Energy Stored in an Inductor Calculator
Solve E = ½ · L · I² in any direction — stored magnetic energy from inductance and current, or work backwards to find L or I. Includes a circuit diagram, the characteristic parabolic E-vs-I curve, step-by-step math, and tolerance sensitivity.
Current flowing through the inductor builds a magnetic field B, and that field stores energy. The stored energy grows linearly with inductance L but with the square of the current I — doubling L doubles E, while doubling I quadruples it.
I ↑ — quadratic growth
Energy scales with the square of current. Doubling I quadruples E; tripling I multiplies E by nine. This is why high-current magnetic applications carry a steep energy cost.
L ↑ — linear growth
At fixed current, energy scales linearly with inductance. A 2× larger inductor stores exactly 2× the energy, and a 10× larger one stores 10× the energy.
The ½ factor
The ½ comes from integrating the instantaneous power p = L·i·(di/dt) as current ramps from 0 to I. Half the total "L·I²" work is stored in the field; the other half is dissipated by whatever resistance the circuit has.
Saturation matters
The formula assumes L stays constant. In a real ferromagnetic core, L drops sharply once the core saturates — so the actual energy stored at high current is usually less than the formula predicts.
How to Use This Calculator
The inductor energy relation links three quantities: inductance L, current I, and the stored magnetic energy E = ½ · L · I². Pick which one you want the tool to solve, fill in the other two, then press Calculate.
1. Choose what to solve for
Pick E (stored energy from L and I), L (inductance from E and I), or I (current from E and L) — the tool rearranges the formula automatically.
2. Pick a preset, or type your own values
Use the quick pills (1 µH → 1 H, 10 mA → 10 A, 1 nJ → 1 J) or type any custom value and choose its unit from the dropdown.
3. Press Calculate — the result takes focus
Clicking Calculate scrolls the result panel into view, focuses it for keyboard and screen-reader users, and pulses a highlight ring so your eye lands on the answer immediately.
4. Study the energy curves
The chart plots E versus I as a parabola and E versus L as a straight line, both with the current operating point marked. The parabola is the visual reason current dominates the energy budget.
5. Switch to Advanced for more depth
Advanced mode adds a tolerance sensitivity panel (why ±1% in I is worse than ±1% in L) plus companion metrics like flux linkage, energy at 2× current, and the current needed for 2× energy.
6. Convert energy to other forms, or copy the result
Use the energy converter further down the page to express the result in joules, watt-seconds, or as a comparison to a small coin-cell battery's capacity.
What This Tool Offers
Built around the fundamental inductor energy relation E = ½ · L · I², the magnetic-field result behind every flyback converter, boost regulator, and electric motor winding calculation.
Solve all three directions
Go from L and I to E, from E and I to L, or from E and L to I — the formula is rearranged for you.
Full SI unit handling
Enter inductance in µH → H, current in µA → kA, and energy in nJ → kJ. The solver auto-picks the cleanest display unit.
Focus-to-result on Calculate
Pressing Calculate scrolls the result into view, focuses it for accessibility, and plays a teal pulse so the answer is impossible to miss.
Parabolic & linear charts
See E vs I as a parabola and E vs L as a straight line, both live at your current operating point — the visual proof that current dominates.
Annotated field diagram
A labelled inductor schematic with current direction, magnetic field lines, and the energy formula, so you can see where the ½LI² comes from.
Companion energy metrics
Advanced mode reports flux linkage λ = LI, energy at 2× current (4×), the current for 2× energy (×√2), and inductance for 2× energy (×2).
Reference Tables & Conversions
An energy converter, plus lookup tables for typical inductor energies, energy vs. current for common inductors, and equivalent expressions for E.
