Capacitive Reactance Calculator Online: Formula & Use

This calculator works out the capacitive reactance (X_C) of a capacitor at a given frequency. You enter the capacitance in farads (or a submultiple like µF or nF) and the frequency in hertz (Hz), and it returns the reactance in ohms (Ω) — the effective opposition the capacitor presents to alternating current.

Formula

The capacitive reactance formula is:

X_C = 1 / (2πfC)

Where:

• X_C = capacitive reactance in ohms (Ω)
• f = frequency in hertz (Hz)
• C = capacitance in farads (F)
• π ≈ 3.14159

The product 2πf is often called the angular frequency (ω), so the formula is sometimes written as X_C = 1/(ωC). The key point is that reactance is inversely proportional to both frequency and capacitance — double the frequency and the reactance halves; double the capacitance and it also halves.

Worked Example

Using the default values from the calculator above: f = 50 Hz, C = 0.0001 F (100 µF).

1. Calculate 2πf: 2 × 3.14159 × 50 = 314.159
2. Multiply by C: 314.159 × 0.0001 = 0.0314159
3. Take the reciprocal: 1 / 0.0314159 = 31.83 Ω

The calculator shows 31.83 Ω, matching the manual calculation. Notice that a 100 µF capacitor at 50 Hz (mains frequency in many countries) has a reactance of only about 32 Ω — quite low, which is why large capacitors are used for power supply filtering.

When to Use Capacitive Reactance

Capacitive reactance matters in any AC circuit where you need to know how much a capacitor limits current. Common applications include:

• Filter design — high-pass and low-pass filters rely on the frequency-dependent reactance to pass or block certain frequency ranges.
• Power supply smoothing — a capacitor across a DC output has low reactance to ripple (AC) frequencies, shunting them to ground.
• Coupling and decoupling — series capacitors block DC but pass AC; their reactance determines the lower cutoff frequency.
• AC motor start/run capacitors — the reactance sets the phase shift and current.
• Tuned circuits — combined with inductive reactance, capacitive reactance determines resonance.

At DC (f = 0), the formula gives infinite reactance — a capacitor blocks direct current entirely. As frequency increases, the reactance drops, eventually approaching a short circuit at very high frequencies (though real capacitors have parasitic inductance and resistance that limit this).

How to Read the Result

The reactance value tells you the opposition to AC current in ohms, just like resistance. To find the current through the capacitor, use Ohm’s law: I = V / X_C, where V is the RMS voltage across the capacitor. For example, if you apply 10 V RMS at 50 Hz to the 100 µF capacitor above (X_C = 31.83 Ω), the current would be 10 / 31.83 ≈ 0.314 A.

Important: capacitive reactance is not a real power loss. An ideal capacitor stores energy in its electric field and returns it to the circuit each cycle; the average power dissipated is zero. In practice, capacitors have a small equivalent series resistance (ESR) that causes some heating, but the reactance itself is purely reactive.

Common Mistakes and Unit Mix-ups

• Using submultiples without converting — the formula requires farads. If you enter 100 µF, you must use 0.0001 F. The calculator above expects you to enter the value in farads, so convert µF to F by dividing by 1,000,000 (or use scientific notation like 1e-4).
• Confusing frequency with angular frequency — the formula uses f in Hz, not ω in rad/s. If you have ω, divide by 2π to get f.
• Forgetting the reciprocal — X_C = 1/(2πfC), not 2πfC. That latter is the inductive reactance formula (X_L = 2πfL).
• Using peak vs RMS — the reactance is the same regardless of whether you use peak or RMS values, but when calculating current or voltage, be consistent (both RMS or both peak).
• Rounding too early — keep several significant figures during intermediate steps to avoid errors in the final result.

Limits of the Formula

The formula X_C = 1/(2πfC) assumes an ideal capacitor. Real capacitors have:

• Equivalent series resistance (ESR) — a small resistance that causes losses and slightly changes the impedance.
• Equivalent series inductance (ESL) — at high frequencies (typically above a few MHz), the parasitic inductance becomes significant and the capacitor behaves more like an inductor.
• Dielectric absorption and leakage — a small DC leakage current and residual charge effects.

For most low-frequency applications (up to a few hundred kHz), the ideal formula is accurate within a few percent. For RF work, you should use a more detailed model or consult the capacitor’s datasheet.

Frequently Asked Questions

What is the difference between capacitive reactance and impedance?

Capacitive reactance is the opposition to AC current specifically due to the capacitor’s capacitance. Impedance is a broader term that includes both resistance and reactance (capacitive and inductive). For a pure capacitor, impedance equals capacitive reactance (Z = X_C), but in a real circuit with resistors and inductors, impedance is the vector sum of resistance and net reactance.

Does capacitive reactance change with frequency?

Yes, it is inversely proportional to frequency. At low frequencies, the reactance is high, so a capacitor blocks low-frequency signals. At high frequencies, the reactance is low, so it passes high-frequency signals easily. This is the basis of high-pass and low-pass filters.

Can capacitive reactance be negative?

In the formula, the reactance is always a positive number. However, in complex impedance notation, capacitive reactance is often written as a negative imaginary value (Z = -jX_C) to distinguish it from inductive reactance, which is positive imaginary. The magnitude is always positive.

How do I convert µF to farads for the formula?

1 µF = 1 × 10^-6 F. So divide the microfarad value by 1,000,000. For example, 470 µF = 470 / 1,000,000 = 0.00047 F. You can also use scientific notation: 4.7e-4 F.

What is the reactance of a capacitor at DC?

At DC (f = 0), the formula gives 1/0, which is infinite. This means a capacitor blocks all direct current once it is fully charged. In practice, there is a tiny leakage current, but for most purposes, a capacitor is an open circuit to DC.

Why does a capacitor pass AC but block DC?

Because the reactance is inversely proportional to frequency. At DC, the frequency is zero, so the reactance is infinite — no current flows. At AC, the frequency is non-zero, so the reactance is finite and current can flow. The capacitor charges and discharges with the alternating voltage, creating a current in the circuit.

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in f | Frequency | Hz | 50 | 0
in c | Capacitance | F | 0.0001 | 0
out xc | Capacitive reactance | Ω | 1 / (2 * pi * f * c) | 2