What is the formula for Magnetic Reluctance?

The Magnetic Reluctance formula is S = l / (µ0 × µr × A), where S—Reluctance (ampere-turns/weber); l—Magnetic path length (m); µr—Relative permeability of the material; A—Cross-sectional area (m²); µ0 = 4π×10⁻⁷ H/m.

What does S mean in the Magnetic Reluctance formula?

S is Reluctance (ampere-turns/weber).

Magnetic Reluctance

Q: How do you calculate Magnetic Reluctance?

Use the formula S = l / (µ0 × µr × A). Reluctance is the magnetic-circuit analogue of resistance: it is the opposition a magnetic path presents to flux. Enter the values you know in the calculator above and it solves for the remaining variable.

S = l / (µ0 · µr · A)

Calculator

Reluctance

Path Length

Relative Permeability

Cross Section Area

Result

—

Formula

S = l / (µ0 × µr × A)

Description

Reluctance is the magnetic-circuit analogue of resistance: it is the opposition a magnetic path presents to flux. A longer path raises reluctance while a larger cross-section or a higher-permeability material lowers it. High-permeability cores have very low reluctance, which is why they concentrate flux so effectively. An air gap, with µr = 1, adds large reluctance.

Variables

S — Reluctance (ampere-turns/weber)
l — Magnetic path length (m)
µr — Relative permeability of the material
A — Cross-sectional area (m²)
µ0 = 4π×10⁻⁷ H/m —

Practical Notes

Reluctances in series add like resistors; a small air gap dominates the total reluctance of an otherwise high-µ core, which is how gapped inductors store energy and resist saturation.

Related Concepts

All Magnetics & Transformers formulas →

Transformer EMF Equation Transformer VA Rating Transformer Voltage Regulation Transformer Current Ratio Transformer Copper Loss Transformer Iron (Core) Loss Transformer Turns-per-Volt Transformer Impedance Matching

Need more features?

Save calculations, import telemetry data, simulate battery discharge, and collaborate with your team.

Try the App