Mutual Inductance Calculator
Enter the linked flux and primary current (or both self-inductances) to compute mutual inductance between two coils.
Input Data
Results
At a glance:Mutual inductance M describes magnetic coupling between two circuits. A changing current I₁ in coil 1 produces flux through coil 2; the total linked flux is N₂·Φ₂₁ = M·I₁, and the induced EMF in coil 2 is ε₂ = −M·dI₁/dt (Faraday's law, Lenz's sign). M is symmetric: M₁₂ = M₂₁. Given the self-inductances L₁ and L₂, M = k·√(L₁·L₂) where k is the coupling coefficient (k=1 for perfect coupling, e.g. a shared iron core; k≪1 for distant coils). Transformers rely on high k to transfer energy efficiently.
Formula
Mutual inductance: M = N₂·Φ₂₁/I₁
From self-inductances: M = k·√(L₁·L₂)
Induced EMF: ε₂ = −M·dI₁/dt
$$M = \frac{N_2 \Phi_{12}}{I_1}, \quad \varepsilon_2 = -M\frac{dI_1}{dt}, \quad k = \frac{M}{\sqrt{L_1 L_2}}$$How to Use
- Enter secondary turns N₂, linked flux Φ and primary current I₁, or enter L₁ and L₂ with k.
- The calculator returns the mutual inductance M.
Case Studies
Coupled coils
N₂ = 100, Φ = 2×10⁻⁴ Wb, I₁ = 0.5 A.
M = 100×2e-4/0.5 = 0.04 H.
A 1 A/s change in I₁ induces 0.04 V in coil 2.
FAQ
What is the coupling coefficient k?
k measures how effectively flux from one coil links the other, from 0 (no coupling) to 1 (all flux shared, e.g. tightly wound on a common core). M = k·√(L₁L₂).
Why the minus sign in ε₂ = −M·dI₁/dt?
Lenz's law: the induced EMF opposes the change in flux that created it. The sign indicates direction, not magnitude.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.