Series Inductors Calculator — Total Inductance of a Chain of Coils

Background.

Inductors in series add. Chain a 10 mH, a 22 mH and a 47 mH coil end to end and you have 79 mH, and that is the whole rule — the same arithmetic resistors in series follow, and the exact opposite of what capacitors do. The reason is that series elements all carry the same current, and the voltage across an inductor is L times the rate of change of that current, so summing the voltages around the chain sums the inductances.

Two things the total does not tell you, both stated beside the result. First, every coil in a series chain carries the identical current, so the chain's current rating is the lowest rating in it, and the whole chain saturates the moment the first core does. Adding a small inductor to a large one adds inductance but shares none of the current stress.

Second, and more important: this is the uncoupled answer. If two coils share a core or simply sit close enough for their fields to link, the series value becomes L₁ + L₂ ± 2M, where M is the mutual inductance and the sign depends on whether the windings aid or oppose each other. For two identical, tightly coupled coils wired series-aiding, the true total is four times one of them, not two. This page does not ask for a coupling coefficient and therefore cannot compute that case — so keep coupled coils physically separated, or use a coupled-inductor calculation instead of this one.

What is series inductors calculator?

A series connection wires inductors end to end so that one current path runs through all of them. Because the current is common, each coil develops a voltage vᵢ = Lᵢ di/dt across itself, and Kirchhoff's voltage law says those voltages add. Factoring out the shared di/dt leaves v_total = (ΣLᵢ) di/dt, which is exactly the behaviour of a single inductor of value ΣLᵢ. Hence the plain sum. Two consequences follow. The total always exceeds the largest coil in the chain, because every other term is positive — the same check that catches a mis-applied parallel formula. And the current rating of the chain is set by its weakest member, since all of them carry the full current; the chain saturates when the first core saturates, however generous the others are. The rule assumes the coils are magnetically isolated. Where flux links between them, the mutual inductance term enters and the simple sum no longer holds.

How to use this calculator.

1. 01Type the inductor values into the list box, separated by commas, spaces or new lines. Two to twenty values are accepted.
2. 02Choose the unit that applies to every value in the list — convert first if your chain mixes scales.
3. 03Read the total, then check it against the largest-inductor figure. A series total must exceed it.
4. 04Check the current rating separately: the chain handles only what its lowest-rated coil handles.
5. 05If any two coils share a core or sit close together, treat the answer as a lower bound and work out the mutual inductance term instead.

The formula.

Convert every entered value into henries first, so the sum is dimensionally consistent, then add. With 10, 22 and 47 in millihenries that is 10 + 22 + 47 = 79 mH, or 0.079 H, or 79000 µH. There are no reciprocals and no shortcuts to remember, which is why series inductance is the easier of the two combination rules.

The derivation is one line. Series elements share a current i. Each inductor develops vᵢ = Lᵢ di/dt. Kirchhoff's voltage law makes the total voltage the sum of those, and di/dt is common to all of them, so v = (L₁ + L₂ + … ) di/dt. Comparing with v = L_eq di/dt gives L_eq = ΣLᵢ.

The arithmetic check that catches a mistake is that the total must exceed the largest single coil: 79 mH is greater than 47 mH. If your answer comes out below the largest value, you have applied the parallel rule by accident.

What the sum leaves out is mutual inductance. Two coils that link flux are not independent, and the series result becomes L₁ + L₂ + 2M when the windings aid and L₁ + L₂ − 2M when they oppose, where M is the mutual inductance between them. The size of the error is not small: for two identical coils with perfect coupling, M equals L, so the series-aiding total is 4L rather than 2L — a factor of two wrong — and the series-opposing total is zero. This page reports the uncoupled sum and says so beside every result, rather than quietly producing a number that could be that far out.

Rounding happens once, at the end, to ten decimal places, with all intermediate arithmetic at forty significant digits. Outputs are in millihenries and microhenries rather than henries because a nanohenry-scale chain expressed in henries would round away entirely at that precision.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Engineering LibreTexts / James M. Fiore, Introduction to Circuit Analysis, §6.2.2 'Inductance and Inductors'. Primary source for the rule implemented here: 'inductors in series add values just like resistors in series', alongside the parallel counterpart and W = ½LI². Retrieved 2026-07-29.
2. [2]OpenStax (Rice University), University Physics Volume 2, §14.2 'Self-Inductance and Inductors'. Independent second authority for the element law the derivation rests on — the induced emf ε = −L(dI/dt), from which one henry is one volt-second per ampere — and for the definition of self-inductance. It is the shared di/dt across series elements that makes the inductances add. Retrieved 2026-07-29.
3. [3]MIT OpenCourseWare, 6.002 Circuits and Electronics, Spring 2007 (Prof. Anant Agarwal). Course materials on the inductor element law and the series/parallel reduction of energy-storage elements. Landing page verified to load and to list the course number, term and instructor. Retrieved 2026-07-29.