Ac Circuit Impedance Calculator

Physics Electricity and Magnetism • Ac Circuits and Electromagnetic Waves

Written by STEM Calculators Team Published January 18, 2026 Updated February 24, 2026

AC Circuit Impedance Calculator

Computes complex impedance for RLC circuits: \(Z = R + j(X_L - X_C)\) (series) and \(Z = 1/Y\) with \(Y=\frac1R + \frac1{j\omega L}+j\omega C\) (parallel). Also shows \(|Z|\), phase \(\varphi\), and an interactive impedance (phasor) triangle.

Units: \(\Omega\) (ohm), H (henry), F (farad), Hz, rad/s. Inputs accept 1e-6, pi, sqrt(2), sin(), cos(), tan(), ln(), log(), abs().

Inputs

Connection:

Frequency input:

Value:

Resistance \(R\) (Ω):

Reactive elements

Inductor:

Include \(L\)

Capacitor:

Include \(C\)

Output options

Show admittance \(Y=1/Z\) Show resonance (\(\omega_0, f_0\))

Ready

Steps

Enter values and click Calculate.

Phasor (impedance triangle)

Interactive diagram (pan/zoom enabled)

Drag to pan • wheel/trackpad/pinch to zoom in/out.

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Theory

Impedance, reactance, and phasors

In steady-state AC analysis, we model sinusoidal voltages and currents using phasors. A circuit element is represented by a (generally complex) impedance \(Z\) such that \( \tilde V = Z\,\tilde I \). The imaginary unit is written as \(j\) in electrical engineering.

Element impedances

\[ \begin{aligned} Z_R &= R \\ Z_L &= j\omega L \\ Z_C &= \frac{1}{j\omega C} = -\,j\,\frac{1}{\omega C} \end{aligned} \]

The reactance is the imaginary component contribution: \(X_L=\omega L\) (inductive, positive imaginary) and \(X_C=\frac{1}{\omega C}\) (capacitive, negative imaginary).

Series vs parallel RLC

Series (same current through R, L, C)

\[ \begin{aligned} Z_{\text{series}} &= Z_R + Z_L + Z_C \\ &= R + j\left(X_L - X_C\right) \end{aligned} \]

Parallel (same voltage across branches)

In parallel it is typically cleaner to add admittances \(Y=1/Z\).

\[ \begin{aligned} Y_{\text{parallel}} &= \frac{1}{R} + \frac{1}{j\omega L} + j\omega C \\ &= \frac{1}{R} + j\left(\omega C - \frac{1}{\omega L}\right) \\ Z_{\text{parallel}} &= \frac{1}{Y_{\text{parallel}}} \end{aligned} \]

Tip: In series we naturally add impedances. In parallel we naturally add admittances.

Magnitude, phase, and the impedance triangle

For a complex impedance \(Z=R+jX\), the polar form is \(Z=|Z|\angle\varphi\), where:

\[ \begin{aligned} |Z| &= \sqrt{R^2 + X^2} \\ \varphi &= \tan^{-1}\!\left(\frac{X}{R}\right) \end{aligned} \]

The calculator draws the impedance triangle on the complex plane: horizontal leg \(R\), vertical leg \(X\), and hypotenuse \(|Z|\). The angle \(\varphi\) is the phase of \(Z\).

Resonance and a university-level extension

Resonance (ideal RLC)

When both L and C are present, the inductive and capacitive reactances can cancel. The resonance condition is \(X_L=X_C\).

\[ \begin{aligned} \omega_0 L &= \frac{1}{\omega_0 C} \\ \omega_0 &= \frac{1}{\sqrt{LC}},\qquad f_0 = \frac{\omega_0}{2\pi} \end{aligned} \]

Mutual inductance (extension)

In coupled-coil problems, two inductors can interact via mutual inductance \(M\). For series-connected coupled inductors, an equivalent inductance can appear:

\[ \begin{aligned} L_{\text{eq}} &= L_1 + L_2 \pm 2M \end{aligned} \]

The sign depends on whether the coupling is aiding (+) or opposing (−), based on the dot convention.

Steps

Phasor (impedance triangle)

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