Energy unit converter
Typical Stored Energy in Real Inductors
Representative values across common component classes. Note how quickly energy climbs with current — the same inductor can span several decades of stored energy across its useful current range.
| Inductor | L | I | E = ½LI² | Typical application |
|---|---|---|---|---|
| RF choke | 1 µH | 10 mA | 50 pJ | Signal filtering |
| Small power inductor | 10 µH | 100 mA | 50 nJ | Low-power SMPS |
| Boost converter | 100 µH | 1 A | 50 µJ | Battery step-up |
| Buck converter | 10 µH | 5 A | 125 µJ | Point-of-load regulator |
| Motor phase winding | 1 mH | 10 A | 50 mJ | Small BLDC motor |
| Relay / solenoid coil | 100 mH | 50 mA | 125 µJ | Electromechanical actuation |
| Large flyback transformer | 1 mH | 20 A | 200 mJ | Offline power supply |
| EV traction motor | 100 µH | 400 A | 8 J | Electric vehicle drive |
Energy vs. Current — Same Inductor
A 1 mH inductor across its current range. Because energy scales with I², the last few amps hold most of the energy.
| Current I | E for L = 1 mH | Relative to 1 A |
|---|---|---|
| 0.5 A | 125 µJ | 0.25× |
| 1 A | 500 µJ | 1× |
| 2 A | 2 mJ | 4× |
| 5 A | 12.5 mJ | 25× |
| 10 A | 50 mJ | 100× |
| 20 A | 200 mJ | 400× |
Equivalent Expressions for Inductor Energy
The same stored energy viewed through different electromagnetic quantities — all equivalent at the terminals.
| Form | Expression | When it's useful |
|---|---|---|
| Inductance form | E = ½ · L · I² | Circuit-level calculations |
| Flux linkage form | E = ½ · λ · I | Magnetic design, λ = L·I |
| Flux/inductance | E = λ² / (2L) | When flux is known |
| Field density | E = ∫ (B² / 2µ) dV | Core/air-gap sizing |
What Does E = ½ · L · I² Measure?
It measures the magnetic energy stored in an inductor while current I flows through it. Unlike a capacitor, which stores energy in an electric field between its plates, an inductor stores energy in the magnetic field surrounding its windings. That energy is what sustains current flow when the source is removed, and it is what must be safely handled (or recycled) whenever an inductive load is switched off.
The Inductor Energy Formula
The defining relationship is:
Rearranged for the other two unknowns:
Where the ½ comes from integrating the instantaneous power delivered to the inductor as its current ramps from 0 to I:
Inductor Energy Variables
| Symbol | Meaning | Unit |
|---|---|---|
| E | Energy stored in the magnetic field | joules (J) |
| L | Inductance | henries (H) |
| I | Steady current through the inductor | amperes (A) |
| λ | Flux linkage, λ = L · I | weber-turns (Wb·t) |
| B | Magnetic flux density in the core | tesla (T) |
Why Current Dominates the Energy
Inductance enters the formula linearly but current enters as a square. This has practical consequences. Doubling the inductance doubles the stored energy, but doubling the current quadruples it. Tripling the current makes stored energy nine times larger. That is why high-current magnetic designs — motor windings, high-power converters, magnetic energy storage — put so much engineering effort into keeping peak currents under control.
It is also why inductive kick events are so violent. When current through a large inductor is suddenly interrupted, the stored ½LI² has to go somewhere, and the resulting voltage spike V = −L·(di/dt) can easily destroy switch transistors or relay contacts unless a snubber, freewheeling diode, or clamp circuit is provided to absorb or recycle the energy.
Inductor Energy Calculation Examples
L = 1 × 10⁻³ H · I = 1 A
E = ½ × 1 × 10⁻³ × 1²
E = 0.5 mJ = 5 × 10⁻⁴ J
E = 0.05 J · I² = 100 A²
L = 2 × 0.05 / 100
L = 1 × 10⁻³ H = 1 mH
I = √( 2 × 8 / 1 × 10⁻⁴ )
I = √( 160,000 )
I = 400 A
Frequently Asked Questions
It falls out of the integration. Power delivered to the inductor is p = L·i·(di/dt), and to find total energy you integrate that from i = 0 up to i = I. The integral of i·di is i²/2, evaluated at I — giving ½·L·I². The same ½ appears in the capacitor formula ½CV², because the underlying mathematics of ramping a linear element from zero to a final value is identical.
