Inductive Reactance Calculator
An inductor ignores steady current and fights alternating current harder the faster it alternates. Enter the frequency and the inductance, and this calculator returns the reactance in ohms — the inductor’s effective resistance to AC, with the phase story that makes it different from a resistor.
Why Frequency Is Half the Formula
The inductor's opposition comes from its back-EMF: a changing current builds a changing magnetic field, which induces a voltage fighting the change — and the fight's strength is the rate of change. Double the frequency and the same current swing happens twice as fast, doubling the induced opposition; hence XL = 2πfL, reactance proportional to both frequency and inductance. At DC (f = 0) the formula returns its famous zero: an ideal inductor is a plain wire to steady current, which is why it passes the DC and blocks the AC in filter design — the dual of the capacitor, which does exactly the opposite, and the pair of them, priced by this page and its sibling, are the two hands of all frequency-selective circuitry.
Worked Example: Ten Millihenries at a Kilohertz
The defaults run a bench-standard part: L = 10 mH at f = 1,000 Hz. XL = 2π × 1,000 × 0.010 = 62.83 Ω — a respectable opposition from a component that a multimeter's DC ohmmeter would read as a fraction of an ohm of winding. The note converts to current: at 12 V AC, about 0.191 A flows, all of it "wattless" in the ideal — sloshing into and out of the magnetic field twice per cycle. Slide the frequency to the 50 Hz mains and the same coil offers only 3.14 Ω (it is nearly a wire to the grid, which is why mains chokes are enormous iron-cored affairs piling up inductance); at 100 kHz it offers 6,283 Ω, a wall — one component, three personalities, all from the f in the formula.
Reactance Is Not Resistance
The ohms are shared; the physics is not. A resistor converts electrical energy to heat, permanently, at a rate VI with voltage and current in step. A pure reactance stores and returns energy, voltage and current a quarter-cycle out of step, average power zero — which is why inductors can throttle AC motors' current without the bonfire a resistor of the same ohms would light, and why power companies and circuit boards both prize them. Real inductors sit between the ideals (winding resistance, core losses), and the quality factor Q = XL ÷ R prices the mixture — but the calculator's job is the pure figure, the reactance itself, against which the real part's losses are then honestly measured.
The Ballast: Reactance as a Light Switch's Partner
The fluorescent tube's ballast is this formula wearing a hard hat: a discharge lamp, once struck, would draw unlimited current and destroy itself, so an iron-core inductor sits in series whose reactance — computed exactly as here, at mains frequency — throttles the current wattlessly, decade after decade, in every office ceiling of the twentieth century. The same trick, miniaturised and moved to high frequency, is the electronic ballast and then the LED driver's inductor. Civilisation lit itself for a hundred years on the principle that 2πfL can stand in for a resistor without the heat, and the hum of a ageing ballast is the sound of the formula's magnetic field flexing its laminations at twice the mains rate.
Why Microphones and Pickups Care About Henries
A guitar pickup is an inductor of several henries — thousands of times the worked example's millihenries — and its reactance against the cable's capacitance draws the pickup's resonant peak, the frequency where the instrument's voice blooms before the highs roll off. Pickup winders trade inductance against brightness with this page's arithmetic open beside the winding machine: more turns, more L, more output, a lower and louder resonance. Microphone transformers, moving-coil phono cartridges (whose loading recommendations are reactance negotiations) and loudspeaker voice coils all carry an L that the designer must price at the working frequency before anything else can be decided — the formula's cultural reach extends from power grids down to the last millihenry in a Stratocaster.
The Choke in the Radio's Power Cord
The little cylinder bulging on a laptop's power lead is a ferrite choke — an inductor by another name — whose reactance at the hundred-megahertz frequencies of radio interference is enormous while at DC it is nothing at all, so the computer's power flows through while the radio hash is throttled. It is this page's frequency proportionality weaponised as hygiene: at f = 0 the device vanishes electrically, at f = 10⁸ it is a wall, and nothing in between needs deciding. The same bead, threaded on cables throughout electronics, is the cheapest sentence in the EMC engineer's vocabulary — and a reminder that the formula's two variables, f and L, are both design choices, not merely measurements. When a product fails its emissions test at one frequency, the fix is frequently nothing more glamorous than a different bead — the reactance raised at exactly the offending f, by exactly this multiplication.
