What is a good coupling coefficient?

Depends on the application. Power transformers need tight coupling at 0.95 to 0.99. Wireless charging operates at 0.1 to 0.5. EMI coupling between PCB traces is typically below 0.05.

Can mutual inductance exceed either individual inductance?

No. The maximum mutual inductance is the geometric mean of the two inductances at k equals 1. If L1 equals L2 then M max equals L. If they differ then M max is between the two values.

How do I measure coupling coefficient?

Measure L1 and L2 individually then measure them in series aiding and series opposing. k equals the difference divided by four times the geometric mean of L1 and L2. Or measure the open circuit voltage ratio.

Mutual Inductance Calculator – Coupling Coefficient & Transformer Design

M = k × √(L₁ × L₂)

Find mutual inductance from coupling coefficient, or find k from measured M.

Find M from k Find k from M

L₁ Primary Inductance

L₂ Secondary Inductance

k Coupling Coefficient (0 to 1)

Mutual Inductance Analysis

Mutual Inductance M
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Coupling k
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Max M (k=1)

L₁

L₂

Turns Ratio

Coupling Assessment

Mutual Inductance Between Two Coils

When two inductors share magnetic flux, a change in current in one induces a voltage in the other. The coupling coefficient k (0 to 1) measures how much flux is shared. k = 1 means perfect coupling (all flux links both coils); k = 0 means no coupling.

L₁ — Primary inductance. The coil where the driving current flows.
L₂ — Secondary inductance. The coil where voltage is induced.
k — Coupling coefficient. Iron core: 0.95–0.99. Air core: 0.01–0.3. Wireless power: 0.1–0.5.
M — Mutual inductance in henries. The shared inductance between the two coils.

Mutual Inductance Calculator

Mutual inductance describes the magnetic coupling between two inductors. When current changes in one coil, it induces a voltage in the other through shared magnetic flux. The coupling coefficient k (0 to 1) quantifies how much of the flux from the primary actually links the secondary. This calculator finds mutual inductance from the coupling coefficient and individual inductances, or finds k from a measured mutual inductance.

What Is Mutual Inductance?

Self-inductance (L) describes a coil's own magnetic field. Mutual inductance (M) describes how much of that field links to a second coil. The unit is henries, the same as self-inductance. A mutual inductance of 1 H means that a current change of 1 A/s in the primary induces 1 V in the secondary. The fundamental relationship is V₂ = M × dI₁/dt — the voltage induced in the secondary is proportional to the rate of current change in the primary. This is the principle behind every transformer. For the energy stored in each individual inductor, see the Inductor Energy Calculator.

The Formula and Coupling

M = k × √(L₁ × L₂)

k = M / √(L₁ × L₂) — coupling coefficient (0 ≤ k ≤ 1)
M_max = √(L₁ × L₂) — theoretical maximum at k = 1

Induced voltage: V₂ = M × dI₁/dt

Coupling Coefficient Reference

k = 0.95–0.99 — Iron-core transformer. Nearly all flux links both windings. Standard power and audio transformers.
k = 0.5–0.9 — Gapped ferrite core. Flyback transformers, some SMPS designs. Deliberate leakage for energy storage.
k = 0.1–0.5 — Wireless power transfer (Qi charging). Coils separated by a few mm of air and plastic.
k = 0.01–0.1 — Air-core coils at moderate distance. RFID, NFC, inductive sensors.
k < 0.01 — Parasitic coupling. PCB trace crosstalk, EMI between adjacent inductors.

Iron-Core Transformer (k = 0.98)

L₁ = 10 mH, L₂ = 10 mH, k = 0.98
M = 0.98 × √(10 mH × 10 mH) = 0.98 × 10 mH = 9.8 mH
M_max = 10 mH (at k = 1)

98% of the flux links both windings. The 2% leakage flux does not couple — it causes leakage inductance, which appears as a series inductance on each winding. Leakage limits the transformer's high-frequency response and causes voltage spikes during switching.

Air-Core Coils (k = 0.15)

L₁ = L₂ = 100 µH, k = 0.15
M = 0.15 × √(100 µH × 100 µH) = 0.15 × 100 µH = 15 µH

Only 15% of the flux links. Typical of RFID reader coils, near-field communication antennas, and inductive proximity sensors. The low coupling means most of the primary's energy stays in the primary — only a small fraction transfers to the secondary.

Wireless Power Transfer (k = 0.3)

L₁ = L₂ = 5 µH, k = 0.3
M = 0.3 × 5 µH = 1.5 µH

Qi wireless charging pads operate at k = 0.2–0.5 depending on alignment and distance. The low coupling is compensated by resonant tuning — both coils are tuned to the same frequency so that even weakly coupled energy transfers efficiently. For the current flowing through the primary coil, see the Inductor Current Calculator.

Applications

Power Transformers

The voltage ratio equals the turns ratio, which is related to the inductance ratio: N₂/N₁ = √(L₂/L₁). Tight coupling (k > 0.95) ensures efficient power transfer with minimal leakage.

EMI and Crosstalk

Unwanted mutual inductance between PCB traces or adjacent inductors causes crosstalk. Even k = 0.01 at high dI/dt (fast switching edges) induces significant noise. Minimise by increasing distance, using perpendicular orientation, or adding shielding.

Current Transformers

A current transformer uses tight coupling (k ≈ 0.99) to measure AC current non-invasively. The primary is the wire carrying the current to measure. The secondary outputs a proportional voltage across a burden resistor.

Frequently Asked Questions

Can coupling coefficient exceed 1?

No. k = 1 means perfect coupling — all flux from the primary links the secondary. This is a theoretical limit. Real transformers achieve k = 0.99 at best because some flux always leaks through air paths.

Does mutual inductance depend on frequency?

The coupling coefficient k is primarily a geometric property and does not change much with frequency. However, at very high frequencies, skin effect and proximity effect alter the current distribution in the windings, which can slightly change the effective coupling.

How do I increase coupling?

Use a magnetic core (iron or ferrite) to guide flux through both coils. Wind the coils closer together or interleave the windings. Reduce the air gap. Use bifilar winding for maximum coupling. All of these reduce the flux that escapes without linking the secondary.

What is leakage inductance?

The inductance associated with flux that links only one winding, not both. It equals L × (1 − k²) for each winding. Leakage causes voltage spikes in switching circuits and limits transformer bandwidth. It is the complement of mutual inductance.

How do I measure mutual inductance?

Measure the inductance with both coils in series aiding (L_a) and series opposing (L_o). M = (L_a − L_o) / 4. This method cancels self-inductance and isolates the mutual component.

Last updated: March 2026