Inductors in Series Calculator
Enter the inductance of each inductor in your series circuit and choose a unit for each one. The calculator adds them using the series inductance formula and displays the total equivalent inductance, the inductive reactance at a frequency you specify, and the magnetic energy stored at a given current. Switch to Missing Inductor mode to find the value a single inductor must have to reach a target total. All results update as you type.
How inductors in series work
When two or more inductors are connected end-to-end in a series circuit, the same current flows through every one of them. Each inductor opposes changes in that current by generating a back-EMF proportional to its own inductance. Because the back-EMFs add together, the circuit behaves exactly as if there were a single, larger inductor in their place. The equivalent inductance is simply the sum of all individual inductances: L_total = L1 + L2 + L3 + ... + Ln. This assumes the inductors are far enough apart that their magnetic fields do not overlap; if they are close together, mutual coupling adds an extra term (the mutual inductance M) to the formula.
Series vs. parallel inductors
Putting inductors in series always increases the total inductance beyond any individual value, mirroring the way resistors behave in series. Connecting them in parallel does the opposite: the reciprocal of the total equals the sum of the reciprocals (1/L_total = 1/L1 + 1/L2 + ...), so the result is always smaller than the smallest individual inductor, again just like resistors. Choosing series or parallel depends on whether you need more or less inductance than you have on hand. If you only own a few values, series lets you build any sum; parallel gives you fractions.
Inductive reactance and energy storage
The inductive reactance of the equivalent series inductor is XL = 2 * pi * f * L_total, measured in ohms. It rises linearly with both frequency and total inductance, so doubling either will double XL and halve the AC current for the same voltage. At DC (f = 0) the reactance is zero: an ideal inductor is a short circuit to direct current. The magnetic energy stored in the equivalent inductor at any instant is E = 0.5 * L_total * I^2, where I is the instantaneous current. This is useful when sizing inductors for switching power supplies, where energy is shuttled in and out of the inductor on every switching cycle.
Practical notes for real circuits
Real inductors have winding resistance (DCR), a self-resonant frequency (SRF), and a saturation current rating. When you connect them in series the DCR values add, which increases resistive loss. The SRF of the series combination will generally be lower than any individual SRF, limiting the usable frequency range. If the inductors share a magnetic core (such as a bifilar winding or a transformer with a shared leg) mutual coupling becomes significant, and you must add 2M (positive coupling) or subtract 2M (opposing coupling) from the simple sum. For separate, well-spaced inductors on a PCB, mutual coupling is usually small enough to ignore.
Standard inductance unit prefixes
| Unit | Symbol | Value in henries | Typical application |
|---|---|---|---|
| Henry | H | 1 | Power supply filters, large transformers |
| Millihenry | mH | 0.001 | Audio crossover networks, RF chokes |
| Microhenry | uH | 0.000001 | RF circuits, switch-mode power supplies |
| Nanohenry | nH | 1e-9 | High-frequency PCB traces, chip inductors |
Quick reference for converting between inductance units.
Frequently asked questions
What is the formula for inductors in series?
The total inductance of n inductors in series is L_total = L1 + L2 + L3 + ... + Ln. All individual inductances must be in the same unit before you add them. The formula assumes no mutual coupling between the inductors; if magnetic fields overlap, a mutual inductance term M must be added (aiding coupling: + 2M, opposing: - 2M).
Why does series connection increase inductance?
In a series circuit the same current flows through every inductor. Each one generates a back-EMF that opposes changes in that current. The back-EMFs are independent and add together, so the circuit resists current changes more strongly than any single inductor could. From Kirchhoff's voltage law the combined effect equals a single inductor whose value is the sum of all the individual values.
Do inductors in series add like resistors?
Yes, for inductors that are magnetically uncoupled. Inductors in series add directly (L_total = L1 + L2 + ...), exactly as resistors in series add. Inductors in parallel combine by the reciprocal-sum rule (1/L_total = 1/L1 + 1/L2 + ...), also like resistors in parallel. The analogy breaks down when inductors are physically close and share magnetic flux through mutual coupling.
What is inductive reactance and how does it relate to total inductance?
Inductive reactance XL is the opposition an inductor offers to alternating current. It is calculated as XL = 2 * pi * f * L, where f is the frequency in hertz and L is the inductance in henries. The unit is ohms. A series combination with higher total inductance will have proportionally higher reactance at any given frequency, which reduces AC current and increases the phase shift between voltage and current.
Can I use this calculator to find a missing inductor value?
Yes. Switch to Missing Inductor mode, enter the inductance values of all the inductors you already have, and enter the target total you need. The calculator subtracts the known sum from the target and tells you the inductance the missing inductor must have. If the result is negative, your existing inductors already exceed the target in series, and you would need to remove one or switch to a parallel arrangement instead.
Does mutual coupling affect the series inductance formula?
It does when inductors are close enough for their magnetic fields to interact. If two inductors are wound in the same direction and placed end to end (aiding configuration), the total is L1 + L2 + 2M, where M is the mutual inductance. If they are wound in opposing directions, the total is L1 + L2 - 2M. For inductors mounted several centimetres apart on a PCB, M is usually negligible and the simple sum is accurate enough.