Capacitive Reactance Calculator

A capacitor blocks steady current entirely and passes alternating current more easily the faster it alternates. Enter the frequency and the capacitance, and this calculator returns the capacitive reactance in ohms — the mirror image of the inductor’s, falling exactly where its twin rises.

The Reciprocal That Runs the Radio Age

The capacitor's current is proportional to how fast the voltage changes (I = C dV/dt), so at higher frequencies the same voltage swing demands more current — equivalently, less opposition: X_C = 1 ÷ (2πfC), reactance falling with both frequency and capacitance. The formula's two corners define the component's career: at DC, X_C is infinite (the charged capacitor is an open switch — the blocking every coupling stage relies on), and at high frequency it approaches a wire (the bypass every power rail relies on). Between the corners sits the whole craft of choosing capacitors for signal paths, and the mirror symmetry with the inductor — this page's reciprocal against its twin's product — is what lets the two components be teamed into filters and resonators that select one frequency from the spectrum.

Worked Example: Ten Microfarads on the Mains

The defaults run the classic transformerless-supply component: 10 µF at the 60 Hz mains. X_C = 1 ÷ (2π × 60 × 10×10⁻⁶) = 265.26 Ω, passing about 0.452 A at 120 V — enough to run a small circuit's supply through a component that dissipates (ideally) nothing, the trick behind cheap capacitive droppers in LED lamps and smart switches. The frequency leverage is the lesson: at 50 Hz the same capacitor is 318 Ω (the design must be re-priced per continent), and at 60 kHz it is 0.265 Ω — effectively absent, which is why small capacitors shepherd radio frequencies around circuits that are opaque to them at audio. One formula, and the component is a wall, a resistor or a wire depending on nothing but f.

Leading by Ninety Degrees

The capacitor's current leads its voltage by 90° — the mirror of the inductor's lag — because current must flow before voltage accumulates (the charging precedes the charged). In phasor terms the two reactances pull the circuit's phase in opposite directions, which is why an inductor's lag can be cancelled by a capacitor's lead — power-factor correction in industry is exactly this cancellation, performed with capacitor banks against a factory of motors, and the utility bills for the uncancelled remainder. This calculator prices one side of that negotiation; its inductive twin prices the other; between them they cover the phase economy of the entire AC world, at the cost of two formulas a student can hold simultaneously.

The Gramophone's Heir: RIAA and the Equalisation Curve

Vinyl's RIAA equalisation — bass cut on cutting, boosted on playback, treble the reverse — is drawn entirely in this page's currency: resistor-capacitor networks whose reactance crossings set the curve's three turnover frequencies (50, 500 and 2,122 Hz). Every phono preamp is a small essay in X_C = 1 ÷ (2πfC), choosing capacitances so the reactance meets the companion resistor at exactly the standard's corners. The same arithmetic voices guitar tone controls, loudspeaker crossovers' high-pass legs and the coupling choices of a million amplifier schematics — a formula so domesticated that its users call the results "values" and reach for this calculation only when a value misbehaves.

Touchscreens: Reactance as a Sense Organ

The capacitive touchscreen under your finger is this formula turned into a sense: the panel's electrodes carry a small AC signal, and a fingertip's arrival changes the local capacitance by picofarads — a change in X_C at the sensing frequency that the controller detects row by column to locate the touch. Nothing is pressed and nothing flows through you; the "button" is a measured shift in a reactance, priced by the same 1 ÷ (2πfC) with f in the hundreds of kilohertz and C in trillionths. The component this page treats as a circuit obstacle moonlights, at small values and high frequencies, as the most successful human interface ever manufactured — a career turn the formula predicts perfectly, since at those frequencies even a picofarad is a negotiable reactance.

The Stray Capacitance That Isn't Stray

Every pair of conductors in a circuit is secretly a small capacitor, and at high enough frequency this page's formula convicts them all: a picofarad of "stray" capacitance between a tube amplifier's grid and plate is 1.6 kΩ of feedback path at 100 MHz — an oscillator where the schematic shows an amplifier. RF design is largely the discipline of pricing these ghost components with the same reciprocal, layout first and schematic second. The calculator's honest domain is the components you chose; its lesson generalises to the ones geometry chose for you, which is why experienced designers run the 1 ÷ (2πfC) of everything, intended or not, before blaming the parts they can see. The ghost picofarads are why a circuit that simulates perfectly can oscillate on the bench — the schematic omitted a component that the formula, applied to the layout, would have caught.

