Calculate the capacitive reactance (Xc) of a capacitor at any AC frequency using the standard formula Xc = 1 / (2πfC). Enter frequency and capacitance to get the reactance in ohms. Capacitance can be entered in microfarads (µF), nanofarads (nF), or picofarads (pF).
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Standard Formula
Xc = 1 / (2πfC) per IEC 60027 and standard AC circuit theory.
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.
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.
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