The reactance formula, and why frequency is what moves it
Capacitive reactance is the opposition a capacitor gives to alternating current, measured in ohms. It depends on frequency (f, in Hz) and capacitance (C, in farads): double the frequency and the reactance halves. That is the whole reason a capacitor blocks DC but passes high-frequency AC.
Reactance for common capacitors across frequency
Read across for one capacitor value. Small capacitors (pF, nF) suit radio-frequency work; larger ones (µF) suit audio and power.
| Capacitance | 50 Hz | 1 kHz | 100 kHz | 1 MHz |
|---|---|---|---|---|
| 100 pF | 31.8 MΩ | 1.59 MΩ | 15.9 kΩ | 1.59 kΩ |
| 1 nF | 3.18 MΩ | 159 kΩ | 1.59 kΩ | 159 Ω |
| 100 nF | 31.8 kΩ | 1.59 kΩ | 15.9 Ω | 1.59 Ω |
| 1 µF | 3.18 kΩ | 159 Ω | 1.59 Ω | 0.159 Ω |
| 100 µF | 31.8 Ω | 1.59 Ω | 0.016 Ω | 0.0016 Ω |
A rule of thumb: a 1 µF capacitor is about 160 Ω at 1 kHz. Scale from there, since reactance is inversely proportional to both f and C.
Where the answer goes wrong
- Convert the units first. 10 µF is 10×10⁻⁶ F, and 1 kHz is 1000 Hz. Plugging in µF or kHz directly gives an answer off by a factor of millions.
- Impedance is not R + Xc. If a resistor is in the circuit, combine them as Z = √(R² + Xc²), because the capacitor's opposition is 90° out of phase with the resistor's.
- Reactance is in ohms, not farads. If your result carries units of farads or F/Hz, a conversion step went the wrong way.
Common questions
What is the formula for capacitive reactance?
Xc equals 1 divided by (2 times pi times frequency times capacitance), with frequency in hertz and capacitance in farads. The answer comes out in ohms.
Why does capacitive reactance fall as frequency rises?
A higher frequency gives the capacitor less time to oppose each cycle, so it charges and discharges faster and lets more current through. At DC (0 Hz) reactance is infinite and the capacitor blocks everything; at very high frequency it acts almost like a plain wire.
How do I find the capacitor value for a reactance I want?
Rearrange the formula to C equals 1 divided by (2 times pi times frequency times Xc). For 159 ohms at 1 kHz you get about 1 microfarad.