Related Tools
More from the Physics Calculators hub: the Capacitive Reactance Calculator — the mirror twin, falling as frequency rises — and the Capacitor Energy Calculator for field storage priced in joules.
Frequently Asked Questions
What happens to an inductor at very high frequency, then?
The ideal formula climbs forever; the real component defects: the winding's own turn-to-turn capacitance resonates with the inductance at the self-resonant frequency, above which the "inductor" behaves capacitively and the page's number inverts its meaning. Core materials also retire at their own frequencies (ferrites for the megahertz, iron for the mains, air when nothing else is honest). Component selection is therefore frequency-first: the calculator gives the reactance the datasheet promises at your f, and the datasheet's SRF line tells you whether the promise is still in force — a two-step every RF designer performs in their sleep.
Why does the current lag the voltage by 90 degrees?
Because the inductor's voltage is proportional to the rate of change of current (V = L dI/dt), and a sine's rate of change is a cosine — the same wave shifted a quarter-cycle earlier. The voltage peaks exactly when the current is changing fastest (crossing zero) and vanishes when the current peaks (momentarily steady, nothing to fight). The mnemonic generations of students chant — ELI the ICE man, voltage (E) leads current (I) in an inductor (L) — encodes this page's physics in five syllables, and the 90° is exact for the ideal part at any frequency the formula prices.
How are inductors and capacitors combined in a filter?
By their opposite frequency habits: a series inductor (rising reactance) with a shunt capacitor (falling reactance) passes lows and blocks highs — a low-pass — and swapping their positions inverts the service. At the crossover the two reactances meet in magnitude, and the frequency where XL = XC is the resonance both this page and its sibling compute toward: f₀ = 1 ÷ (2π√(LC)). Audio crossovers, radio tuners and switch-mode supplies are all negotiations between the two formulas, and the working designer keeps both open — which is why the hub files them as neighbours and this page links its twin without embarrassment.
What is impedance, then?
The honest total: resistance and reactance combined as vectors, Z = √(R² + (XL − XC)²) for a series circuit, with the angle between them the phase the pure parts introduced. Reactance alone (this page) is impedance with the resistance set to zero — the right idealisation when the winding is a few milliohms against tens of ohms of XL, and the wrong one when it isn't. Engineering judgement is knowing which zero you may assume; the calculator computes the reactance exactly so the judgement has a clean number to stand on.
Why do switch-mode supplies use small inductors at high frequency?
Because the formula pays for frequency in size: to hold a target reactance (or a target energy per cycle), raising f lets L shrink proportionally — a 500 kHz converter's inductor is a fingernail where a 50 Hz transformer's is a brick. The entire miniaturisation of modern power electronics — phone chargers that were once laptop bricks — is this proportionality, exploited at the price of switching losses and EMI discipline. The calculator's quiet 2πfL is thus a size equation in disguise: quote any two of frequency, inductance and reactance, and the third is the component's physical bulk, deciding itself.
Does an inductor resist DC at switch-on?
Transiently, yes — that is its finest hour: at the instant of connection the current is zero and cannot jump (the field must be built), so the inductor initially opposes the full voltage and the current ramps over the time constant L ÷ R. Steady DC then flows unopposed (this page's f = 0 corner), but the switch-on ramp is why inductors tame inrush, why relay coils kick when switched off (the field collapses fast, making a voltage spike instead), and why flyback diodes guard transistor drivers everywhere. The formula prices the steady AC state; the transient is the same physics caught in the act of becoming it. Between the switch-on ramp and the steady reactance, the inductor's whole biography is a refusal to let current change its mind quickly — a conservatism that circuits exploit for smoothing, filtering, timing and spark, priced everywhere by the same two variables on this page.