Capacitive Reactance & Impedance Calculator

Capacitive reactance X꜀ = 1/(2πfC), where f is frequency in hertz and C is capacitance in farads. It is the AC opposition presented by a capacitor — measured in ohms — and falls as frequency rises. A 10 µF cap at 60 Hz has X꜀ ≈ 26.5 Ω, but at 1 kHz it is only 1.59 Ω.

Reactance (X꜀) is the pure reactive component of a capacitor — the imaginary part of impedance. Impedance (Z) includes both reactance and any series or parallel resistance from wiring, ESR, or external resistors. For a pure capacitor Z = X꜀; for a resistor and capacitor in series Z = √(R² + X꜀²).

Phase angle φ is always negative for a pure capacitor — current leads voltage by exactly 90° (π/2 radians). In a real circuit with resistance, the phase angle sits somewhere between 0° and −90°. For parallel R || C: φ = −arctan(R/X꜀). For series R + C: φ = −arctan(X꜀/R).

X꜀ → 0 as f → ∞. At very high frequencies, a capacitor behaves like a short circuit. That is why decoupling capacitors (100 nF, 10 µF) are placed directly at IC pins — they provide a low-impedance path for high-frequency noise while blocking DC.

At DC (f = 0 Hz), X꜀ = 1/0 is infinite — the capacitor is an open circuit, no current flows. As soon as the voltage changes direction or amplitude (AC), f > 0, X꜀ becomes finite, and a current flows. Higher frequencies see lower X꜀ and more current — exactly the behavior of AC coupling capacitors.

Admittance Y = 1/Z, measured in siemens (S). For a pure capacitor, Y = 1/(−jX꜀) = j/(X꜀), where j is the imaginary unit. The magnitude of admittance is 1/X꜀ = 2πfC. Reactance and admittance are reciprocal in magnitude and have opposite imaginary signs.

Every real capacitor carries a small parasitic inductance (ESL) from its leads and plates. At some frequency the inductive reactance X_L = 2πfL equals the capacitive reactance X꜀ = 1/(2πfC), and the two cancel. Above this self-resonant frequency (SRF), the capacitor stops behaving like a capacitor and becomes inductive — its impedance rises instead of falling with frequency.

Three main jobs. First, sizing AC coupling and decoupling capacitors — pick a cap with X꜀ much lower than your load at the lowest frequency of interest. Second, designing RC filters where the corner frequency fc = 1/(2πRC) determines what gets passed and what gets blocked. Third, motor and AC power factor correction where capacitors supply reactive power to cancel inductive load.