How this instrument works
An inductor resists a change in current by building a magnetic field and storing energy in it; the faster the current tries to move, the harder the coil pushes back, following v = L·di/dt. Wire two coils nose to tail and only one current path exists, so the same changing current i(t) threads both windings at once. Each coil develops its own back-voltage in proportion to its own L, and because a series loop simply sums the voltages around it, those two back-voltages add: L₁·di/dt + L₂·di/dt = (L₁+L₂)·di/dt. The combined coil behaves exactly like a single one whose inductance is that sum — arithmetic that looks trivial until you notice capacitors do the opposite, reserving plain addition for their parallel case instead.
That contrast is not a coincidence but a mirror image running through circuit theory. Charles Proteus Steinmetz's 1893 paper on complex quantities gave engineers a single tool for R, L, and C alike: treat each as an impedance — R, jωL, and 1/(jωC) — and impedances in series always add, full stop, regardless of what built them. Resistance and inductive reactance both sit right-side-up in that fraction, so both sum directly in a chain; capacitance sits upside down in its own reactance term, which is precisely why capacitors in series behave reciprocally while inductors behave like resistors.
The one assumption doing real work here is that the two coils share no magnetic field. Place them far apart or at right angles and that holds almost exactly. Wind them on a shared core, or simply set two toroids close and coaxial, and flux from one winding starts linking through the other — a mutual inductance M that adds or subtracts an extra 2M term depending on how the windings are oriented relative to each other. A pair that reads 0.5 H on the bench when separated can read closer to 0.6 H or 0.4 H once pushed together, which is exactly the effect a transformer is built to exploit and exactly the effect this instrument assumes away.
- Enter your first coil's rated value into Inductance 1, H, read straight off its label or datasheet.
- Enter the second coil's value into Inductance 2, H — order makes no difference, since addition is commutative.
- Read Total inductance, H. A correct answer always sits above your larger single entry, never below it.
- Keep the two coils physically apart or oriented at right angles; the sum assumes no shared magnetic field passes between them.
- For a chain of three or more, feed the running Total inductance, H back into Inductance 1, H and add the next coil in Inductance 2, H.
Worked example — two shelf chokes making a 0.5 H filter
A valve-amp rebuild calls for a 0.5 H choke ahead of the last filter capacitor in the B+ supply, and the parts drawer holds nothing that size on its own — just a 0.2 H unit pulled from one project and a 0.3 H unit pulled from another. Wired nose to tail with their cores kept a hand's width apart, the pair presents a single series inductance of L_total = 0.2 + 0.3 = 0.5 H. Enter 0.2 into Inductance 1, H and 0.3 into Inductance 2, H, and Total inductance, H reads 0.5 exactly, ready to drop straight into the design in place of the single choke the schematic called for.
Setting the two chokes side by side rather than stacked matters more than it looks: bring their cores face to face and an LCR meter would likely read a touch above or below 0.5 H, whichever way the windings happen to line up, because their fields would start to overlap. Kept apart, the reading holds at 0.5 H however the meter's leads are swapped — proof that no mutual term is sneaking into the measurement, only the two coils' own henries doing what plain series addition predicts.
Questions
Why do inductors add in series while capacitors add in parallel?
Because series wiring forces one current through every element, and each inductor's opposition to that shared current scales with its own L, so their back-voltages — and therefore their L values — sum directly. Capacitors instead share one charge in series, and since capacitance is charge per volt, that arrangement combines reciprocally. The two components sit on opposite sides of the same reactance fraction, jωL against 1/(jωC), which is why their series and parallel rules trade places.
What happens if the two coils share a magnetic field?
The simple sum stops being exact. Coils wound on a common core, or simply placed close and aligned, couple through a mutual inductance M, and the true total becomes L₁ + L₂ + 2M when the fields aid each other or L₁ + L₂ − 2M when they oppose. This calculator assumes M is zero, which holds well for parts kept physically apart or crossed at right angles, but not for two windings sharing one bobbin.
Does this addition rule still apply to AC signals, not just steady current?
Yes. Each inductor's impedance at a given frequency is jωL, purely imaginary, and series impedances add regardless of type. Summing the L values first and multiplying by jω afterward gives the identical answer to summing each coil's own jωL — the addition holds at every frequency, not only in the di/dt sense that direct current never actually exercises.
Is the current through both inductors really identical?
Yes, by definition of a series path: with only one route available, whatever current enters the first coil is exactly what leaves it and enters the second, at every instant. That shared current is the entire reason their inductances add rather than combine some other way — it plays the same role here that shared voltage plays for two inductors wired in parallel instead.
How do I combine three or more inductors in series?
Add all of them; the rule extends without change to L_total = L₁ + L₂ + L₃ + …, so long as none of the coils are magnetically coupled to another. With only two input fields on this instrument, total your first pair, then feed that running figure back into Inductance 1, H alongside the next coil in Inductance 2, H, and repeat for however many remain.
Can a very small inductor in a chain be ignored?
Only once it is genuinely dwarfed by the rest, the same way a resistor far below its neighbours barely moves a series total. What differs with inductors is where that small value tends to hide: stray lead and trace inductance runs a few nanohenries per centimetre, invisible beside a 0.3 H choke but often the dominant term in RF work, where every millimetre of wire is itself an uncounted series inductor.