Impedance Calculator

The impedance calculator computes the total AC impedance of a series RLC circuit, along with phase angle, individual reactances, and power factor. Impedance (Z) is the complete opposition to alternating current in a circuit, combining resistive (energy-dissipating) and reactive (energy-storing) components into a single complex quantity: Z = R + j(XL - XC).

Unlike DC circuits where only resistance matters, AC circuit analysis requires impedance because inductors and capacitors introduce frequency-dependent effects. The impedance magnitude |Z| = √(R² + (XL - XC)²) determines how much current flows for a given voltage (I = V/|Z|), while the phase angle θ = arctan((XL - XC)/R) indicates whether current leads or lags the voltage.

In a purely resistive circuit, Z = R and θ = 0° — voltage and current are in phase. When inductive reactance dominates (XL > XC), θ > 0° and current lags voltage — the circuit draws lagging reactive power. When capacitive reactance dominates (XC > XL), θ < 0° and current leads voltage — the circuit draws leading reactive power. At resonance (XL = XC), the circuit is purely resistive with minimum impedance.

Power factor, defined as cos(θ) = R/|Z|, is critical in electrical power systems. A power factor of 1.0 (purely resistive) means all power is useful work. A lagging power factor from inductive loads wastes apparent power (VA) on reactive energy exchange. Utilities often charge industrial customers for low power factor. Capacitor banks are added to correct lagging power factor.

Impedance matching is essential in RF engineering and audio systems. Maximum power transfer from a source to a load occurs when the load impedance is the complex conjugate of the source impedance (ZL = ZS*). Transformer turns ratios and L-networks are used to transform impedances.

This calculator is designed for series RLC circuits. Enter resistance in ohms, inductance in millihenries, capacitance in microfarads, and frequency in hertz to obtain impedance, phase angle, and power factor.