Coupled inductors in series calculator

Enter the two self-inductances and the magnitude of their mutual inductance, all in henries. The result shows the uncoupled sum, the larger series-aiding total, and the smaller series-opposing total. It is useful when checking dot-convention choices, transformer windings, coupled chokes, and laboratory coil connections before placing the pair into a circuit model or calculating its reactance.

What series aiding and series opposing mean

Two nearby coils can share magnetic flux, so their series inductance is not generally just L1 plus L2. A changing current in either winding induces a voltage in the other. The polarity of that induced voltage depends on the winding direction and on which terminals are joined. In a series-aiding connection, the mutually induced voltages reinforce the self-induced voltages, and the equivalent inductance is L1 + L2 + 2M. In a series-opposing connection, those voltages subtract, and the equivalent inductance is L1 + L2 - 2M. This calculator reports both totals at once so that you can compare the two valid orientations without changing an input or interpreting a sign convention. Mutual inductance is entered as a nonnegative magnitude; the aiding or opposing choice supplies the effective sign. On a schematic that uses dots, current entering the dotted terminals of both coils produces aiding magnetic effects. Reversing one winding relative to the other produces the opposing case. Always confirm the actual terminal markings or winding direction before treating a calculated orientation as the physical connection.

Enter consistent inductance values

Enter self_inductance_1, self_inductance_2, and mutual_inductance in henries. The same formulas work for millihenries or microhenries if every value is first converted to henries; mixing unit scales will create a plausible-looking but incorrect answer. Both self-inductances must be greater than zero, while mutual inductance may be zero. A physically realizable passive pair also requires M to be no greater than the square root of L1 multiplied by L2. The calculator enforces this bound because exceeding it would imply a coupling coefficient above one and could make the opposing result unphysical. If your source gives coupling coefficient k instead of M, first calculate M = k times the square root of L1 times L2. The reported uncoupled sum is a useful cross-check: the aiding result must be at least that sum, while the opposing result must be no greater than it. With zero mutual inductance, both orientations reduce to the same ordinary series sum because neither coil links flux into the other.

Use the result in a circuit calculation

The returned totals are equivalent inductances in henries under the usual ideal coupled-inductor model. Choose series_aiding_inductance_h when the connected winding polarities reinforce and series_opposing_inductance_h when one winding is reversed. You can then use the selected value wherever a single equivalent inductance is appropriate, such as estimating reactance with XL = 2πfL, predicting an ideal RL time constant, or comparing a measured series pair with its schematic model. Remember that the result does not include winding resistance, core loss, leakage behavior beyond the supplied mutual inductance, parasitic capacitance, saturation, frequency dependence, or changes in coupling caused by coil movement. Real components may therefore depart from the ideal result, especially near self-resonance or at currents that drive a magnetic core toward saturation. For a bench check, measure each coil separately, connect them in series in one orientation, and then reverse one coil. The higher measured inductance should correspond to aiding and the lower measurement to opposing. The API price is $0.002 per calculation when you automate this comparison.