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Enter the inductance of each inductor in series. Add more inductors with the button below. The total inductance is calculated from all filled fields.
When inductors are connected in series, the total inductance is the sum of all individual values: \[ L_{\text{total}} = L_1 + L_2 + \cdots + L_n \] The result is always greater than any single inductor in the string. This is the simplest combination rule for any passive component, and it mirrors resistors in series exactly. It is also the opposite of capacitors in series, where the reciprocal formula applies and the total is always less than the smallest value.
The derivation is straightforward. All inductors in series carry the same current \( I \), so the voltage across each one is \( V_k = L_k \frac{dI}{dt} \). The total voltage is: \[ V_{\text{total}} = \sum_k V_k = \left(\sum_k L_k\right) \frac{dI}{dt} \] Since \( L_{\text{total}} \) is defined by \( V_{\text{total}} = L_{\text{total}} \frac{dI}{dt} \), the sum formula follows directly.
Note on mutual coupling: the formula above assumes no magnetic coupling between inductors (\( M = 0 \)). When two inductors are wound or placed so their magnetic fields interact, the effective inductance changes. For two coupled inductors in series, the result depends on the winding orientation: \[ L_{\text{total}} = L_1 + L_2 \pm 2M \] where \( M \) is the mutual inductance. Aiding fields (fluxes in the same direction) add \( 2M \), giving a higher total than the simple sum. Opposing fields subtract \( 2M \), giving a lower total. The calculator assumes \( M = 0 \), which is the correct starting point for well-separated, unshielded components.
When all \( n \) inductors have the same value \( L \), the total simplifies to: \[ L_{\text{total}} = n \cdot L \] Two identical 100 µH inductors in series give 200 µH, three give 300 µH, and so on. This is useful when a target inductance is a whole-number multiple of a standard catalogue value.
Series combinations are the more common case in practice. The main reason is reaching a higher inductance than is available from a single component. Wirewound inductors have a limited range of off-the-shelf values, and combining two in series is often simpler than a custom winding. Series inductors are also used to add small parasitic-suppression inductors in line with a main inductor in power supply layouts, where a few extra nanohenries of series inductance can help damp ringing without changing the main filter design significantly.
The total DCR of inductors in series adds directly, unlike the parallel case where DCR halves. For high-current applications where copper loss matters, the inductors in parallel calculator is usually the better route. Once the equivalent series inductance is known, use it in the RL time constant calculator, the inductor impedance calculator, or the LC resonance frequency calculator.
More calculators: blog.hirnschall.net/tools/.
