Find mutual inductance from two coil self-inductances and their coupling coefficient. You can also solve for coupling or the first coil’s self-inductance using the same relationship.
Mutual inductance formula
M = k√(L₁L₂), where M, L₁ and L₂ are in henries and k is the coupling magnitude between 0 and 1. Rearranging gives k = M/√(L₁L₂) and L₁ = M²/(k²L₂).
The model describes linear passive coupled coils. Values in mH and µH are converted before calculation: 1 mH = 0.001 H and 1 µH = 0.000001 H.
Example
With L₁ = 100 mH, L₂ = 400 mH and k = 0.5, M = 0.5√(100 × 400) = 100 mH. Conversely, M = 100 mH with those two self-inductances gives k = 0.5.
Frequently asked questions
Can the coupling magnitude exceed 1?
No in this passive-coil model. An inferred value above 1 is incompatible with the supplied self-inductances; recheck the measurements and units.
Does the result tell me the voltage polarity?
No. This calculator reports mutual-inductance magnitude. Winding orientation, reference-current directions and the dot convention determine induced-voltage signs.
Can zero coupling determine a missing inductance?
No. At k = 0, mutual inductance is zero regardless of the missing positive self-inductance. That inverse is not unique.
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