The inductor energy calculator above returns the energy an inductor holds in its magnetic field, U = ½LI², and then the three consequences that usually matter more than the energy itself: the flux linkage, the power available while that energy is released, and the voltage that appears across the coil if the current is interrupted rather than allowed to decay gently. An inductor stores energy in a field that exists only while current flows, and the field's insistence on maintaining that current is the source of almost every practical problem inductors cause.
Arb Digital publishes free physics and electronics calculators that answer the question behind the question. Almost nobody needs the number of millijoules in a coil for its own sake. What they need is whether a flyback diode is required, how big the snubber has to be, how much power a switching converter can move per cycle, or why a relay coil keeps destroying the transistor driving it. Those all follow from the same three inputs, so this page computes them together.
What This Inductor Energy Calculator Does
You enter an inductance, the current flowing through it, the time over which that current is brought to zero, and how often the cycle repeats. The hero figure is the stored energy, scaled automatically into joules, millijoules, microjoules or nanojoules so a small signal choke does not read as a string of zeros.
The flux linkage, L × I, is the quantity in webers that the magnetic circuit actually has to carry. It is the number that saturates a core, and it is worth watching because two coils with the same stored energy can be very different distances from saturation. The release power is the stored energy divided by the release time, and it is why a small inductor discharged very fast is a genuinely high-power event for a few microseconds. The average power multiplies the energy by the repetition rate, which is the figure that determines how much heat a switching converter's magnetics and switches have to shed.
The spike voltage is the one that surprises people. It is V = L di/dt, approximated here as L × I divided by the interrupt time, and it does not depend on the stored energy at all. A tiny coil interrupted quickly enough produces a very large voltage. Degenerate cases are handled explicitly: a zero interrupt time would give an infinite voltage and the tool says so in words, a zero repetition rate reports a single event rather than dividing by zero, and a zero inductance or current reports zero energy with an explanation instead of a NaN.
How to Use It
- Enter the inductance at the working current. Datasheet inductance is usually measured at low current. A ferrite or powdered-iron core can lose a third or more of its inductance near its rated current, and the stored energy falls with it.
- Use the peak current, not the average. Because energy goes as the square, the peak dominates. In a switching converter with a triangular ripple, use the top of the ripple.
- Pick a realistic interrupt time. This is the single most influential input for the spike voltage. If a clamp or a flyback diode is present, the current decays over the clamp's timescale, not the switch's.
- Set the repetition rate to the switching frequency. For a one-shot event such as a relay releasing, set it to zero and read the release power instead.
- Compare the release power with the average power. The gap between them is the duty factor, and it explains why a component can survive a peak that its continuous rating would forbid.
The Formula: How Inductor Energy Is Calculated
The energy stored in an inductor is U = ½LI², with inductance in henries, current in amperes and the result in joules. It comes from integrating the power delivered to the coil while the current is built up from zero: the inductor opposes the rise with a back-EMF of L di/dt, and the work done against that back-EMF is what ends up in the field. OpenStax University Physics Volume 2, section 14.3 on energy in a magnetic field, derives the same result twice, once by integrating power and once by integrating the magnetic energy density over the coil's volume. HyperPhysics on energy stored in an inductor works through the integration step by step.
Take the defaults. A 10 mH inductor carrying 2 A stores ½ × 0.01 × 2² = 0.02 J, or 20 mJ. The flux linkage is 0.01 × 2 = 0.02 Wb. If that current is interrupted in 10 µs, the average power during the release is 0.02 ÷ 0.00001 = 2,000 W, and the voltage across the coil is 0.01 × 2 ÷ 0.00001 = 2,000 V. At a repetition rate of 100 Hz, the average power the circuit has to handle is 0.02 × 100 = 2 W.
Those four numbers describe the same event and mislead in different directions if taken alone. Twenty millijoules sounds negligible. Two kilowatts sounds alarming but lasts ten microseconds. Two watts is the figure that sets the heatsink. Two thousand volts is the figure that destroys the switch. This is why the page reports all four rather than the energy on its own.
Why the Spike Voltage Has Nothing to Do With the Energy
This is the most commonly misunderstood point about inductors, and it causes real damage. Capacitors resist changes in voltage; inductors resist changes in current. When you open a switch in series with an inductor, the coil will do whatever it takes to keep the current flowing, and what it takes is voltage. The magnitude is set by L di/dt, so the faster the interruption, the higher the voltage, without limit until something breaks down and provides a path.
That is why a relay coil holding a few tens of millijoules routinely kills a transistor rated at 60 V. The energy would not warm the transistor measurably; the voltage punches through its junction in nanoseconds. It is also the mechanism behind the ignition coil in a petrol engine and behind the arc you see when unplugging an inductive load from a socket. The remedy is never to make the coil store less energy but to give the current somewhere to go: a flyback diode, a snubber, or a clamp that limits the voltage and lets the energy dissipate over a longer time.
The tool makes this visible. Hold the inductance and current fixed and change the interrupt time from microseconds to milliseconds. The stored energy does not move at all; the spike voltage falls by a factor of a thousand. Everything that protects an inductive circuit works by moving that one number.
Core Saturation Is the Real Ceiling on Stored Energy
The formula will happily accept any inductance and any current, but a physical inductor cannot store arbitrary energy. The limit is the core. As current rises, the magnetic flux density in the core rises with it, and once the core material saturates the inductance collapses. An inductor that has saturated behaves like a piece of wire: current rises almost without limit, and in a switching converter that is usually the end of the switch.
