Article — Capacitive Reactance Calculator
Capacitive reactance calculator
Capacitive reactance (Xc) is the opposition a capacitor presents to alternating current. It equals 1 ÷ (2π × f × C), with frequency in hertz, capacitance in farads, and the result in ohms. Unlike resistance, Xc depends on frequency and dissipates no power.
The formula sits at the heart of every coupling capacitor, every power-supply filter, every RF tuning circuit. Understanding the magnitude of Xc at the working frequency is what separates a circuit that passes the right signal from one that blocks it. This page walks through the math, the typical values, and the mistakes engineers keep making.
What is capacitive reactance?
A capacitor stores charge on its plates. When you apply DC, current flows briefly while the cap charges up, then stops — the cap blocks DC. Apply AC, and the cap charges and discharges with every cycle, so current keeps flowing. The cap's opposition to that AC current is capacitive reactance.
Xc has units of ohms because it behaves like a frequency-dependent resistance in Ohm's law: V = I × Xc. But it differs from a resistor in two key ways. First, Xc drops as frequency rises, while resistance does not. Second, the current through a capacitor leads the voltage by 90°, so no net power is dissipated. The energy that builds up in the cap's electric field on one half cycle is returned to the circuit on the next.
The very first capacitor — the Leyden jar of 1745 — was just a glass bottle lined with foil inside and out, holding the world's first measurable capacitive reactance. Pieter van Musschenbroek nearly knocked himself unconscious discharging one through his own body.
The capacitive reactance formula
The main formula and its rearrangements solve every common reactance problem:
Xc = 1 ÷ (2π f C) ω = 2π fC = 1 ÷ (2π f Xc) f = 1 ÷ (2π C Xc)fc = 1 ÷ (2π R C) |Z| = √(R² + Xc²)Three quantities, three unknowns. Plug in any two and solve for the third. The most common use is sizing a coupling capacitor: pick the lowest frequency you want to pass, set Xc at that frequency equal to one-tenth of the load resistance, and solve for C.
How frequency changes capacitive reactance
Xc and frequency are inversely proportional. Double the frequency and Xc halves. Drop the frequency by a factor of 100 and Xc rises 100 times. The same 1 µF capacitor measures 1591 Ω at 100 Hz, 159 Ω at 1 kHz, 15.9 Ω at 10 kHz, and 1.59 Ω at 100 kHz.
This frequency sensitivity is what makes capacitors useful as filters. A small-value cap in series with a signal blocks low frequencies (high Xc) and passes high frequencies (low Xc) — a high-pass filter. A cap to ground does the opposite, shunting high frequencies away while letting low ones reach the load.
Capacitive reactance versus resistance
Resistance and reactance both oppose current in ohms, but they cannot be added directly. Resistance is real; reactance is imaginary (in the complex-number sense). They combine as the Pythagorean sum into total impedance: |Z| = √(R² + Xc²). A 100 Ω resistor in series with a 1 µF cap at 1 kHz has impedance √(100² + 159²) = 188 Ω, not 259 Ω.
The reason for this complex-number treatment is that current through a resistor is in phase with voltage, while current through a capacitor leads voltage by 90°. The two contributions are perpendicular vectors, so their magnitudes combine by the Pythagorean theorem. The phase angle of the combined impedance is −arctan(Xc/R) — negative because Xc is imaginary and below the real axis.
Capacitive reactance in RC filters
The corner frequency of a first-order RC filter is the point where Xc equals R. Above this frequency the cap dominates; below it the resistor does. The 3 dB cutoff occurs at fc = 1 ÷ (2π × R × C). A 1 kΩ resistor and a 100 nF cap give fc = 1 ÷ (6.283 × 1000 × 0.0000001) = 1592 Hz — a vocal-range high-pass corner.
Audio crossover networks for speakers use this directly. A second-order low-pass to a woofer might use 1 mH inductor with a 6.8 µF cap, giving fc near 1.9 kHz. RF impedance-matching networks use Xc to cancel inductive reactance at the operating frequency, leaving pure resistive impedance for maximum power transfer.
Above the self-resonant frequency (SRF), a real capacitor behaves as an inductor due to parasitic ESL. The formula Xc = 1/(2πfC) breaks down past the SRF. For ceramic 100 nF caps SRF is typically 10–30 MHz; for electrolytics it can be below 1 MHz.
Common capacitive reactance mistakes
Engineers fumble Xc in predictable ways. The most common is unit drift: plugging in capacitance in microfarads instead of farads, or frequency in kilohertz instead of hertz. The factor 10⁶ between µF and F bites every junior engineer at least once. Pick a unit system, stick to it, and convert at the start.
The second common error is treating Xc like a resistor and adding it directly. A 100 Ω resistor plus a 100 Ω Xc cap in series is not 200 Ω — it is 141 Ω, by the Pythagorean rule above. Confusing this distorts every filter design and impedance-matching calculation.
The third is ignoring phase. Real power in an AC circuit is P = V × I × cos(φ). A purely capacitive load has cos(φ) = 0, so it draws current but consumes zero real power. Utility companies still charge industrial customers for apparent power (V × I), which is why power-factor correction capacitors save money.
Memorize one anchor: 1 µF at 1 kHz is 159 Ω. From there, scale linearly with capacitance (10× more µF gives 10× less Xc) and inversely with frequency (10× higher frequency gives 10× less Xc).
A short history of reactance
The concept of reactance is younger than the capacitor itself. Capacitors (then called condensers) date to 1745. Reactance as a formal quantity entered electrical engineering with Charles Proteus Steinmetz around 1893, when he introduced complex-number notation to AC circuit analysis at General Electric. Steinmetz's method turned messy sinusoidal differential equations into algebra, and it remains the backbone of every electrical-engineering curriculum today.
Before Steinmetz, AC circuits were so hard to analyze that some engineers (including Thomas Edison) argued AC could not be tamed for practical distribution. Steinmetz's formalism made AC mathematics tractable, helped settle the war of currents in favor of Tesla and Westinghouse, and gave us a clean Xc = 1 ÷ (2πfC) that any student can derive from Maxwell's equations in an afternoon.