Only indirectly, through the current. E = ½LI² contains no voltage term at all. The steady current I is normally V/R (for a series RL circuit), so changing V changes I and therefore E — but the energy itself is fundamentally a function of current and inductance, not voltage.
It has to go somewhere, and that's what makes inductive switching tricky. In a plain circuit it dissipates as heat in the resistance and in the arc across the switch contacts, often accompanied by a large voltage spike. With a freewheeling diode it circulates through the diode. With an active clamp it can be recycled back to the supply. This is why switching an inductor without any energy-absorbing path is a classic way to destroy transistors.
Both have the form ½·X·Y², but the variables differ: an inductor stores ½LI² in a magnetic field, and a capacitor stores ½CV² in an electric field. The inductor behaves like the "dual" of the capacitor — current plays the role voltage plays, and inductance plays the role capacitance plays. Field energetics are otherwise parallel.
Flux linkage λ is defined as λ = L·I, and it's the magnetic analogue of electric charge on a capacitor. Substituting I = λ/L into E = ½LI² gives E = λ²/(2L), and substituting L = λ/I gives E = ½·λ·I. All three forms — ½LI², ½λI, λ²/(2L) — describe the same physical energy in different variables.
Only below saturation. The formula assumes L is constant, which is true for air-core inductors and for ferrite-core inductors below their saturation current. Once a ferromagnetic core saturates, L collapses — sometimes by an order of magnitude — and the real stored energy falls well short of what ½LI² predicts. Real inductors also have winding resistance, which dissipates energy over time.
Yes — that's what the "equivalent capacitor voltage" metric in Advanced mode does. For a chosen reference capacitance, it tells you the voltage the capacitor would need to hold the same stored energy: V = √(2E/C). It's a useful sanity check when deciding whether a magnetic or capacitive energy buffer is the better fit for an application.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| E | Energy | J |
| L | Inductance | H |
| I | Current | A |
What it means
The energy stored in an inductor is given by E = ½ L I², where L is the inductance and I is the current flowing through it. This energy is stored in the magnetic field around the coil. Similar to capacitors, the energy depends on the square of the current. Inductors are used to store energy in power supplies, in transformers, and in motors. The stored energy is released when the current decreases, which can cause voltage spikes (back EMF). Understanding the stored energy is important for designing flyback converters, relay drivers, and for protecting circuits from inductive kickback. The energy density of inductors is typically lower than capacitors, but they are essential in AC applications. Example: An inductor of 10mH carrying 5A stores E = 0.5 * 0.01 * 5² = 0.5 * 0.01 * 25 = 0.125 joules (125 mJ).
Worked example
Energy Stored in an Inductor – Practical Example
Real‑World| Parameter | Value |
|---|---|
| L | 10 mH = 0.01 H |
| I | 2 A |
| Formula | E = ½·L·I² |
Common mistakes
- Units: L in henries, I in amperes → E in joules.
- Energy stored: Proportional to the square of the current – doubling current quadruples energy.
- Alternative: E = ½·L·I² – no other form.
- Sign: Positive.
- Magnetic field: Energy is stored in the magnetic field around the inductor.
Applications
Energy stored in an inductor is E = ½·L·I², depending on inductance and the square of current. This energy is stored in the magnetic field and is released when the current decreases. Engineers use this formula to design inductors for power supplies, to calculate the energy in relay and solenoid coils, and to ensure that the energy is safely dissipated during switching. In switched‑mode power supplies, the stored energy is transferred to the output. In motor drives, it contributes to torque. By understanding the energy relationship, professionals can select inductors with adequate current ratings and design snubber circuits to protect switches.
- Inductor design for switching regulators and converters
- Energy‑recovery circuits and flyback converters
- Relay and solenoid coil energy management
- Motor control and drive design
- Safety considerations for inductive loads
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