Loading Calculator...
Please wait a moment
Please wait a moment
XC = 1 / (2πfC)
XL = 2πfL
f0 = 1 / (2π√LC)
At resonant frequency, XL = XC and they cancel out. The circuit appears purely resistive.
| Application | Frequency |
|---|---|
| Power Line (US) | 60 Hz |
| Power Line (EU) | 50 Hz |
| Audio Low | 20 Hz |
| Audio High | 20 kHz |
| AM Radio | 1 MHz |
| FM Radio | 100 MHz |
| WiFi 2.4GHz | 2.4 GHz |
| WiFi 5GHz | 5 GHz |
Reactance is the opposition that capacitors and inductors present to alternating current (AC), measured in ohms (Ω). Unlike resistance, which dissipates energy as heat, reactance stores energy temporarily in electric fields (capacitors) or magnetic fields (inductors) and returns it to the circuit. Inductive reactance (XL = 2πfL) increases with frequency, causing inductors to block high-frequency signals while passing low frequencies. Capacitive reactance (XC = 1/(2πfC)) decreases with frequency, allowing capacitors to block DC while passing AC signals. Together with resistance, reactance forms impedance (Z), the complete opposition to AC current flow that governs the behavior of all AC circuits from audio amplifiers to power transmission lines.
Determine whether you have a capacitor (measured in farads, F) or inductor (measured in henrys, H). Convert to base units: microfarads (µF) to farads by multiplying by 10⁻⁶, millihenrys (mH) to henrys by multiplying by 10⁻³. The component value directly affects the magnitude of reactance at any frequency.
Find the frequency of the AC signal in hertz (Hz). For power line applications, this is 60 Hz (US) or 50 Hz (Europe). For audio, the range is 20 Hz to 20 kHz. For RF circuits, frequencies range from kHz to GHz. Convert all frequencies to Hz before using the formulas.
For inductive reactance: XL = 2πfL (increases with frequency). For capacitive reactance: XC = 1 / (2πfC) (decreases with frequency). For example, a 100 µF capacitor at 60 Hz has XC = 1 / (2 × 3.14159 × 60 × 0.0001) = 26.5 Ω.
If the circuit includes resistance, calculate total impedance as Z = √(R² + X²) for a simple RL or RC circuit. For RLC circuits with both types of reactance, use Z = √(R² + (XL - XC)²). The net reactance determines whether the circuit behaves inductively or capacitively.
Reactance determines the cutoff frequency and attenuation characteristics of electronic filters. Low-pass, high-pass, band-pass, and notch filters all rely on the frequency-dependent nature of reactance to selectively pass or block signal frequencies. Accurate reactance calculations ensure filters perform to specification in audio, communications, and power supply applications.
Industrial motors and transformers create inductive reactance that causes current to lag voltage, reducing power factor. Utilities charge penalties for low power factor. By calculating the inductive reactance at the line frequency, engineers size correction capacitors to cancel the reactive component, bringing power factor close to unity and reducing electricity costs.
When inductive and capacitive reactances are equal (XL = XC), the circuit resonates at f0 = 1/(2π√LC). Resonance is exploited in radio tuners, oscillators, impedance matching networks, and wireless power transfer. Precise reactance calculations enable circuits to be tuned to exact frequencies with predictable bandwidth and gain.
| Frequency | XC (10 µF) | XC (100 nF) | XC (1 nF) | XL (10 mH) | XL (100 µH) |
|---|---|---|---|---|---|
| 50 Hz | 318 Ω | 31.8 kΩ | 3.18 MΩ | 3.14 Ω | 0.031 Ω |
| 60 Hz | 265 Ω | 26.5 kΩ | 2.65 MΩ | 3.77 Ω | 0.038 Ω |
| 1 kHz | 15.9 Ω | 1.59 kΩ | 159 kΩ | 62.8 Ω | 0.628 Ω |
| 10 kHz | 1.59 Ω | 159 Ω | 15.9 kΩ | 628 Ω | 6.28 Ω |
| 100 kHz | 0.16 Ω | 15.9 Ω | 1.59 kΩ | 6.28 kΩ | 62.8 Ω |
| 1 MHz | 0.016 Ω | 1.59 Ω | 159 Ω | 62.8 kΩ | 628 Ω |
| 10 MHz | 0.002 Ω | 0.16 Ω | 15.9 Ω | 628 kΩ | 6.28 kΩ |
| 100 MHz | ~0 Ω | 0.016 Ω | 1.59 Ω | 6.28 MΩ | 62.8 kΩ |
Values calculated using XC = 1/(2πfC) and XL = 2πfL
Reactance (X) is the imaginary part of impedance, representing energy storage in capacitors and inductors. Impedance (Z) is the complete opposition to AC, combining both resistance (R) and reactance (X) as a complex number: Z = R + jX. The magnitude is |Z| = √(R² + X²). In a purely resistive circuit, impedance equals resistance. In a purely reactive circuit, impedance equals reactance.
Capacitive reactance XC = 1/(2πfC) approaches infinity as frequency approaches zero (DC). At DC, the capacitor fully charges and no more current flows -- it acts as an open circuit. At higher frequencies, the capacitor continuously charges and discharges, allowing current to flow. This makes capacitors ideal for AC coupling and DC blocking in audio and signal processing circuits.
At resonance (f0 = 1/(2π√LC)), inductive and capacitive reactances are equal and cancel each other out. In a series RLC circuit, impedance drops to just the resistance value, allowing maximum current flow. In a parallel RLC circuit, impedance reaches a maximum. The quality factor (Q = XL/R) determines the sharpness of the resonance peak and the circuit's bandwidth.
Real components have parasitic elements: resistors have small inductance from their leads, capacitors have equivalent series resistance (ESR) and inductance (ESL), and inductors have winding capacitance. At high frequencies, these parasitics dominate -- a capacitor can become inductive above its self-resonant frequency. Always check component datasheets for self-resonant frequency and impedance curves at your operating frequency.
In a purely capacitive circuit, current leads voltage by 90 degrees (remembered as "ICE" -- I leads in a Capacitor). In a purely inductive circuit, voltage leads current by 90 degrees ("ELI" -- E leads I in an Inductor). Combined as "ELI the ICE man." In circuits with both resistance and reactance, the phase angle is between 0° and 90°, calculated as θ = arctan(X/R).
Calculate total impedance, phase angle, and resonant frequency for series and parallel RLC circuits with resistance, inductance, and capacitance.
Analyze RC time constants, charging/discharging curves, and cutoff frequencies for resistor-capacitor filter and timing circuits.
Calculate equivalent inductance for series and parallel inductor combinations, stored energy, and coil inductance from physical dimensions.