This inductor calculator covers the four computations an inductor demands: its reactance at any frequency (XL = 2πfL), the energy stored in its magnetic field (½LI²), the RL time constant governing how fast its current can change (τ = L/R), and the inductance of a wound solenoid from its geometry (µN²A/l). An inductor is current’s flywheel — every answer here flows from that one personality trait.

Inductance used –
Inductive reactance XL at f –
Stored energy at I –
RL time constant τ = L/R –

Reactance is frequency’s lever on the inductor: double the frequency, double XL — the mirror image of a capacitor. DC steady-state (f = 0) makes an ideal inductor a short circuit; its resistance to change is the whole story.

Current’s Flywheel

An inductor resists changes in current the way a flywheel resists changes in speed. Apply voltage and current ramps gradually (the growing magnetic field pushes back with an opposing EMF — Lenz’s law again); remove the voltage and the collapsing field keeps the current flowing, briefly, at whatever voltage it must invent to do so (the inductive kick that arcs across opening switch contacts and that flyback diodes are hired to absorb). Everything on this page is that behavior quantified: XL prices the opposition at each AC frequency, ½LI² counts the energy parked in the field at a given current, and τ = L/R clocks how long current changes take in a real circuit with real resistance.

The solenoid estimator closes the loop from the other side: inductance isn’t bought, it’s geometry. L = µ₀µᵣN²A/l — turns squared (double the turns, quadruple the inductance, because each turn links the flux of all the others), core area linearly, and the core’s permeability as the multiplier that makes iron-core inductors hundreds to thousands of times stronger than air-core at the same winding — until the core saturates, when µᵣ collapses toward 1 at high field and the inductance falls off a cliff. Saturation current, not inductance, is the rating that kills underspecified inductors in power supplies.

Worked Examples (Verified)

  • 0.1 H choke at mains frequency (defaults): XL = 2π×60×0.1 = 37.7 Ω — at 230 V mains that’s a 6-amp-class gatekeeper; at 10 kHz the same part presents 6,283 Ω, which is why one component can pass power and strangle switching noise simultaneously.
  • Energy bookkeeping: 0.1 H carrying 2 A stores ½×0.1×4 = 0.20 J — modest until you scale to an MRI magnet (hundreds of henries at hundreds of amps = megajoules parked in the field, and a quench is that energy arriving as heat all at once).
  • Air-core solenoid: 500 turns, 2 cm² core, 10 cm long → L = µ₀×500²×(2×10⁻⁴)/0.1 = 0.628 mH. Slip in a ferrite core (µᵣ ≈ 800 at low field) and the same winding reads ~0.5 H — the entire reason cores exist, in one dropdown change.
  • Time constant: 0.1 H with 10 Ω winding resistance: τ = 10 ms — relay coils and solenoid valves live here, which is why a relay’s drop-out delay is measured in milliseconds, set by this division.

Inductor Discipline

  • Never open-circuit a live inductor casually. Its field will raise whatever voltage is needed to keep current flowing — hundreds of volts from a humble relay coil. Flyback diodes, snubbers or TVS devices give the current a planned path.
  • DCR is real: winding resistance wastes power (I²R), heats the part, and sets τ. Datasheets list it; designs that ignore it run hot and mistimed.
  • Self-resonance: winding capacitance parallels every real inductor, so above its self-resonant frequency the “inductor” behaves capacitively. RF parts specify SRF; check your f against it.
  • Saturation before elegance: choose the part by saturation and RMS current ratings first, inductance second — a saturated inductor is a resistor with delusions, and switch-mode supplies fail exactly there.
  • Coupling is a feature or a bug: nearby inductors share flux (transformers exploit it; layout engineers fight it) — orientation and distance are design variables, not afterthoughts.

Where Inductors Earn Their Keep

Buck/boost converters (the inductor as energy bucket, filled and emptied 100,000+ times a second), motor windings (inductance shapes the torque’s smoothness), fluorescent and HID lamp ballasts (current limiting by pure reactance — no heat-wasting resistor), EMI filters on every mains inlet (common-mode chokes are two coupled inductors in a trench coat), and the tank circuits of our Resonance Frequency Calculator, where this component meets its capacitive partner. If a circuit must store energy without chemistry, smooth current without waste, or remember a magnetic state, an inductor is doing it.

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Frequently Asked Questions

How do you calculate inductive reactance?

XL = 2πfL — frequency times inductance times 2π. A 0.1 H inductor at 60 Hz has XL = 37.7 Ω; at 600 Hz, 377 Ω; at DC, zero (an ideal inductor is a short to steady current). Reactance limits AC current exactly like resistance but dissipates no average power — the energy borrows into the field and returns each cycle, which is why lamp ballasts and chokes can limit current without cooking themselves.

How much energy does an inductor store?

E = ½LI², in the magnetic field. Our example: 0.1 H at 2 A stores 0.20 J. The quadratic in current is the safety story: double the current, quadruple the parked energy — and all of it must go somewhere when the circuit opens, which is the entire engineering of flyback protection. This calculator returns the energy for your L and I directly.

What is the RL time constant?

τ = L/R, in seconds — the time for current to reach 63.2% of its final value after a step change (or decay to 36.8%). 0.1 H against 10 Ω gives 10 ms. It is the direct analog of the RC time constant with the roles inverted: inductors smooth current changes over τ; capacitors smooth voltage changes. Relay timing, solenoid response, and converter ripple analysis all read τ before anything else.

How do you calculate a solenoid’s inductance?

L = µ₀µᵣN²A/l for a long solenoid: turns squared, times core cross-section area, times the core’s permeability, divided by coil length. The defaults (500 turns, 2 cm², 10 cm, air core) give 0.628 mH; a ferrite core at µᵣ = 800 multiplies it to ~0.5 H. The calculator’s solenoid mode takes turns, area, length and µᵣ directly. End effects make short, fat coils read lower than the formula — treat it as a close estimate, exact for length ≫ diameter.

Why do inductors block AC but pass DC?

Because their opposition is to change, priced by frequency: XL = 2πfL is zero at DC (f = 0, once the start-up transient passes) and grows without bound as frequency rises. A capacitor is the exact mirror (blocks DC, passes AC) — the duality that lets LC filters sort signals by frequency, and that powers the frequency-selective world from crossovers to converters.

What does saturation mean for an inductor?

A ferromagnetic core can only align so many domains; beyond its saturation flux density (ferrites ~0.3–0.5 T, iron powder higher) extra current buys no extra field, µᵣ collapses toward 1, and inductance craters — current then spikes, switches overheat, and converters fail. Datasheets rate a saturation current (Isat) alongside inductance; designing past it is the classic first-prototype bonfire. Air-core inductors never saturate (and never get the µᵣ bonus either).

Inductor vs transformer — what’s the difference?

A transformer is two inductors sharing one core so their flux couples; an inductor is one winding using its own field privately. The same equations describe both — a transformer’s “magnetizing inductance” is literally its primary acting as an inductor. Leakage inductance (flux that fails to couple) behaves like a small series inductor in each winding, which is why real transformers are drawn as an ideal transformer plus loose inductors around it.

Is this inductor calculator free?

Yes — free, instant, no sign-up. Reactance, stored energy, RL time constant, and solenoid inductance from geometry in one tool.