RLC Circuit Calculator — Q Factor and Bandwidth
Resonance, selectivity and damping for a series RLC circuit. Gives the resonant frequency, the Q factor, the −3 dB bandwidth and whether the circuit rings.
Share sends a link that reopens these numbers. Copy details pastes the full breakdown as a list.
The formula
f₀ = 1 ÷ (2π√(LC)) Q = (1 ÷ R) × √(L ÷ C) bandwidth = f₀ ÷ Q ζ = (R ÷ 2) × √(C ÷ L)
Q and the damping ratio are the same fact stated two ways — ζ = 1 ÷ 2Q. Q is the natural language of filters and tuned circuits, where you want a sharp peak; ζ is the natural language of control and transient response, where you want to know whether it will overshoot.
What to watch out for
Resistance is the whole story here. L and C fix where resonance happens; R decides what it looks like.
- Low R gives high Q — a sharp, narrow peak that rings for many cycles. Good for selecting one radio station, bad for a step response.
- High R gives low Q — a broad, flat response with little or no ringing.
- ζ = 1 is the boundary. Below it the circuit oscillates; above it, it does not. Exactly at it the circuit settles as fast as possible without overshoot, which is usually what you want from a mechanical system and almost never what you want from a filter.
These formulas are for the series circuit. A parallel RLC has the same resonant frequency but Q inverts — there, higher resistance means higher Q.
Frequently Asked Questions
What is the Q factor of an RLC circuit?
For a series circuit, Q = (1 ÷ R)√(L ÷ C). It measures how sharply the circuit selects its resonant frequency: a Q of 50 means the −3 dB bandwidth is one fiftieth of the centre frequency.
What is the difference between Q factor and damping ratio?
They are reciprocals of each other, scaled: ζ = 1 ÷ 2Q. High Q means low damping and lots of ringing. A Q of 0.5 is ζ of 1, which is critical damping — the dividing line between ringing and not.
How do I calculate bandwidth from Q?
Bandwidth is the resonant frequency divided by Q. A circuit resonating at 1.59 MHz with a Q of 100 has a −3 dB bandwidth of about 15.9 kHz, centred on resonance.