Enter values and press Calculate.
Impedance (Z) extends resistance to AC circuits by combining resistance with reactance. It is a complex number, Z = R + jX, whose magnitude sets how much current a given voltage drives, and whose phase angle shows how far the current leads or lags the voltage.
| Quantity | Series | Parallel |
|---|---|---|
| Combine | Z = R + j(XL−XC) | 1/Z = 1/R + j(1/XL−1/XC) |
| Magnitude | |Z| = √(R²+X²) | |Z| = 1/|Y| |
| Phase angle | θ = atan(X/R) | θ = atan(Im(Y)/Re(Y)) |
A positive angle means inductive (current lags voltage); negative means capacitive (current leads voltage).
Impedance (Z) is the total opposition to AC current, combining resistance (which dissipates energy) and reactance (which stores and returns energy). It is written as a complex number Z = R + jX.
Resistance only opposes current and dissipates power; impedance also accounts for the frequency-dependent, phase-shifting effect of capacitors and inductors.
The angle by which current leads or lags voltage. A positive angle means inductive behaviour (current lags); a negative angle means capacitive behaviour (current leads).
Add the resistances and reactances separately: Z = R + j(XL−XC), then find the magnitude √(R²+X²) and phase atan(X/R).
Add their admittances (1/Z) rather than the impedances directly, since parallel impedances do not simply average like parallel resistors with reactance involved.
XL and XC cancel, so a series circuit's impedance drops to just R (minimum), while a parallel circuit's impedance rises to its maximum.
The phase angle of the impedance is the same as the angle between voltage and current, which directly sets the power factor: PF = cos(θ).
The reciprocal of impedance, Y = 1/Z, measured in siemens. It is convenient for combining parallel branches, since admittances simply add.
Yes — resistance is constant, but XL = 2πfL grows with frequency and XC = 1/(2πfC) shrinks with frequency, so total impedance changes across the spectrum.
One where the reactive part is zero (XL=XC, or no reactive components at all), so the phase angle is 0° and Z = R.
A source delivers maximum power to a load when the load impedance matches (or is the complex conjugate of) the source impedance, minimizing reflections and maximizing transfer.
The magnitude is always positive, but the reactive part X can be negative (capacitive) or positive (inductive), which shows up as a negative or positive phase angle.
Reactance (XC & XL) • RLC Resonant Frequency • Power Triangle • All Calculators