Inductor Energy Calculator

Calculator

This calculator solves for energy \( E \), inductance \( L \), or current \( I \) when you provide the other two. The flux linkage \( \lambda \) is always shown as an additional output.

• Inductance (L):
• H mH µH nH

• Current (I):
• A mA

• Energy (E):
• J mJ µJ kJ

Please fill in exactly two variables.

Calculate

Energy Stored in an Inductor — Explanation

When current flows through an inductor, a magnetic field builds up around the windings. The energy required to establish that field is stored within it and returned to the circuit when the current falls. The amount of energy stored depends on both the inductance and the current: \[ E = \frac{1}{2} L I^2 \] Where:

• \( E \) is the stored energy (in Joules, \( \text{J} \)),
• \( L \) is the inductance (in Henrys, \( \text{H} \)),
• \( I \) is the current through the inductor (in Amperes, \( \text{A} \)).

The \( I^2 \) dependence is the key point: doubling the current quadruples the stored energy, just as doubling the voltage quadruples the energy in a capacitor. In practice this matters most in switching power supplies, where the inductor in a boost or buck converter stores energy during one phase of the switching cycle and releases it during the next. The peak current through the inductor sets how much energy is available per cycle, and therefore the maximum power the converter can deliver.

The flux linkage \( \lambda \) is the magnetic analogue of stored charge in a capacitor. It is defined as: \[ \lambda = L \cdot I \] and has units of Weber (Wb). Substituting into the energy formula gives two equivalent forms: \[ E = \frac{\lambda^2}{2L} = \frac{1}{2} \lambda I \] These are useful when flux linkage rather than current is the known quantity, as in some motor and transformer analyses.

Purpose of the Calculator

Given any two of \( E \), \( L \), and \( I \), the calculator solves for the missing one. The rearranged formulas are:

• To solve for \( E \) (checking how much energy a known inductor carries at a given current): \[ E = \frac{1}{2} L I^2 \]
• To solve for \( L \) (sizing an inductor to store a target energy at a given peak current): \[ L = \frac{2E}{I^2} \]
• To solve for \( I \) (finding the current needed to store a target energy in a known inductor): \[ I = \sqrt{\frac{2E}{L}} \]

In all cases the flux linkage \( \lambda = L \cdot I \) is shown as an additional output. If the inductance comes from a combination of inductors, compute the equivalent value first with the inductors in series or inductors in parallel calculator.

Note on saturation: the formula assumes a linear, non-saturating core. Real inductors have a saturation current above which the effective inductance drops sharply, and beyond that point the stored energy no longer follows \( \frac{1}{2}LI^2 \) with the nominal \( L \). Always check the datasheet saturation current rating when operating near peak current.

Comparison with Capacitor Energy

Inductors and capacitors both store energy, but in different fields and with different governing variables. The structural parallel is exact:

	Inductor	Capacitor
Stores	magnetic field energy	electric field energy
Driving variable	\( I \) (current)	\( V \) (voltage)
Energy formula	\( \tfrac{1}{2}LI^2 \)	\( \tfrac{1}{2}CV^2 \)
Charge analogue	\( \lambda = LI \) (flux linkage, Wb)	\( Q = CV \) (charge, C)

See the capacitor energy calculator for the capacitive equivalent.

Related Tools

• Capacitor Energy Calculator — the capacitive equivalent: \( E = \frac{1}{2}CV^2 \).
• Inductor Impedance Calculator — find the inductive reactance \( X_L \) and impedance at a given frequency.
• RL Time Constant Calculator — how quickly current builds up in an RL circuit after a voltage step.
• Inductors in Series / Inductors in Parallel — compute the equivalent inductance of a network.

More calculators: blog.hirnschall.net/tools/.