Inductor Energy Calculator

Energy stored in an inductor follows directly from Faraday's law. The voltage across the coil is L times di/dt, instantaneous power is that voltage times the current, and integrating power from zero current up to I gives one half L I squared. The quadratic dependence on current is the practical headline: doubling current quadruples stored energy, while doubling inductance only doubles it. A 10 mH filter choke carrying 5 A holds 0.125 J, whereas a 100 micro-H RF coil at 200 mA holds only about 2 micro-J. Physically the energy is not in the copper but distributed through the magnetic field, with density B squared over 2 mu, which explains the counterintuitive result that deliberately gapping a ferrite core lowers inductance yet raises the energy the component can store, because the high field in the low-permeability gap holds most of it. The companion quantities describe how the same coil behaves in a circuit. Inductive reactance rises linearly with frequency as 2 pi f L, so the 10 mH choke presents 3.77 ohms at 60 Hz but 628 ohms at 1 MHz for a 100 micro-H part. Combined with winding resistance it gives impedance as the square root of R squared plus X squared, and the ratio X over R is the quality factor Q, typically 10 to 50 for power inductors and 200 to 500 for good RF coils. The L over R time constant sets how fast current settles, reaching 63.2 percent of final value in one time constant and about 99.3 percent in five. Two limits matter more than the formula. Core saturation caps usable energy: ferrites saturate near 0.3 to 0.5 tesla and silicon steel near 1.5 to 2.0 tesla, and past that point inductance collapses and current runs away. And interwinding capacitance creates a self-resonant frequency above which the part behaves capacitively, so datasheet limits govern rather than the ideal equations.

Electromagnetic induction was discovered by Michael Faraday in 1831, and within a year Joseph Henry, working at the Albany Academy and later the Smithsonian Institution, had characterized self-induction, the property by which a coil opposes changes in its own current. Henry observed the vivid spark drawn when a circuit containing a large coil was broken, the first encounter with what engineers now call inductive kickback. Heinrich Lenz stated the direction rule in 1834, and the unit of inductance was named the henry by the international electrical congress that met in Chicago in 1893, placing it alongside the volt, ohm, and farad in the practical system. The energy interpretation came with field theory. James Clerk Maxwell's treatment in the 1860s and 1870s located the energy of a current-carrying circuit in the surrounding magnetic field rather than in the conductor, which is what makes the B squared over 2 mu density expression meaningful and why an air gap stores energy so effectively. Engineering practice then developed around exploiting or suppressing that stored energy. The automotive ignition coil, in production from the early 1900s, is nothing more than controlled inductive kickback used to generate tens of kilovolts from a low-voltage battery. Ferrite cores developed in the 1930s and 1940s at Philips and elsewhere made compact high-frequency magnetics possible, and the switching power supplies that spread from the 1960s onward, particularly buck, boost, and flyback topologies, are built entirely on cycling energy into and out of an inductor thousands of times per second. Modern amorphous and nanocrystalline core materials continue the same trade-off between permeability, saturation flux density, and loss.