This is why the flux linkage figure is in the grid. Energy alone does not tell you how close a design is to saturation, because energy depends on LI² while saturation depends on flux, which tracks LI. Two inductors storing the same energy at very different currents sit at quite different points on their magnetisation curves. An air-cored coil has no saturation limit at all, which is why it is preferred where large stored energy matters, at the cost of far more turns for the same inductance.
The practical consequence is that the number on this page is an upper bound assuming the inductance you entered is real at that current. If you are designing rather than analysing, get the inductance-versus-current curve from the manufacturer and read the value at your peak. The inductance converter handles the unit arithmetic when a datasheet quotes microhenries and your calculation is in millihenries.
How This Compares With Energy Stored in a Capacitor
The two are duals of each other and it is worth holding both formulas side by side. A capacitor stores ½CV² in an electric field between plates; an inductor stores ½LI² in a magnetic field around a winding. A capacitor holds its energy indefinitely with no current flowing; an inductor holds its energy only while current keeps flowing, so an inductor is not a storage device you can leave on a shelf.
Energy density is where they differ most in practice. Capacitors, and especially supercapacitors, store far more energy per unit volume than inductors do, which is why energy storage in power electronics is nearly always capacitive and inductors are used as transfer elements rather than reservoirs. Our capacitor energy calculator runs the dual calculation, and putting the two side by side for a real converter shows immediately why the capacitor is the bulk store and the inductor is the pump.
Where the two are combined deliberately, the energy sloshes between them at the resonant frequency. The LC resonant frequency calculator gives that frequency for a given inductance and capacitance, the reactance calculator gives each component's opposition at a chosen frequency, and the RLC circuit calculator adds the resistance that damps the exchange. For the exponential rise of current in an inductor fed through a resistance, the timescale is L/R, the direct analogue of the RC constant covered by the RC time constant calculator.
Assumptions and Range of Validity
Four assumptions sit behind every number on this page, and each one has a range outside which the answer stops being useful. The inductance is taken as constant, which fails once a core saturates. The winding is taken as lossless, so the energy figure is what is stored, not what was drawn from the supply; real copper and core losses mean rather more went in than comes back out. The release is treated as linear, so the release power and spike voltage are averages over the interval rather than instantaneous peaks, which in a real interruption are higher still.
Finally, the model assumes all the energy is in the intended inductance. In a fast transient, the stray inductance of the wiring and the parasitic capacitance of the winding both take part, which is why a real spike rings rather than rising and falling cleanly. For low-frequency, well-defined coils the model is accurate; for nanosecond-scale events it gives the right order of magnitude and no more.
Anything connected to mains voltage is a different matter entirely. Inductive loads on mains circuits — motors, transformers, contactors, fluorescent ballasts — produce switching transients that interact with protective devices, and the design of that protection is work for a qualified electrician or electrical engineer, who signs off the real installation against the applicable code. This page publishes no ampacity, breaker or insulation rating of its own. If your question is about mains circuit protection, our breaker size calculator and voltage drop calculator are the right starting points, and they carry the same caveat.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using the datasheet inductance at the working current — small-signal inductance is measured near zero current, and a saturating core can be well below it where you actually operate.
- Using average current instead of peak — energy goes as the square of current, so a triangular ripple stores considerably more at its peak than the mean would suggest.
- Assuming a small energy means a safe voltage — the spike is set by how fast the current changes, not by how much energy is stored, and a millijoule coil can produce kilovolts.
- Mixing millihenries with microhenries — a factor of a thousand in inductance is a factor of a thousand in energy and in spike voltage. Use the unit selector rather than converting by hand.
- Forgetting the repetition rate when sizing thermals — peak power says nothing about heating. A device is warmed by the average, and the average is the energy multiplied by how often the cycle repeats.
Related Free Tools From Arb Digital
The dual calculation for the electric field is on our capacitor energy calculator, and the inductance converter rescales henries between prefixes. For circuits that combine both, see the LC resonant frequency calculator, the RLC circuit calculator and the reactance calculator. For the exponential-decay analogy in a resistive circuit, use the RC time constant calculator. Basic circuit arithmetic lives on the Ohm's law calculator and the electrical power calculator, and the energy converter restates joules in whatever unit a specification uses. Everything Arb Digital publishes is on the free online tools hub.
Frequently Asked Questions
Half the inductance multiplied by the square of the current, with inductance in henries and current in amperes giving joules. Because the current is squared, doubling the current quadruples the stored energy while doubling the inductance only doubles it.
No. Unlike a capacitor, an inductor's field exists only while current flows through the winding. Cut the current and the field collapses within microseconds, dumping its energy into whatever path it can find — which is exactly why flyback diodes exist.
Because the voltage is inductance multiplied by the rate of change of current, not by the stored energy. Interrupting two amperes in ten microseconds through ten millihenries gives two thousand volts, even though the coil holds only twenty millijoules.
Flux linkage is inductance times current, in webers, and it is the quantity that saturates a magnetic core. Energy alone does not tell you how close a design is to saturation, because two coils storing the same energy at different currents sit at different points on the magnetisation curve.
Yes, substantially. Once a core saturates the inductance collapses, so the energy actually stored is well below what the small-signal inductance predicts. Use the inductance from the manufacturer's curve at your peak current rather than the headline figure.
The peak of the ripple, not the average. The energy transferred each cycle is set by the peak, and using the mean current can understate the stored energy by a large margin when the ripple is significant.
Rarely. Its energy density is far lower than a capacitor's and it holds nothing once current stops, so inductors are used as energy transfer elements in converters rather than as reservoirs. The bulk store in almost every power supply is capacitive.
This tool is provided for educational and design-estimation use. It assumes constant inductance and a lossless winding, and it publishes no component, insulation or circuit-protection rating; any mains-connected installation must be designed and signed off by a qualified electrical professional.
