Impedance Calculator | Z = √(R²+(XL-XC)²)
Calculate the total impedance of an RLC circuit. Enter resistance R, inductive reactance XL, and capacitive reactance XC to find Z and phase angle.
How to Use
- Enter the resistance R in ohms (real part of impedance).
- Enter inductive reactance XL in ohms: XL = 2π × f × L.
- Enter capacitive reactance XC in ohms: XC = 1 / (2π × f × C).
- Click 'Calculate' to find total impedance Z = √(R² + (XL − XC)²).
- Phase angle θ = arctan((XL − XC) / R). Positive θ = inductive, negative = capacitive.
- Use the Reactance Calculator tool to first compute XL and XC from frequency and component values.
About Impedance
What is Impedance?
Impedance (Z) is the total opposition to AC current flow in a circuit, combining resistance (R) and reactance (X). It is a complex quantity: Z = R + jX, where j is the imaginary unit. The magnitude is |Z| = √(R² + X²) and the phase angle θ = arctan(X/R). Unlike resistance (which is frequency-independent), reactance varies with frequency, making impedance frequency-dependent.
Inductive vs. Capacitive Reactance
Inductive reactance XL = 2πfL increases with frequency — inductors oppose rapid changes in current. Capacitive reactance XC = 1/(2πfC) decreases with frequency — capacitors oppose DC but allow AC. In a series RLC circuit, the net reactance is X = XL − XC. If XL > XC, the circuit is inductive (current lags voltage); if XC > XL, it is capacitive (current leads voltage); if XL = XC, resonance occurs.
Phase Angle and Power Factor
The phase angle θ = arctan((XL − XC) / R) represents the phase difference between voltage and current. The power factor PF = cos(θ) indicates what fraction of apparent power (VA) is real power (W). At θ = 0° (pure resistance), PF = 1 and all power is real. At θ = ±90° (pure reactance), PF = 0 and all power is reactive (no real energy consumed). Practical loads have PF between 0 and 1.
Impedance Matching
Maximum power transfer occurs when the source impedance equals the complex conjugate of the load impedance (Z_source = Z_load*). For real impedances, this means Z_source = Z_load. In RF circuits, impedance matching networks (L-networks, T-networks, π-networks) transform the load impedance to match the source, maximizing power transfer and minimizing reflections. This is critical in antenna systems and RF power amplifiers.
Key Features
- Calculates total impedance Z = √(R² + (XL−XC)²)
- Computes phase angle θ = arctan((XL−XC)/R) in degrees
- Shows whether the circuit is inductive, capacitive, or at resonance
- Direct input of R, XL, and XC for flexibility
Common Applications
- RLC series and parallel circuit analysis
- Audio crossover network design
- RF impedance matching network calculations
- Power factor correction in AC systems
- Filter design verification