What is capacitive reactance and how is it calculated?

Capacitive reactance (Xc) is the opposition a capacitor offers to alternating current (AC). Unlike resistance, which is constant, reactance depends on both the capacitance value and the frequency of the AC signal. The formula is Xc = 1 / (2 x pi x f x C), where f is the frequency in hertz and C is the capacitance in farads. The result is in ohms. A larger capacitor or a higher frequency results in lower reactance, meaning the capacitor passes more current.

How does frequency affect capacitive reactance?

Capacitive reactance is inversely proportional to frequency. As frequency increases, reactance decreases. At very high frequencies a capacitor acts almost like a short circuit (very low opposition). At very low frequencies or DC (zero Hz), a capacitor blocks current entirely, giving theoretically infinite reactance. This behaviour makes capacitors useful as high-pass filters, coupling elements in audio circuits, and bypass capacitors in power supplies.

What is the difference between reactance and impedance?

Reactance (Xc) is the imaginary component of impedance that arises from the capacitor alone. Impedance (Z) is the total opposition to AC in a circuit and combines both resistance (R) and reactance (Xc or XL). In a circuit containing a resistor and a capacitor in series, the total impedance is Z = sqrt(R squared + Xc squared). Reactance is measured in ohms, as is impedance, but reactance involves a 90-degree phase shift between voltage and current whereas pure resistance has no phase shift.

Capacitive Reactance Calculator

This calculator works out the capacitive reactance (Xc) of a capacitor in an AC circuit, the opposition it presents to alternating current at a given frequency, using the standard formula Xc = 1 / (2πfC). Enter a frequency value and choose its unit (Hz, kHz or MHz), then enter a capacitance value and choose its unit (µF, nF or pF). The calculator returns the capacitive reactance in ohms, plus the frequency and capacitance converted into standard hertz and farads. A calculation breakdown shows each step, including 2 × π × f in radians per second and the full 2 × π × f × C term, so you can follow how the result is reached. A context panel shows the reactance category, from very low to very high, the 90 degree phase shift between voltage and current, and how the reactance changes if you double or halve the frequency. Because reactance falls as frequency rises, the same capacitor behaves very differently at mains frequency compared with radio frequencies, which matters for filter design and coupling circuits. Use it to check component values when designing AC circuits or resonant circuits, or to see how a capacitor responds at a given signal frequency. Results assume an ideal capacitor with no series resistance or parasitic inductance, so treat them as an engineering reference figure rather than a substitute for datasheet values.

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Standard Formula Xc = 1 / (2πfC) per IEC 60027 and standard AC circuit theory.

Xc = 1 / (2π × f × C)

1. Frequency

Frequency value

Frequency unit

2. Capacitance

Capacitance value

µF

Capacitance unit

Capacitive Reactance Result

Capacitive Reactance (Xc)
-
Ohms (Ω)

Frequency (f)

Hertz (Hz)

Capacitance (C)

Farads

Calculation Breakdown

Frequency (f)50.00 Hz

Capacitance (C)100.0 μF

2 × π × f314.16 rad/s

2 × π × f × C0.031416 S (siemens)

Xc = 1 / (2πfC)-

Context and Behaviour

Reactance categoryLow-moderate reactance

Phase shift (V vs I)Voltage lags current by 90°

At double frequency-

At half frequency-

Impedance roleImaginary (j) component

Worked Example (Default Values)

Frequency: 50 Hz (NZ mains). Capacitance: 100 µF (100 × 10⁻⁶ F)

Xc = 1 / (2 × π × 50 × 100 × 10⁻⁶)

Xc = 1 / (2 × 3.14159 × 50 × 0.0001)

Xc = 1 / 0.031416 = 31.83 Ω

What is Capacitive Reactance?

Capacitive reactance (symbol Xc, unit ohms) is the opposition that a capacitor presents to the flow of alternating current (AC). In a DC circuit, a capacitor blocks current altogether once it is fully charged. In an AC circuit, the constantly reversing voltage means the capacitor is always charging or discharging, so current does flow. The amount of opposition depends on both the capacitance value and the frequency of the AC signal.

The key characteristic of capacitive reactance is that it decreases as frequency increases. A 100 µF capacitor at 50 Hz has a reactance of 31.83 ohms. At 500 Hz it drops to 3.18 ohms. At very high frequencies it approaches zero, meaning the capacitor is almost a short circuit to high-frequency signals.

The Formula: Xc = 1 / (2πfC)

The formula for capacitive reactance is derived from the relationship between charge, voltage, and current in a capacitor:

Xc = capacitive reactance in ohms (Ω)
f = frequency in hertz (Hz)
C = capacitance in farads (F)
2π = angular frequency multiplier (approximately 6.2832)

The term 2πf is often written as ω (omega), the angular frequency in radians per second, so the formula is also written as Xc = 1 / (ωC).

Common Capacitance Units

Unit	Symbol	Value in Farads	Typical use
Microfarad	µF	10⁻⁶ F	Power supply filter caps, audio circuits
Nanofarad	nF	10⁻⁹ F	RF decoupling, timing circuits
Picofarad	pF	10⁻¹² F	High-frequency and RF circuits

Reactance vs Resistance vs Impedance

Resistance (R) opposes current flow and converts electrical energy to heat. It is constant regardless of frequency. Capacitive reactance (Xc) opposes current flow but stores and returns energy rather than dissipating it. It varies with frequency. Impedance (Z) is the combined opposition in a circuit that contains both resistance and reactance. In a series RC circuit, Z = √(R² + Xc²).

A key difference is the phase relationship. In a purely resistive circuit, voltage and current are in phase. In a purely capacitive circuit, current leads voltage by 90 degrees (or equivalently, voltage lags current by 90 degrees).

Practical Applications

Filter circuits: Because Xc decreases with frequency, capacitors in RC filters allow high frequencies to pass while attenuating low frequencies (high-pass filter), or the opposite when combined with resistors in low-pass configurations.
Power factor correction: Capacitors are used in industrial power systems to offset inductive reactance from motors and transformers, improving the power factor.
Coupling and decoupling: Capacitors block DC while allowing AC signals to pass between circuit stages.
Resonant circuits: In LC circuits, inductive reactance and capacitive reactance cancel each other at the resonant frequency.

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Sources and method: Capacitive reactance formula Xc = 1 / (2πfC) from IEC 60027-1 (Letter symbols used in electrical technology) and Hayt & Kemmerly, Engineering Circuit Analysis (8th ed). Angular frequency convention ω = 2πf per standard AC circuit theory.

This calculator is for educational and engineering reference purposes. Results assume an ideal capacitor with no series resistance or parasitic inductance. Real capacitors deviate from ideal behaviour at high frequencies. Always verify calculations against component datasheets for precision applications.