Free Series Inductors Calculator

When working with circuits that contain multiple coils, determining the total or equivalent inductance is a fundamental step for predicting how the circuit will behave. This series inductor calculator—also called an equivalent inductance calculator—gives you a fast way to compute the total inductance in a series circuit by simply entering the individual inductance values. Whether you are adding inductors in series during a design or verifying a textbook exercise, this series inductor calculator provides the answer instantly.

Series Inductor Configuration

Inductors are considered to be connected in series when they are placed end‑to‑end along a single conductive path. In this arrangement, the same alternating current $I$ flows through every inductor because there is no branching. Nevertheless, the electromotive force (EMF) induced in each coil is not necessarily the same; it depends on the inductance of that particular coil and the shared rate of change of current ($dI/dt$). According to Faraday’s law of induction, the back‑EMF across an inductor is

$$e = -L \frac{dI}{dt}.$$

For a group of $n$ inductors connected in series, the individual back‑EMFs are

$$e_1 = -L_1 \frac{dI}{dt},\quad e_2 = -L_2 \frac{dI}{dt},\quad \dots,\quad e_n = -L_n \frac{dI}{dt}.$$

Formula for Equivalent Inductance in Series

The total voltage across the series combination equals the sum of the voltages across each inductor. Hence,

$$e_{\text{total}} = e_1 + e_2 + \cdots + e_n = -(L_1 + L_2 + \cdots + L_n)\frac{dI}{dt}.$$

Using the definition of self‑inductance ($e = -L_{\text{eq}}\, dI/dt$), the equivalent inductance of the series circuit is simply the arithmetic sum of all the individual inductances:

$$L_{\text{series}} = L_1 + L_2 + \cdots + L_n.$$

This formula is analogous to how resistors add in a series resistive circuit.

How to Use the Calculator

1. Choose the calculation mode – Select “equivalent inductance” from the options.
2. Enter the inductance values – Input the known inductances (for example, $L_1 = 5\ \text{H}$, $L_2 = 10\ \text{H}$, $L_3 = 15\ \text{H}$). You can add up to ten inductors.
3. Read the result – The tool instantly displays the total inductance, in this case $30\ \text{H}$.

If you need to find an unknown inductance in a series circuit, just switch the calculator to “find missing inductor” mode and fill in the known values together with the desired total inductance.

Worked Example: Adding Inductors in Series

Suppose you have three inductors: $L_1 = 5\ \text{H}$, $L_2 = 10\ \text{H}$, and $L_3 = 15\ \text{H}$. Using the series inductance formula:

$$L_{\text{series}} = 5\ \text{H} + 10\ \text{H} + 15\ \text{H} = 30\ \text{H}.$$

Thus, the entire series branch behaves as a single $30\ \text{H}$ inductor.

Series vs. Parallel Inductors: A Comparison

The behavior of inductors changes drastically depending on whether they are wired in series or in parallel. The table below highlights the main differences.

Property	Series Connection	Parallel Connection
Arrangement	End‑to‑end, single path	All one ends together, other ends together
Current	Same current through every inductor	Current splits among the branches
Voltage / EMF	Induced EMF may differ across each inductor	Same voltage across each inductor
Equivalent inductance formula	$L_s = L_1 + L_2 + \cdots + L_n$	$\displaystyle \frac{1}{L_p} = \frac{1}{L_1} + \frac{1}{L_2} + \cdots + \frac{1}{L_n}$

From the table, it is clear that adding inductors in series increases the total inductance (the equivalent inductance is always greater than the largest individual value), while a parallel combination yields a smaller equivalent inductance.

Practical Notes

• The unit of inductance is the henry (H). Common sub‑units are millihenries (mH) and microhenries (µH). The calculator works with any consistent unit—just make sure all inputs share the same unit.
• The calculator assumes ideal inductors with no mutual coupling. In real circuits, magnetic coupling between coils can alter the effective inductance; in such cases more advanced models are needed.

By using this series inductor calculator, you save time and prevent arithmetic mistakes when determining the total inductance in a series circuit. Whether you are a student, hobbyist, or professional engineer, having a reliable equivalent inductance calculator at hand simplifies the task of dealing with multiple inductors in a series configuration.