How this instrument works
An inductor objects to change, not to current. Hold current steady and your coil settles into being an ordinary lump of wire; force that current to reverse a hundred times a second, as 50 Hz mains does, and every reversal drags flux back and forth through the winding, inducing a voltage that fights whatever caused it. That is what v = L·di/dt says, and because sine-wave slope grows steeper in proportion to frequency, voltage needed to sustain a given current amplitude grows likewise. Inductive reactance is that ratio — volts per ampere, quoted in ohm — with frequency and inductance both sitting in the numerator, so doubling either doubles the opposition.
Michael Faraday found induction in 1831. Within a year Joseph Henry, teaching at the Albany Academy in New York, chased down something Faraday had left alone: a long coil shocks you when you break its own circuit, with no second winding anywhere in sight. Self-induction was his name for it, and a fat blue spark across an opening switch remains its everyday proof. Emil Lenz added the minus sign in 1834 — an induced current opposes the change that bred it — which is exactly why a coil reads as opposition rather than as a source. Henry's name was fixed to the unit of inductance in 1893, and 2πfL is little more than Lenz's objection written in ohm.
Three conditions have to hold for this formula to mean anything: inductance constant, waveform a single clean sinusoid, part nothing but a coil. Hardware breaks all three. Ferrite and iron saturate, so one choke measuring 100 mH at one milliamp may measure 60 mH at rated current, its reactance sagging along with it. Turn-to-turn capacitance sits across every winding, giving each inductor a self-resonant frequency beyond which it behaves as a capacitor — small radio chokes give up in the low megahertz, heavy mains chokes far sooner. Copper loss, hysteresis and eddy currents add genuine resistance that climbs faster than reactance does, which is why every datasheet prints a quality factor Q instead of pretending any winding is ideal. Pulses and switching edges have no one reactance worth quoting; integrate v = L·di/dt against the clock instead.
- Type your coil value into Inductance (H), expressed in henries: 0.1 for a 100 mH mains choke, 0.000022 for a 22 µH radio part.
- Give Frequency whichever operating point concerns you — 50 or 60 for mains, kilohertz for switching supplies, megahertz once radio work begins.
- Take Inductive reactance straight off the readout. Ohm, kohm and Mohm are selectable; whichever you pick, it means volts per ampere at that one frequency.
- Choosing a filter choke? Look for reactance far above load impedance where blocking is wanted, and far below it where power still has to flow.
- Multiply Frequency by ten and your answer multiplies by ten. Plotted on log paper, inductive reactance draws a rising diagonal rather than a curve.
Worked example — a 100 mH choke on 50 Hz mains
An iron-cored 100 mH choke sits in series with a 230 V 50 Hz supply, fitted to keep switching hash out of the incoming wiring. Set Inductance (H) to 0.1, leave Frequency at 50, and the sheet returns X_L = 2π × 50 × 0.1 = 10π = 31.4159265359 ohm. Ten pi to every digit shown, because 2 × 50 × 0.1 lands exactly on 10 — a tidy coincidence worth remembering as a sanity check.
From there the practical numbers follow. Current through the choke comes to 230 ⁄ 31.416 = 7.32 ampere, and the coil shuttles roughly 1.68 kVAr back and forth each cycle without burning any of it. Winding resistance of perhaps 1.5 ohm lifts the impedance magnitude to 31.45 ohm, under 0.2% more, so at mains frequency reactance is the whole story. Take the same part up to a switching supply's 20 kHz and it presents 12.57 kohm — four hundred times stiffer, which is precisely the trick: power passes, noise does not.
Questions
Why does inductive reactance rise with frequency?
Because a coil opposes the rate of change of current, and faster alternation means a steeper slope. At fixed current amplitude the induced voltage scales directly with frequency, so reactance scales with it too — ten times the frequency, ten times the ohm. A 10 mH choke shows 3.14 ohm at 50 Hz, 62.8 ohm at 1 kHz and 62.8 kohm at 1 MHz. That straight-line climb is what lets a single part carry mains power while blocking switching noise riding along that same pair of wires.
My meter reads 2 ohm across the choke — is that the reactance?
No, and this is the error made most often with inductors. A multimeter measures using direct current, so it reports winding resistance — DCR on a datasheet, set by copper length and gauge alone. Reactance exists only while current is changing, and never shows up on an ohmmeter. A 100 mH choke might read 1.5 ohm on the bench yet present 31.4 ohm to 50 Hz mains. Both figures matter: DCR decides how warm the part runs, reactance decides how much alternating current gets past.
Should I enter frequency or angular frequency?
Plain frequency in hertz — this sheet inserts the 2π for you. Written with ordinary frequency f the factor is explicit, X_L = 2πfL; written with angular frequency ω in radians per second it hides inside ω = 2πf, giving X_L = ωL. Losing that factor is a classic arithmetic slip and leaves every answer 6.283 times too small, so a 100 mH coil on 50 Hz would come out near 5 ohm instead of 31.4 ohm. If a textbook hands you ω already, divide by 2π before typing.
Why does a transformer draw such a large current at switch-on?
Because reactance is zero at zero frequency and needs a moment to establish itself. Close the switch and for a few instants only winding resistance and stray impedance limit anything. Worse, energising at a voltage zero crossing can drive core flux to nearly twice its normal peak, pushing iron into saturation, where inductance collapses and takes its opposing reactance along with it. Inrush of ten to twenty times rated current is routine, which is why such circuits get slow-blow fuses or a dedicated inrush limiter.
Does doubling the number of turns double the reactance?
No — it roughly quadruples it. Inductance of a solenoid or wound core goes as the square of turn count, L = μN²A ⁄ l, so twice the turns gives about four times the henries and four times the ohm at any chosen frequency. Winding resistance meanwhile only doubles, so quality factor improves as the coil grows. That square law explains why small changes to a hand-wound part move the answer so much, and why air-cored coils for radio work get specified turn by turn.
Why does a choke stop working above its self-resonant frequency?
Every winding carries capacitance between adjacent turns, sitting in parallel with its own inductance. Where those two reactances match, the pair resonates and impedance peaks; above that point capacitance dominates and that part passes exactly those high frequencies it was fitted to stop. Datasheets list the self-resonant frequency for this reason, and 2πfL is trustworthy only well below it. Working rule: stay under one third of that quoted figure, or split the job between one large choke and one small one.