The inductor combination calculator above finds the equivalent inductance of a group of inductors wired in series or in parallel, and handles the case that makes inductors genuinely different from every other passive component: two of them sharing a magnetic field. When that happens the arithmetic that works for resistors and capacitors stops being sufficient, and the answer depends not just on the values but on which way the windings face.
Arb Digital publishes free engineering calculators that complete a family rather than leaving gaps in it. This page is the third of three: the resistor combination calculator covers series, parallel and mixed resistor networks, the capacitor combination calculator covers capacitors, where series and parallel behave the opposite way round, and this one covers inductors. Only this one has to deal with coupling, and that is the whole reason it needs its own page.
What This Inductor Combination Calculator Does
Inductors in series carry the same current and their voltages add, so their inductances add. Inductors in parallel share a common voltage and their currents add, so their reciprocals add. Both rules are identical in form to the resistor case, which is why the resistor page and this one look so similar at first glance.
The difference appears as soon as two inductors are close enough for the magnetic field of one to pass through the other. Now a changing current in the first induces a voltage in the second, and that mutual inductance either adds to or subtracts from the self-inductance depending on the winding sense. The tool lets you set the coupling coefficient and the orientation, and shows how far the answer moves.
The hero figure is the equivalent inductance of the connection you selected. The grid gives the uncoupled series total, the uncoupled parallel total, the mutual inductance implied by your coupling coefficient, and the reactance the combination presents at your test frequency.
How to Use It
- Type the values as a comma-separated list. All of them are read in the single unit you choose below, so convert first if your parts are a mixture of microhenries and millihenries.
- Choose series or parallel. The uncoupled figures for both connections are always shown in the grid regardless, so you can compare the two arrangements at a glance.
- Set the coupling only when it is real. Leave it at none for parts that are physically separated, on different axes, or shielded. Coupling applies only to a two-inductor list.
- Pick aiding or opposing. This is a wiring decision, not a component property. If you are unsure which one your board implements, measure the series inductance and see which figure it matches.
- Read the reactance. The inductance is what the datasheet quotes, but the reactance is what the rest of the circuit actually experiences at your operating frequency.
The Formula: How Inductors Combine
Without coupling, series inductance is L = L1 + L2 + … and parallel inductance follows 1 ÷ L = 1 ÷ L1 + 1 ÷ L2 + …. The parallel result is always smaller than the smallest member, for the same reason it is with resistors: adding another path can only make it easier for current to change.
With coupling between two inductors, the mutual inductance is M = k√(L1L2), where k lies between 0 and 1. Series then becomes L = L1 + L2 ± 2M, positive for aiding and negative for opposing. Parallel becomes L = (L1L2 − M²) ÷ (L1 + L2 ∓ 2M), where the sign in the denominator is negative for aiding and positive for opposing. Reactance at frequency f is XL = 2πfL, the standard relation described in the OpenStax University Physics section on RL circuits.
Work the defaults through by hand. Two inductors of 10 µH and 40 µH with k = 0.5 give M = 0.5√(10 × 40) = 0.5 × 20 = 10 µH. Uncoupled, the series total is 50 µH and the parallel total is (10 × 40) ÷ 50 = 8 µH. Connected in series aiding, the total becomes 10 + 40 + 20 = 70 µH; series opposing gives 50 − 20 = 30 µH. In parallel the numerator is 400 − 100 = 300 in both cases, so aiding gives 300 ÷ 30 = 10 µH and opposing gives 300 ÷ 70 = 4.286 µH. At 1 MHz, 70 µH presents a reactance of 2π × 106 × 70 × 10−6 = 439.8 Ω.
Mutual Coupling Is the One Thing Resistors Never Do
This is the single point that justifies a separate page. Two resistors sitting next to each other on a board are electrically independent: their equivalent resistance depends only on their values and how they are wired. Two capacitors are the same. Two inductors are not, because inductance is stored magnetic field and magnetic fields do not stop at the component body.
Look at the range in the worked example. The same two parts, wired in series, give anything from 30 µH to 70 µH depending only on which way round one of them is connected. That is a factor of more than two, from a change that no schematic capture tool will flag and no component substitution will fix. If a filter is not behaving and the inductance seems wrong by a large factor, coupling between two nearby coils is one of the first things worth suspecting.
The parallel case has a trap of its own. As k approaches 1 with two equal inductors in parallel aiding, the denominator L1 + L2 − 2M approaches zero and the formula diverges. That is not a physical infinity; it is the model telling you that at perfect coupling with equal values the two branches are no longer independent and the ideal lumped description has broken down. Real parts never reach k = 1, and real windings always have resistance.
How to Tell Whether Your Inductors Are Coupled
Measure rather than guess. Put the two inductors in series one way and measure the total, then reverse one of them and measure again. Call the results La and Lb. The mutual inductance is M = (La − Lb) ÷ 4, and if the two readings are equal there is no coupling. This is a genuinely useful bench technique and it needs nothing more than an inductance meter.
