Magnetic Coupling Coefficient

k = M / √(L1 · L2)

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Formula

k = M / √(L1 × L2)

Description

The coupling coefficient quantifies how much of one coil’s magnetic flux links a second coil, ranging from 0 (no coupling) to 1 (perfect coupling). It relates the mutual inductance M to the two self-inductances. Tightly wound transformers on a shared core approach k = 1, while loosely coupled air-core coils may have k far below 0.5.

Variables

  • k — Coupling coefficient (0–1)
  • M — Mutual inductance (H)
  • L1, L2 — Self-inductances of the two coils (H)

Practical Notes

Power transformers aim for k > 0.98; loosely coupled resonant wireless-power and tuned-RF coils deliberately use lower k. Leakage inductance is (1 − k)·L and directly sets a transformer’s voltage regulation.

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

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