Related Tools

More from the Physics Calculators hub: the Inductive Reactance Calculator — the twin whose reactance climbs with frequency — and the Capacitor Energy Calculator for the joules behind the phase.

Frequently Asked Questions

How can current flow through an open gap at all?

It doesn't — not through the dielectric, anyway: the "current" in a capacitor circuit is charge arriving at one plate and leaving the other, the field across the gap doing the bookkeeping (Maxwell's displacement current is the formal completion of the sentence). For circuit purposes the distinction is invisible — ammeters in series read the full AC value this page predicts — but it explains the DC corner: steady voltage means, after the first charging moment, no charge needs to move at all, so the current stops and the reactance reads infinite. The gap passes change and blocks constancy, which is also a fair motto for the component.

What size capacitor blocks mains hum but passes audio?

Price both ends with the formula: to pass 20 Hz audio with reactance small against, say, a 10 kΩ load (target X_C ≈ 1 kΩ), C = 1 ÷ (2π × 20 × 1,000) ≈ 8 µF — hence the familiar microfarad-scale coupling capacitors of audio design, and the electrolytic values on every amplifier schematic. The hum question inverts: the same 8 µF at 100/120 Hz ripple has X_C near 170 Ω, far too leaky to be the only filter — which is why supplies pair bulk capacitance with regulators rather than asking one component to be both door and wall. The calculator turns these folklore values into checkable arithmetic.

Why do real capacitors fail at high frequency?

Parasitics collect their tax: the leads and plates carry inductance (ESL) that eventually out-reacts the capacitance itself, so above the self-resonant frequency the part behaves inductively and this page's falling line turns upward. Dielectric losses (the dissipation factor) also convert a slice of the wattless current into heat, worst in cheap electrolytics asked to do RF work. The formula is the ideal; the datasheet's impedance-versus-frequency curve is the biography, and the two agree exactly in the region the part was designed for — which is the region a competent designer stays inside, calculator in hand.

What is a capacitive dropper, and is it safe?

The worked example's circuit promoted to a power supply: a mains-rated (X-class) capacitor whose reactance, priced by this page, drops most of the mains voltage wattlessly to feed a low-voltage circuit. It is cheap, efficient and genuinely used in sealed products — and it provides no isolation from the mains, so every node of the circuit must be treated as live, enclosures must be touch-proof, and the capacitor must be a safety-rated type that fails open rather than short. The calculator gives the reactance the design stands on; the safety discipline is a separate, non-negotiable literature that this page flags rather than replaces.

How does reactance differ between series and parallel resonance?

The reactances themselves do not change — X_L and X_C are component properties at a frequency — but the circuit's total reverses its manners: in series, the two cancel at resonance and the impedance bottoms out at the resistance (maximum current); in parallel, they cancel into an open (maximum impedance, currents circulating inside the tank). Radio tuning lives on the parallel behaviour, band-stop and supply filtering on the series, and both knees are located by the same equality X_L = X_C — computable from this page and its twin in two lookups, which is the practical definition of understanding a resonant circuit.

Why is the reactance of a bigger capacitor smaller?

Because a bigger capacitance stores more charge per volt, so at a given voltage swing and frequency it must move more charge per cycle — more current for the same voltage, which is precisely what "less opposition" means. The inverse proportionality (X_C ∝ 1/C) is the whole content, and it pairs with the inductor's direct proportionality (X_L ∝ L) into the designer's reflex: to lower a reactance at a fixed frequency, enlarge the capacitor or shrink the inductor. Two pages, two proportionalities, and the frequency-selective half of electronics is a pair of sentences long. The reader who can estimate both reactances at a glance — rising line against falling line, their crossing the resonance — holds the working core of analogue design in a single picture.