Calculate mutual inductance between coils, coupling coefficient, induced voltage, and energy transfer. Supports coaxial, parallel, and transformer coil configurations.
The Mutual Inductance Calculator computes the magnetic coupling between two coils — a fundamental concept in transformer design, wireless power transfer, and electromagnetic compatibility. When current changes in one coil, it induces a voltage in nearby coils through their shared magnetic flux.
Mutual inductance M relates the voltage induced in coil 2 to the rate of current change in coil 1: V₂ = -M × dI₁/dt. The coupling coefficient k = M/√(L₁L₂) ranges from 0 (no coupling) to 1 (perfect coupling). Power transformers achieve k > 0.95, while wireless chargers operate at k = 0.1-0.5.
Enter coil parameters — self-inductance, number of turns, dimensions, and separation — to calculate mutual inductance, coupling coefficient, induced voltage, and transformer performance metrics.
Use the preset examples to load common values instantly, or type in custom inputs to see results in real time. The output updates as you type, making it practical to compare different scenarios without resetting the page.
Use this calculator when you need to estimate how strongly two coils interact before building the circuit. It is useful for transformer design, wireless charging, sensor coupling, and checking induced voltage or leakage behavior. That helps you compare coupling assumptions before winding coils or laying out a magnetic path in a transformer or charger.
Mutual inductance: M = k√(L₁L₂). Coupling coefficient: k = M/√(L₁L₂). Induced voltage: V₂ = -M × dI₁/dt = -M × ω × I₁_peak (sinusoidal). Coaxial solenoids: M = μ₀N₁N₂A/l (when fully coupled). Transformer: V₂/V₁ = N₂/N₁.
Result: M = 9.50 mH, V₂ = 17.9 V_peak
Two 10 mH coils at k=0.95: M = 0.95 × √(0.01 × 0.01) = 9.50 mH. At 60 Hz with 5A peak: V₂ = M × 2π × 60 × 5 = 0.0095 × 377 × 5 = 17.9 V peak.
An ideal transformer converts voltage by the turns ratio: V₂/V₁ = N₂/N₁, while conserving power: V₁I₁ = V₂I₂. Real transformers have losses from leakage inductance, winding resistance, core losses (hysteresis and eddy currents), and magnetizing current. The coupling coefficient k determines how close to ideal the transformer behaves.
The equivalent circuit of a real transformer includes the magnetizing inductance (L_m = kL₁), leakage inductances on both sides, winding resistances, and core loss resistance. For power transformers, the magnetizing current is typically 1-5% of full-load current.
Wireless power transfer (WPT) operates at coupling coefficients far below transformer levels (k = 0.1-0.5 typically). To transfer power efficiently at low k, resonant circuits are used — both transmitter and receiver coils are tuned to the same frequency, creating a resonant "channel" that efficiently transfers energy despite weak coupling.
Modern Qi wireless chargers use resonant inductive coupling at 100-200 kHz with close-range (< 10mm) coupling. Longer-range systems (like EV wireless charging) use lower frequencies (85 kHz) with larger coils.
Coupled inductors are used in multi-output DC-DC converters, common-mode chokes, and coupled filter networks. The design challenge is achieving the desired coupling coefficient while meeting self-inductance, current capacity, and core saturation requirements. Simulation tools and empirical testing are typically needed for optimization.
Mutual inductance M is the property by which a changing current in one coil induces a voltage in a nearby coil. M depends on the coils' self-inductances and their coupling coefficient: M = k√(L₁L₂). It's measured in Henries (H).
k ranges from 0 (no shared flux) to 1 (all flux links both coils). Iron-core transformers: k = 0.95-0.99. Air-core RF transformers: k = 0.1-0.5. Wireless chargers: k = 0.1-0.6. k depends on geometry, distance, and core material.
For air-core coils, coupling falls off roughly as 1/d³ at distances much greater than the coil dimensions. This rapid falloff is why wireless charging requires close proximity and why transformer cores are used to channel flux efficiently.
Leakage inductance is the portion of a coil's self-inductance that doesn't couple to the other coil: L_leak = L(1-k²). It causes voltage drops and limits power transfer at high frequencies. Minimizing leakage is key in transformer design.
By using high-permeability magnetic cores (iron, ferrite) that channel virtually all flux through both coils. Interleaving windings, using toroidal cores, and minimizing air gaps all push k toward 1.0.
Power transformers, current transformers (CTs), wireless power transfer (Qi charging), RFID, inductive sensors (proximity, metal detection), coupled filters in RF circuits, and electromagnetic interference (EMI) — both intended coupling and unwanted crosstalk. The same idea shows up in both useful magnetic coupling and the unwanted pickup designers try to reduce.