permeability variations), they prevent saturation during DC bias, and they store magnetic energy (primarily in the gap). The trade-off is reduced inductance per turn, requiring more turns or a larger core.
The gap length is typically 0.1-2 mm for power inductors. Distributed gaps (iron powder cores) provide similar benefits with less fringing flux and EMI than discrete gaps.
Material choice depends on frequency and flux density requirements. Laminated silicon steel is optimal for 50/60 Hz power transformers (high Bsat, high μᵣ). MnZn ferrites suit 20 kHz-2 MHz switching converters. NiZn ferrites work at MHz frequencies. Iron powder cores handle high DC bias but have lower permeability.
Permeance (Λ) is the reciprocal of reluctance and measures how easily a magnetic circuit conducts flux. Higher permeance means more flux for a given MMF. It's analogous to electrical conductance (G = 1/R).
Air has relative permeability μᵣ = 1, while magnetic steel has μᵣ = 2,000-10,000. Even a tiny air gap can have more reluctance than the entire core. A 1mm gap in a core with μᵣ = 5000 equals the reluctance of 5 meters of core path.
Air gaps reduce inductance (L = N²/ℛ) because they increase total reluctance. However, they also stabilize inductance against core saturation and temperature variations, which is why many inductors are intentionally gapped.
Silicon steel: μᵣ = 3,000-10,000. Iron powder: μᵣ = 50-200. Ferrites: μᵣ = 500-10,000 (frequency dependent). Permalloy (Ni-Fe): μᵣ = 50,000-100,000. Mu-metal: μᵣ = 20,000-50,000 (used for shielding).
Just like electrical resistances: series ℛ_total = ℛ₁ + ℛ₂ + ...; parallel: 1/ℛ_total = 1/ℛ₁ + 1/ℛ₂ + ... This is the basis of magnetic circuit analysis for complex core geometries.
MMF (NI) ↔ EMF (V). Flux (Φ) ↔ Current (I). Reluctance (ℛ) ↔ Resistance (R). Permeance (Λ) ↔ Conductance (G). Permeability (μ) ↔ Conductivity (σ). This analogy makes analyzing magnetic circuits intuitive for electrical engineers.