Inductors in Series & Parallel + Energy Calculator

Understanding the inductors in series and parallel calculator — concept and principle

This calculator finds the equivalent inductance of inductors in series or parallel and the magnetic energy stored in the series combination at a given current. Use it to build a filter or choke from standard values or to estimate the energy a coil releases when its current is cut.

How it is calculated

• Series: L_ser = L₁ + L₂ + … + Lₙ.
• Parallel: 1/L_par = 1/L₁ + 1/L₂ + … + 1/Lₙ.
• Energy (series): E = ½ · L_ser · I², with L converted from mH to henries (÷ 1000), giving joules.

Enter inductances as a comma-separated list in millihenries (mH) and the current in amperes. The calculator assumes there is no mutual coupling, meaning the coils do not share magnetic flux.

The principle

An inductor resists changes in current by producing a voltage v = L · di/dt. In series, the same current flows through every coil, so each changes at the same rate and the voltages add: v = (L₁ + L₂ + …) di/dt. The inductances therefore add, exactly like resistors in series. In parallel, every coil has the same voltage, and the total rate of change of current is the sum of each branch's rate: di/dt = v/L₁ + v/L₂ + … . That gives the reciprocal sum, again like resistors in parallel. Stored energy ½LI² is the work done against the self-induced voltage while the current rises from 0 to I; it lives in the magnetic field of the coil.

Worked example

1. Inputs: inductors 10 mH and 22 mH; current 2 A.
2. Series: 10 + 22 = 32 mH.
3. Parallel: 1/10 + 1/22 = 0.1 + 0.0454545 = 0.1454545 per mH, so L = 1 ÷ 0.1454545 = 6.875 mH (also 10 × 22 ÷ 32 for two coils).
4. Energy: ½ × 0.032 H × 2² = 0.5 × 0.032 × 4 = 0.064 J.

How to read the result

Series always gives more than the largest coil; parallel always gives less than the smallest. Because energy rises with the square of current, doubling the current quadruples the stored energy. Switching off a large inductor suddenly forces that energy out as a voltage spike, which is why relays and motors need flyback diodes.

Common mistakes

• Placing coils close together or on a shared core and ignoring mutual inductance. Coupled coils in series give L₁ + L₂ ± 2M, not just L₁ + L₂.
• Forgetting the mH to H conversion, which makes the energy 1000 times too large.
• Exceeding the saturation current: above it, the core can no longer hold more flux and the inductance drops sharply.

Frequently asked questions

Why does the inductor formula look like the resistor formula?

Both elements have a voltage proportional to a property of the current (I for resistors, di/dt for inductors), so the same series and parallel algebra applies.

Where does the energy go when the current stops?

It is released into the circuit, as an arc across a switch, heat in a resistor or diode, or a charge on a capacitor.

Sources: D. Halliday, R. Resnick and J. Walker, Fundamentals of Physics, Wiley, chapter on inductance · C. K. Alexander and M. N. O. Sadiku, Fundamentals of Electric Circuits, McGraw-Hill