Capacitive Reactance Calculator
Calculate the capacitive reactance (XC) of a capacitor at a given frequency. Capacitive reactance is the opposition to AC current flow caused by a capacitor, measured in ohms. See also our Inductive Reactance Calculator and Resonant Frequency Calculator.
How to Calculate Capacitive Reactance
Capacitive reactance (XC) is the opposition that a capacitor presents to alternating current. Unlike inductive reactance which increases with frequency, capacitive reactance decreases with frequency — capacitors pass high frequencies easily and block low frequencies. At DC (f=0), a capacitor has infinite reactance (open circuit). As frequency increases, reactance decreases, allowing more current to flow.
In an ideal capacitor, current leads voltage by exactly 90 degrees. This is the opposite phase relationship to an inductor, which is why capacitors and inductors can cancel each other's reactance at the resonant frequency. The inverse relationship between capacitive reactance and frequency makes capacitors essential for high-pass filters, coupling circuits, and bypass/decoupling applications.
Capacitive Reactance Formula
Capacitive Reactance:
XC = 1 / (2πfC) = 1 / (ωC)
Where:
XC = capacitive reactance (Ω)
f = frequency (Hz)
C = capacitance (F)
ω = angular frequency = 2πf (rad/s)
Impedance of Capacitor:
Z = -jXC = 1/(jωC) (complex notation)
|Z| = XC (magnitude)
Current Through Capacitor:
I = V / XC = V × 2πfC (magnitude)
Phase: I leads V by 90°
With Series Resistance:
|Z| = √(R² + XC²)
θ = -arctan(XC/R)
Example Calculation
Calculate the capacitive reactance of a 100nF capacitor at 1kHz:
C = 100 nF = 100 × 10⁻⁹ F = 10⁻⁷ F
f = 1 kHz = 1000 Hz
XC = 1/(2π × 1000 × 10⁻⁷) = 1/(6.283 × 10⁻⁴)
XC = 1,592 Ω ≈ 1.59 kΩ
If 10V AC is applied:
I = V/XC = 10/1592 = 6.28 mA
Current leads voltage by 90°
At 10 kHz (10× frequency):
XC = 1/(2π × 10000 × 10⁻⁷) = 159.2 Ω (1/10 the reactance)
I = 10/159.2 = 62.8 mA (10× the current)
This demonstrates why capacitors pass high frequencies
and block low frequencies (high-pass filter behavior)
Capacitive Reactance Reference Table
| Capacitance | Frequency | XC (Ω) |
|---|---|---|
| 10 pF | 1 MHz | 15,915 Ω |
| 100 pF | 1 MHz | 1,592 Ω |
| 1 nF | 1 MHz | 159.2 Ω |
| 1 nF | 100 kHz | 1,592 Ω |
| 10 nF | 10 kHz | 1,592 Ω |
| 100 nF | 1 kHz | 1,592 Ω |
| 100 nF | 10 kHz | 159.2 Ω |
| 1 µF | 60 Hz | 2,653 Ω |
| 1 µF | 1 kHz | 159.2 Ω |
| 10 µF | 60 Hz | 265.3 Ω |
| 100 µF | 60 Hz | 26.53 Ω |
| 1000 µF | 60 Hz | 2.65 Ω |
Frequently Asked Questions
Why does capacitive reactance decrease with frequency?
At higher frequencies, the capacitor charges and discharges more rapidly, allowing more current to flow per cycle. The capacitor doesn't have time to fully charge before the voltage reverses, so it never develops enough voltage to significantly oppose the current. At infinite frequency, the capacitor acts as a short circuit (XC → 0).
Why does current lead voltage in a capacitor?
Current must flow into a capacitor before voltage can build up across it (Q = CV, so V follows Q). When AC voltage begins to rise, current is already at maximum (charging the capacitor). When voltage reaches its peak, current is zero (capacitor fully charged). The result is that current peaks 90° before voltage — current leads voltage.
How do I choose a coupling capacitor value?
A coupling capacitor should have low reactance at the signal frequency compared to the load impedance. Rule of thumb: XC should be less than 1/10 of the load impedance at the lowest frequency of interest. For audio (20Hz) into 10kΩ: XC < 1kΩ → C > 1/(2π×20×1000) = 8µF. A 10µF capacitor would work well.
What is the difference between XC and impedance?
XC is the magnitude of the capacitor's opposition to AC current. Impedance (Z) is the complete complex representation: Z = -jXC for an ideal capacitor. For a real capacitor with ESR: Z = ESR - jXC, and |Z| = √(ESR² + XC²). At low frequencies, XC dominates. At high frequencies, ESR and parasitic inductance (ESL) dominate.
How does capacitive reactance relate to power factor correction?
Capacitive reactance provides leading reactive power that cancels the lagging reactive power from inductive loads. To correct power factor, add capacitance whose reactance at line frequency provides the needed reactive power: QC = V²/XC = V² × 2πfC. The capacitor supplies reactive current locally, reducing the reactive current drawn from the utility.
Why do bypass capacitors need to be close to ICs?
Wire and PCB trace inductance adds series impedance that increases with frequency. A bypass capacitor far from the IC has significant trace inductance between them, reducing its effectiveness at high frequencies. Placing the capacitor within a few millimeters minimizes this parasitic inductance, ensuring low impedance at the frequencies where the IC needs instantaneous current (during switching transitions).
Capacitive vs Inductive Reactance
Capacitive and inductive reactances are complementary: XC = 1/(2πfC) decreases with frequency while XL = 2πfL increases with frequency. At the resonant frequency, XL = XC and they cancel. Below resonance, XC > XL (circuit is capacitive). Above resonance, XL > XC (circuit is inductive). This frequency-dependent behavior is the basis for all passive filter design — low-pass, high-pass, bandpass, and band-reject filters all exploit the different frequency responses of inductors and capacitors.
Practical Applications
- AC coupling: Capacitors block DC while passing AC signals between amplifier stages
- Bypass/decoupling: Low XC at switching frequencies shunts noise to ground
- High-pass filters: Series capacitor blocks low frequencies, passes high frequencies
- Power factor correction: Capacitor banks provide leading reactive power
- Motor start capacitors: Provide phase shift for single-phase motor starting
- Tone controls: Variable capacitive reactance shapes audio frequency response