RLC Impedance Calculator — Impedance, Phase Angle & Q Factor

RLC Impedance Calculator

This RLC impedance calculator will help you determine the impedance, the phase difference, and the Q-factor of an RLC circuit for a given sinusoidal signal frequency. You only need to know the resistance, the inductance, and the capacitance values connected in series or parallel.

With this calculator, you will quickly learn what an RLC circuit is, how to calculate the impedance in an RLC circuit, what the resonant frequency of an RLC circuit is, and what a phase angle is in an RLC circuit.

What is an RLC circuit?

An RLC circuit (or LCR circuit — we can change the order of the letters) consists of a resistance (R), an inductance (L), and a capacitance (C) connected in series or parallel. Today, it is hard to imagine the world of electronics without RLC circuits — they are commonly used in radio receivers, televisions, and attenuator circuits in analog applications.

• Series connection — all elements are located one behind another, and the same current flows through each of them.
• Parallel connection — the resistor, inductor, and capacitor are connected in parallel across a supply voltage. The applied voltage stays the same across all components while the current is divided.

When an AC signal is connected to an RLC circuit, the charging and discharging of the capacitor are repeated cyclically, leading to oscillation. Energy losses in the form of heat cause the oscillation to stop after some time.

Resonant frequency of an RLC circuit

The resonant frequency is the natural frequency of the RLC circuit. If we supply an electrical charge to the capacitor, the circuit starts to oscillate at precisely this frequency:

f₀ = 1 / (2π × √(L × C))

At the resonant frequency, the impedance of a series RLC circuit is at its minimum. When we connect the resistor, inductor, and capacitor in parallel, the impedance of the circuit becomes maximum.

How to calculate the impedance of an RLC circuit?

The impedance of an RLC circuit is denoted as Z and plays an analogous role to the resistance in Ohm's law. Impedance creates resistance to current flow because of the presence of the resistor R, the inductor L, and the capacitor C. The SI unit of impedance is the Ohm (Ω).

For a series RLC circuit:

Z = √(R² + (ωL − 1/ωC)²)

For a parallel RLC circuit:

Z = 1 / √( (1/R)² + (ωC − 1/ωL)² )

Where:

• R — resistance (Ω);
• L — inductance (H);
• C — capacitance (F); and
• ω — angular frequency, ω = 2πf (rad/s).

The inductive reactance is X_L = ωL and the capacitive reactance is X_C = 1/(ωC).

Phase angle in an RLC circuit

The phase angle (φ) describes the phase difference between the voltage and the current in the circuit. For a series RLC circuit:

φ = arctan((X_L − X_C) / R)

• φ > 0 — the circuit is inductive (X_L > X_C); the current lags the voltage.
• φ < 0 — the circuit is capacitive (X_C > X_L); the current leads the voltage.
• φ = 0 — the circuit is at resonance; impedance equals the resistance R.

Q factor of an RLC circuit

The quality factor (Q) describes how underdamped the circuit is — the ratio of energy stored to energy dissipated per cycle. A high Q means a sharp, selective resonance; a low Q means a broad response.

• Series RLC: Q = (1/R) × √(L/C)
• Parallel RLC: Q = R × √(C/L)

Unit systems

This calculator supports both Metric (SI) and American engineering unit conventions:

• Metric (SI): H, mH, µH, nH for inductance; F, mF, µF, nF, pF for capacitance; Ω, kΩ, MΩ for resistance; Hz, kHz, MHz, GHz for frequency.
• American: common RF engineering values — µH, nH for inductance; pF, nF for capacitance, with MHz/GHz signal frequencies.

FAQs

What happens to impedance at the resonant frequency?
In a series RLC circuit, inductive reactance equals capacitive reactance (X_L = X_C), so they cancel. The impedance drops to its minimum value, Z = R, and current is maximum. In a parallel RLC circuit, the impedance reaches its maximum at resonance.

Why is the phase angle important?
The phase angle tells you whether the circuit behaves more like an inductor or a capacitor at the chosen frequency, which matters for power factor, filtering, and impedance matching.

Can I use this calculator for both series and parallel circuits?
Yes. Select the circuit type (series or parallel) and the calculator applies the correct impedance and phase formulas automatically.