Layout controls the result more than anything else. Two solenoids on the same axis couple strongly; the same two rotated ninety degrees to each other couple weakly, because the field of one crosses the other's turns at right angles and the net flux linkage falls close to zero. Toroids confine most of their field inside the core and couple far less than air-cored solenoids, which is a large part of why they are chosen in dense filter designs. Shield cans, ground planes and physical spacing all reduce it further.
When coupling is what you want rather than what you are fighting, the same mathematics describes a transformer. A high coupling coefficient is the design goal there, and the leakage inductance quoted on a transformer datasheet is simply the part of the winding inductance that the coupling failed to capture.
What the Ideal Model Leaves Out
A real inductor is not just an inductance. It has winding resistance, which sets the copper loss and the Q. It has distributed capacitance between turns, which resonates with the inductance at a self-resonant frequency above which the part behaves as a capacitor rather than an inductor. If it has a magnetic core it also has core loss and a saturation current, beyond which the inductance collapses.
Combination arithmetic assumes none of that. Two 10 µH parts in series really do give 20 µH at low frequency, but the self-resonant frequency of the pair is lower than either part alone, and the usable band shrinks accordingly. Putting inductors in parallel to share current has the opposite problem: unequal winding resistance means the current does not divide the way the inductances suggest, and one part can saturate while the other is barely warm. The solenoid inductance calculator covers what a single coil's geometry produces before any of this arithmetic starts.
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Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Assuming no coupling because the schematic shows none — coupling is a physical layout property, and two coils on the same axis will share flux whatever the drawing says.
- Mixing units in the value list — every entry is read in the single unit selected below the box, so a millihenry typed alongside microhenries becomes a thousand times too small.
- Trusting a parallel result near perfect coupling — with equal values and k close to 1 the aiding formula diverges, which signals that the ideal model has stopped applying rather than that the inductance is enormous.
- Ignoring self-resonance — combining parts lowers the frequency at which the group stops behaving as an inductor, so the arithmetic can be right while the circuit is wrong.
- Paralleling inductors to share current — winding resistance rather than inductance sets the DC split, so one part can saturate long before the other.
Related Free Tools From Arb Digital
This page completes a set of three. Use the resistor combination calculator for series, parallel and mixed resistor networks, and the capacitor combination calculator for capacitors, which behave the opposite way round in series and parallel. For a single component, the solenoid inductance calculator derives inductance from coil geometry and the inductance converter moves between henries, millihenries and microhenries. Once you have an equivalent value, the reactance calculator and the RLC impedance calculator take it into the frequency domain, and the inductor energy calculator gives the stored energy at a given current. Everything Arb Digital publishes is on the free online tools hub. The underlying circuit relationships are set out in the OpenStax University Physics treatment of Ohm's law and in MIT OpenCourseWare's 6.013 Electromagnetics and Applications.
Frequently Asked Questions
Yes, provided they are magnetically isolated. Series inductances add and parallel inductances combine as the sum of reciprocals, exactly matching the resistor rules. The difference is that inductors can also couple magnetically, and once they do the plain sum no longer applies.
It is the shared inductance created when the magnetic field of one coil passes through another, given by M equal to k times the square root of the product of the two inductances. On the bench, measure the series inductance one way, reverse one winding and measure again; the mutual inductance is a quarter of the difference between the two readings.
It is the fraction of one winding's magnetic flux that links the other, ranging from 0 for complete isolation to 1 for perfect coupling. Air-cored coils a few centimetres apart are typically well below 0.01. A closely wound transformer on a closed ferrite core can exceed 0.99, but nothing real reaches exactly 1.
It is purely a wiring and winding-direction question. Aiding means the two magnetic fields reinforce, so the mutual inductance adds twice over and the total exceeds the plain sum. Opposing means they partly cancel, and the total falls below the plain sum. Reversing the connections of one inductor switches between the two without changing any component.
Because with two equal inductors in parallel aiding, the denominator approaches zero as the coupling coefficient approaches one. That is a limitation of the ideal lumped model rather than a physical result. Real components never reach perfect coupling, and real windings have resistance that the ideal formula ignores.
Separate them, rotate one so their axes are at right angles, or use toroidal cores that confine most of the flux inside the core. Shield cans and intervening ground planes help further. Orientation is often the cheapest and most effective change, because two coils at ninety degrees link very little of each other's flux.
The same mutual inductance mathematics describes a transformer, and the coupling coefficient is exactly the quantity that distinguishes a good one from a poor one. This page computes the equivalent inductance a circuit sees, not turns ratios or power transfer, so it is useful for understanding leakage inductance but is not a transformer design tool.
This tool is provided for educational and preliminary design use. It models ideal inductors and does not account for winding resistance, distributed capacitance, self-resonant frequency, core loss or saturation, all of which limit how closely a real combination follows this arithmetic. Verify critical designs by measurement.
