Inductor Energy Calculator
Calculate energy stored in an inductor from inductance and current. Enter values for instant results with step-by-step formulas.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
E = 0.5 x L x I^2
Where E is stored energy in joules, L is inductance in henries, and I is current in amperes. The energy is stored in the magnetic field surrounding the inductor. Additional calculations include inductive reactance XL = 2*pi*f*L, impedance Z = sqrt(R^2 + XL^2), quality factor Q = XL/R, and time constant tau = L/R.
Worked Examples
Example 1: Power Supply Filter Inductor
Problem:A 10 mH inductor in a power supply filter carries 5A of DC current with 0.5 ohms of winding resistance at 60 Hz. Calculate stored energy and circuit parameters.
Solution:L = 10 mH = 0.010 H\nI = 5 A\nEnergy = 0.5 x 0.010 x 5^2 = 0.5 x 0.010 x 25 = 0.125 J = 125 mJ\nXL = 2 x pi x 60 x 0.010 = 3.77 ohms\nZ = sqrt(0.5^2 + 3.77^2) = 3.80 ohms\nQ = 3.77 / 0.5 = 7.54\nTime constant = 0.010 / 0.5 = 0.020 s = 20 ms
Result:Energy: 125 mJ (0.125 J) | Reactance: 3.77 ohms | Impedance: 3.80 ohms | Q: 7.54 | Time constant: 20 ms
Example 2: RF Inductor Energy Calculation
Problem:A 100 uH inductor carries 200 mA of current at 1 MHz with 2 ohms resistance. Calculate energy stored and quality factor.
Solution:L = 100 uH = 0.0001 H\nI = 0.2 A\nEnergy = 0.5 x 0.0001 x 0.2^2 = 0.5 x 0.0001 x 0.04 = 2 uJ\nXL = 2 x pi x 1,000,000 x 0.0001 = 628.3 ohms\nQ = 628.3 / 2 = 314.2\nTime constant = 0.0001 / 2 = 50 us
Result:Energy: 2 uJ | Reactance: 628.3 ohms | Q Factor: 314.2 (excellent) | Time constant: 50 us
Frequently Asked Questions
What is inductor energy and how is it stored?
Inductor energy is the energy stored in the magnetic field created when electric current flows through an inductor coil. The energy is stored in the form of a magnetic field that surrounds and permeates the inductor windings, not in the physical material of the inductor itself. The energy storage formula is E = 0.5 times L times I squared, where E is energy in joules, L is inductance in henries, and I is current in amperes. This quadratic relationship with current means that doubling the current quadruples the stored energy. The magnetic field builds up as current increases through the inductor, and when the current source is removed, the inductor releases this stored energy, which is why inductors resist changes in current. This property is fundamental to the operation of power supplies, filters, and energy storage applications.
What is the time constant of an inductor circuit?
The time constant (tau) of an inductor-resistor (LR) circuit equals L divided by R, where L is inductance in henries and R is resistance in ohms. The time constant represents the time required for the current to reach approximately 63.2% of its final value when voltage is applied, or to decay to 36.8% of its initial value when the source is removed. After five time constants, the current has reached approximately 99.3% of its final value, which is considered the practical steady-state condition. The time constant is critically important in circuit design because it determines how quickly the inductor responds to changes in applied voltage. Shorter time constants mean faster response but potentially higher voltage transients. Longer time constants provide smoother current changes but slower response. In switching power supply design, the time constant relative to the switching period determines whether the inductor operates in continuous or discontinuous conduction mode.
What are common applications of inductor energy storage?
Inductor energy storage is fundamental to many electronic and electrical systems. In switching power supplies (buck, boost, and buck-boost converters), inductors store energy during one phase of the switching cycle and release it during the other, enabling efficient voltage conversion. In automotive ignition systems, an inductor stores energy from the battery and releases it as a high-voltage spark across the spark plug gap. Inductive energy storage is used in pulse power systems for generating high-power, short-duration pulses for applications like radar transmitters, particle accelerators, and electromagnetic forming. Electromagnetic launchers (coilguns and railguns) rely on rapid inductor energy discharge. In power factor correction circuits, inductors help shape the current waveform to match the voltage waveform. Superconducting magnetic energy storage (SMES) systems use large superconducting coils to store significant amounts of energy for grid stabilization applications.
How does inductor energy relate to magnetic field energy density?
The energy stored in an inductor is actually distributed throughout the volume of the magnetic field, and the energy density (energy per unit volume) equals B squared divided by 2 times mu, where B is the magnetic flux density and mu is the permeability of the medium. This relationship reveals that energy density depends on the square of the magnetic field strength and inversely on the permeability of the core material. Paradoxically, air gaps in magnetic cores actually increase energy storage capacity despite reducing inductance, because the high field strength in the air gap stores significant energy. This is why many power inductor designs intentionally include air gaps. For a given inductor volume, the maximum stored energy is limited by core saturation, where the magnetic field reaches its maximum value and additional current no longer increases the field proportionally. Core material selection, including ferrite, iron powder, and amorphous metals, involves trading off saturation flux density, permeability, core losses, and temperature performance.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy