Impedance Calculator

Calculate the total impedance of RLC series and parallel circuits at any frequency. Get magnitude, phase angle, phasor diagram, resonant frequency, Q factor, and step-by-step breakdown.

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About Impedance Calculator

The Impedance Calculator computes the total impedance of series and parallel RLC circuits at any given frequency. Enter your resistance, inductance, and capacitance values along with the operating frequency to get the impedance magnitude, phase angle, an animated phasor diagram, resonant frequency, quality factor, and a full step-by-step calculation breakdown.

What Is Impedance?

Impedance (Z) is the total opposition that a circuit presents to alternating current (AC). Unlike resistance, which only opposes DC current, impedance accounts for the frequency-dependent effects of inductors and capacitors. It is a complex quantity with a real part (resistance) and an imaginary part (reactance), measured in ohms (Ω).

$$Z = R + jX$$

where $R$ is resistance, $X = X_L - X_C$ is net reactance, $X_L = 2\pi f L$ is inductive reactance, and $X_C = \frac{1}{2\pi f C}$ is capacitive reactance.

Series vs. Parallel RLC Circuits

Series RLC: Components are connected end-to-end in a single path. The impedance is simply the sum of individual impedances:

$$Z_{series} = R + j\left(\omega L - \frac{1}{\omega C}\right)$$

Parallel RLC: Components share the same voltage across them. The total admittance (Y = 1/Z) is the sum of individual admittances:

$$\frac{1}{Z_{parallel}} = \frac{1}{R} + j\left(\omega C - \frac{1}{\omega L}\right)$$

Resonant Frequency

When both an inductor and capacitor are present, the circuit has a resonant frequency where inductive and capacitive reactances cancel:

$$f_0 = \frac{1}{2\pi\sqrt{LC}}$$

At resonance in a series circuit, impedance reaches its minimum ($Z = R$). In a parallel circuit, impedance reaches its maximum. Resonance is widely used in filters, oscillators, and tuning circuits.

Quality Factor and Bandwidth

The quality factor (Q) measures how sharply a circuit resonates. A higher Q means a narrower bandwidth and more selective frequency response:

$$Q_{series} = \frac{\omega_0 L}{R} = \frac{1}{\omega_0 C R} \qquad Q_{parallel} = \frac{R}{\omega_0 L} = \omega_0 C R$$

Bandwidth is defined as $BW = \frac{f_0}{Q}$, representing the range of frequencies over which the circuit operates effectively.

How to Use This Calculator

Select circuit type — Choose Series or Parallel using the visual toggle at the top of the form.
Enter component values — Input resistance (R), inductance (L), and capacitance (C) with appropriate units. Leave a field empty if that component is not in your circuit (e.g., leave C empty for an RL circuit).
Set the frequency — Enter the operating frequency of your AC signal. Select the unit (Hz, kHz, MHz, or GHz).
Calculate — Click the "Calculate Impedance" button.
Analyze results — Review the impedance magnitude and complex form, phase angle indicator, phasor diagram, component contribution analysis, resonance data, and step-by-step formulas.

Practical Applications

Filter design — RC and RLC circuits form the basis of low-pass, high-pass, band-pass, and band-stop filters
Speaker crossover networks — Audio systems use RLC circuits to direct frequency ranges to appropriate drivers
RF tuning circuits — LC tanks select specific radio frequencies in receivers and transmitters
Power factor correction — Capacitors are added to inductive loads to improve power factor
Motor analysis — Understanding RL impedance helps predict motor behavior at line frequency

FAQ

What is impedance in an AC circuit?

Impedance (Z) is the total opposition a circuit presents to alternating current. It combines resistance (R), which opposes current flow, with reactance (X), which arises from inductors and capacitors. Unlike pure resistance, impedance is a complex quantity with both magnitude and phase angle, expressed as Z = R + jX in ohms.

What is the difference between impedance and resistance?

Resistance opposes current equally at all frequencies and dissipates energy as heat. Impedance includes resistance plus reactance from inductors and capacitors, which varies with frequency. Resistance is a real number measured in ohms, while impedance is a complex number with magnitude and phase angle.

How is impedance calculated for a series RLC circuit?

For a series RLC circuit, impedance Z = R + j(X_L − X_C), where X_L = 2πfL is inductive reactance and X_C = 1/(2πfC) is capacitive reactance. The magnitude is |Z| = √(R² + (X_L − X_C)²) and phase angle is θ = arctan((X_L − X_C)/R).

What happens at the resonant frequency of an RLC circuit?

At resonance, inductive reactance equals capacitive reactance (X_L = X_C), so they cancel out. In a series RLC circuit, impedance drops to its minimum value (Z = R). In a parallel RLC circuit, impedance reaches its maximum. The resonant frequency is f₀ = 1/(2π√(LC)).

What is the quality factor (Q) of a circuit?

The quality factor Q measures how sharply a circuit resonates. Higher Q means a narrower bandwidth and more selective frequency response. For series RLC, Q = (2πf₀L)/R. For parallel RLC, Q = R/(2πf₀L). Q also equals the ratio of resonant frequency to bandwidth: Q = f₀/BW.

What is a phasor diagram?

A phasor diagram is a graphical representation of impedance as a vector in the complex plane. The horizontal axis represents resistance (real part) and the vertical axis represents reactance (imaginary part). The length of the vector is the impedance magnitude, and the angle from the horizontal is the phase angle between voltage and current.

Reference this content, page, or tool as:

"Impedance Calculator" at https://MiniWebtool.com/impedance-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Mar 18, 2026

Developer API available: Run this tool from your app, automation, or agent with one JSON HTTP request. View API docs

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