Every coil of wire resists a change in its own current, and the strength of that resistance — its inductance — depends entirely on geometry: how many turns, how wide, how long. This calculator ties that geometry to two practical follow-on questions: how much energy does the coil store while current flows, and how big a voltage spike does it produce when that current changes quickly.
Why inductance depends on turns squared
The solenoid formula L = µ₀N²A/l has an N² term, not just N, because each additional turn does double duty: it adds another loop for the magnetic field to link through, and it also strengthens the field that every other turn experiences. Wind twice as many turns into the same coil and the inductance quadruples, not doubles — which is why small increases in turn count can matter a lot for a compact inductor design, and why transformer and choke datasheets are so sensitive to winding counts.
What the stored energy is actually doing
The ½LI² energy isn't dissipated as heat — it's stored in the coil's magnetic field the same way a stretched spring stores mechanical energy. That's precisely why interrupting current through an inductor (opening a switch, a relay contact bouncing) can be dangerous to nearby components: the stored energy has to go somewhere, and without a path to dissipate gradually, it forces current to keep flowing at the moment of interruption — producing the voltage spikes this calculator's EMF tab quantifies.
Lenz's law, in one line
The minus sign in EMF = −L(ΔI/Δt) is Lenz's law in equation form: the induced voltage always opposes the change that created it. If current is increasing, the induced EMF pushes back against the increase; if current is decreasing, it pushes to sustain it. This calculator reports the magnitude of that EMF and explains the direction in words, since the sign convention depends on which way you've defined positive current flow.