Series Inductance Calculator

Series Inductance Formula

A series chain carries one current, and the voltage across an inductor is set by how fast that current changes. Since the same changing current passes through every coil, each one produces its own voltage and those voltages add.

Summing the voltages around the loop, with the same di/dt in every term because the current is shared:

The rate of change divides out, leaving the plain sum — series inductance behaves exactly like series resistance:

What happens when the coils couple

That derivation quietly assumed each coil only responds to its own current. If two coils are close enough for one field to pass through the other, a mutual inductance M appears and the total changes:

The sign depends on the winding sense and the direction of current, and the factor of two catches people out — coupling can raise or lower the total by twice the mutual inductance, not once. Two 10 µH coils wound on one core with strong coupling can measure anywhere from near zero to about 40 µH.

The mutual inductance itself follows from the coupling coefficient k, which runs from 0 for coils at right angles to nearly 1 for a shared core:

The calculator above assumes k = 0, which is the right assumption for separate surface-mount inductors a few millimetres apart and the wrong one for two windings on one core.

Worked example

Valid only if the three coils do not couple. Keep them apart, or at right angles.

Keeping Series Inductors From Coupling

Because coupling can shift the total by twice the mutual inductance, physical layout is part of the calculation for inductors in a way it is not for resistors. Three things reduce k towards zero:

• Distance. Coupling falls off quickly with separation — a few coil diameters is usually enough for air-core parts.
• Orientation. Two coils at right angles couple very little, because one field passes across the other rather than through it.
• Shielded or closed-core parts. A shielded SMD inductor or a toroid keeps most of its flux inside itself, which is why they are preferred where several sit together on a board.

If the total inductance of a series pair does not measure as the sum, coupling is the first thing to suspect — and the sign of the error tells you the relative winding sense.

Series Inductance in Filters and Chokes

Series inductors are how a supply line is kept quiet. An inductor in series with a load opposes changes in current, so it blocks high-frequency noise while passing DC — the mirror image of a capacitor to ground.

Combined with a capacitor to ground it forms an LC low-pass filter whose corner is:

Chaining inductors in series raises L, which lowers the corner frequency and attenuates more — at the cost of more DC resistance in the path and more voltage drop under load. That trade-off, not the inductance arithmetic, is usually what limits how much series inductance a design can afford.

What Limits a Real Series Chain

• DC resistance adds along the chain, and it is in series with the load. Two inductors of 0.5 Ω each put 1 Ω in the supply path.
• Saturation current is set by the smallest-rated part. A chain saturates when the weakest coil does, and a saturated inductor loses most of its inductance suddenly.
• Self-resonant frequency falls as inductance rises. Above it the part behaves as a capacitor, so a large series inductance can be useless at the frequency you wanted to filter.
• Core losses rise with frequency and flux, and they appear as heat rather than as inductance.

Common mistakes

• Using the reciprocal formula. Series inductors add; parallel inductors use reciprocals.
• Ignoring mutual inductance between coils that sit close together, which can shift the total by twice M in either direction.
• Forgetting the factor of two in L1 + L2 ± 2M.
• Adding the inductances but not the DC resistances, then wondering where the voltage drop came from.
• Rating the chain for the average saturation current rather than the lowest one in it.
• Assuming more series inductance always filters better, when self-resonance may already have turned the part capacitive at that frequency.

Frequently asked questions

How do you calculate inductors in series?

Add them: Leq = L1 + L2 + … + Ln, the same as resistors in series. This assumes the coils do not couple magnetically. If they do, the mutual inductance adds or subtracts twice: Leq = L1 + L2 ± 2M.

Does inductance add in series?

Yes, for magnetically independent coils. The same changing current flows through each one, so their voltages add and the inductances add with them. The total is larger than the largest single inductor.

What is mutual inductance in a series connection?

It is the extra inductance that appears when one coil field passes through another. It changes the total by ±2M, positive when the fields aid each other and negative when they oppose. M = k√(L1L2), where k is the coupling coefficient.

How far apart should series inductors be?

Far enough that coupling is negligible — a few coil diameters for air-core parts, or much less for shielded and toroidal types that keep their flux internal. Mounting two coils at right angles also reduces coupling substantially.

Do series inductors share the current?

They carry the same current, since there is one path. That means the chain saturates when its lowest-rated part does, so the saturation rating of the chain is the smallest in it, not the average.