Capacitive reactance:
1 ÷ (2π × f × C)

What capacitive reactance is

Capacitive reactance is how strongly a capacitor opposes alternating current, measured in ohms. For a 1 µF capacitor on a 50 Hz supply it is about 3,183.1 Ω. Unlike a resistor, its opposition changes with frequency.

A capacitor passes AC more easily as the frequency rises, because it charges and discharges more quickly. At very low frequency it behaves almost like an open circuit, and in a DC circuit it blocks current once it is charged. Reactance puts a number on that behaviour.

The Xc formula

How frequency and capacitance change Xc

Because both frequency and capacitance sit in the denominator, increasing either one lowers the reactance. This is the reason a small capacitor can pass a high-frequency signal and block a low one.

Audio engineers use this behaviour when they choose a coupling capacitor, which lets music through while blocking a steady DC voltage. Designers of simple filters pick a capacitor so that its reactance matches the resistor at the frequency where the filter should start to act.

The microfarad trap, and the inductor's opposite

The most common slip is the unit. The formula needs farads, but capacitors are labelled in microfarads, nanofarads and picofarads. Convert before you enter: 1 µF is 0.000001 F, 100 nF is 0.0000001 F, and 10 pF is 0.00000000001 F.

An inductor does the opposite. Its reactance is XL = 2π × f × L, with L in henries, so it rises with frequency. A 0.5 H coil at 50 Hz has an XL of about 157.08 Ω. This calculator handles the capacitor side only.

Neither reactance is a resistance in the heating sense. An ideal capacitor stores energy and returns it each cycle instead of turning it into heat, although real components have small losses.

Where reactance matters in practice

Reactance appears in tone controls, speaker crossovers, radio tuning and power supplies. A capacitor in series with a mains load can drop part of the voltage without producing much heat, which is why small capacitive dropper circuits exist, although they need careful design because they connect directly to the supply.

To find the current through a capacitor on an AC supply, divide the voltage by the reactance, as Ohm's law suggests. With 1 µF at 50 Hz and 3,183 Ω of reactance, a small voltage drives only a few milliamps.

Common mistakes with capacitive reactance

• Entering microfarads as if they were farads, which gives an answer a million times too small.
• Using angular frequency in the formula that already contains 2π.
• Expecting reactance to be a fixed property of the capacitor. It depends on frequency.
• Adding reactance and resistance directly. In a series circuit they combine as impedance, not as a simple sum.
• Using a very small frequency, which makes Xc enormous and is close to a DC case.