Last updated: 2026-06-16

RLC Q Factor & Bandwidth

A series RLC circuit — a resistor, inductor and capacitor in a single loop — resonates at one particular frequency. The quality factor $Q$ describes how sharp that resonance is, and the bandwidth $\Delta f$ tells you how wide a band of frequencies the circuit responds to. This calculator takes the resistance $R$, inductance $L$ and capacitance $C$ and returns the resonant frequency $f_0$, the quality factor $Q$ and the bandwidth $\Delta f$.

Formula

At resonance the inductive reactance and capacitive reactance are equal and opposite, so they cancel and the circuit's impedance is purely resistive. The quality factor compares the energy stored in $L$ and $C$ to the energy dissipated in $R$ each cycle.

Worked example

A circuit has $R = 10\ \Omega$, $L = 10\ \text{mH}$ and $C = 1\ \mu\text{F}$.

The resonance is centred near 1.59 kHz, and the circuit responds strongly across a band about 159 Hz wide around it.

How Q changes with the components

For $L = 10\ \text{mH}$ and $C = 1\ \mu\text{F}$ (so $f_0 \approx 1591.55\ \text{Hz}$):

Lowering the resistance raises $Q$ and narrows the bandwidth; raising it does the opposite.

Why it matters

The quality factor sets the selectivity of tuned circuits. A high-Q circuit picks out a narrow band of frequencies and rejects everything else, which is exactly what a radio tuner or a narrowband filter needs. A low-Q circuit passes a broader range, which suits wideband coupling or damping. Because $Q$, $f_0$ and $\Delta f$ are tied together by $\Delta f = f_0 / Q$, knowing any two of them fixes the third, making $Q$ a compact way to specify the shape of a resonance.