Inductor Energy Calculator

How this inductor energy calculator works

This calculator computes the magnetic energy stored in an ideal inductor from its inductance and the current flowing through it. You enter the inductance L in henries (H) and the current I in amperes (A), and the tool returns the stored energy E in joules (J). This is useful when sizing inductors for power supplies, filters, or energy storage applications, or for checking textbook problems and lab measurements.

Formula for energy stored in an inductor

The energy stored in an ideal inductor is given by:

E = 1/2 · L · I²

where:

• E is the energy in joules (J)
• L is the inductance in henries (H)
• I is the current in amperes (A)

In more formal mathematical notation, the same relationship can be expressed as:

Key implications of this formula include:

• Energy grows linearly with inductance L.
• Energy grows quadratically with current I (doubling current multiplies energy by four).
• If the current goes to zero, the stored magnetic energy also becomes zero.

Derivation from basic inductor relationships

For users who want to see where the formula comes from, the energy in an inductor can be derived from standard circuit relationships.

Inductance and flux linkage

Inductance L relates magnetic flux linkage to current. Flux linkage, usually written as λ, is the total magnetic flux passing through all turns of the coil. In simple linear inductors:

λ = L · I

Here, λ (lambda) is measured in weber-turns, and it increases proportionally with current as long as the core material remains unsaturated.

Voltage across an inductor

From Faraday’s law of electromagnetic induction, the voltage across an inductor is:

V = L · dI/dt

This tells us that an inductor resists changes in current. A fast change in current (large dI/dt) requires a large voltage.

Energy as the integral of power

Power is the product of voltage and current: P = V · I. The energy needed to increase the current in an inductor from 0 to a final value I is the integral of power over time:

E = ∫ P dt = ∫ V I dt

Substituting V = L · dI/dt gives:

E = ∫ L · (dI/dt) · I dt

Because (dI/dt) · dt = dI, we can change the variable of integration from time to current:

E = ∫ L I dI

Assuming L is constant over the current range (linear inductor), we take it outside the integral:

E = L ∫ I dI = L · (1/2 I²) = 1/2 L I²

This recovers the calculator’s core formula.

Magnetic energy density and core materials

The energy in an inductor is stored in its magnetic field, not in the wire itself. The energy density (energy per unit volume) in a magnetic field is:

u = 1/2 · B² / μ

where:

• u is magnetic energy density (J/m³)
• B is magnetic flux density (tesla, T) — a measure of how strong the magnetic field is
• μ is the magnetic permeability of the material (H/m), indicating how easily it supports magnetic field lines

Integrating this energy density over the volume of the inductor’s core and surrounding space gives the total stored energy, which matches the result from 1/2 L I² for an ideal, linear inductor.

Using a high-permeability core (large μ) allows a given inductance to be achieved in a smaller volume, but real cores also have limits such as saturation and losses, discussed below.

Interpreting the calculator's results

When you enter L and I, the calculator returns a single number in joules. Here is how to make sense of it:

• Small values (microjoules to millijoules) are typical in RF inductors, small filters, and signal-level circuits.
• Moderate values (0.01 J to a few joules) occur in power supply inductors, DC-DC converters, and motor drive chokes.
• Large values (tens to thousands of joules) are associated with large energy storage inductors, pulsed power systems, and some grid or fusion research applications.

Keep in mind:

• At the instant current is interrupted, that stored energy must go somewhere (for example, into a clamp resistor, a snubber network, or a freewheel diode).
• Because energy scales with I², operating slightly above the intended current can significantly increase energy and associated stress on components.

Worked example

Suppose you have a 10 mH inductor in a DC-DC converter, and it carries a peak current of 5 A. What is the peak energy stored in the inductor?

Step 1: Convert units

Inductance is given as 10 mH (millihenries). Converting to henries:

• 10 mH = 10 × 10^-3 H = 0.01 H

The current is already in amperes (5 A), so no conversion is needed.

Step 2: Apply the formula

Use E = 1/2 · L · I²:

• L = 0.01 H
• I = 5 A → I² = 25 A²

So:

E = 1/2 · 0.01 · 25

First multiply L and I²:

• 0.01 × 25 = 0.25

Then apply the 1/2 factor:

• E = 1/2 × 0.25 = 0.125 J

Result: The inductor stores 0.125 joules of energy at 5 A peak current. This is the amount of energy that will be transferred or dissipated when the current is forced to change to a lower value.

Comparison of example values

The table below shows how the stored energy changes with different inductance and current values, using the same formula that the calculator implements.

Assumptions and limitations

The calculator assumes an ideal, linear inductor. Real inductors depart from this ideal in several important ways. When using the results for design or safety decisions, keep the following limitations in mind:

• No core saturation: The formula E = 1/2 L I² treats L as constant. In real magnetic cores, inductance decreases once the core approaches saturation, so the actual energy vs. current curve can flatten at high current.
• Negligible resistance: Wire resistance and core losses are ignored. In practice, some of the input power is dissipated as heat in the winding and core, not stored as recoverable magnetic energy.
• Uniform current: The calculation uses the instantaneous current value. In switching converters or AC circuits, the current may vary within each cycle; designers often calculate energy at peak or ripple extremes.
• No coupling effects: Mutual inductance between coils (as in transformers or coupled inductors) is not modeled. The calculator only considers a single, standalone inductance value.
• Frequency-independent behavior: Frequency-dependent phenomena such as skin effect, proximity effect, and frequency-dependent permeability are not included. The inductance you enter is treated as valid at the operating conditions of interest.
• Safe operating margins: The result does not check against the inductor’s rated current, temperature rise, or insulation limits. Always compare your operating current and energy to the component’s datasheet ratings.

For quick estimates and educational use, these assumptions are usually acceptable. For critical power electronics design, especially at high energy levels, you should also consider detailed core loss models, saturation curves, and thermal analysis.

Related concepts and next steps

The inductor energy formula is closely related to other basic relationships in circuits and electromagnetics:

• Capacitor energy: Capacitors store energy electrically using E = 1/2 C V², where C is capacitance and V is voltage. Together, inductors and capacitors form resonant LC circuits.
• RL time constants: In RL circuits, the rate at which current (and therefore stored energy) builds up or decays is governed by the time constant τ = L/R, where R is resistance.
• Inductance value selection: Choosing L for a given application involves trade-offs among ripple current, size, core material, efficiency, and allowable energy storage.

If you are exploring these topics, you may also find calculators for capacitor energy, RL time constants, and general inductance design helpful for cross-checking your results and understanding how different components share and transfer energy in a circuit.