Quality Factor (Q) Calculator
This quality factor calculator works out the Q factor, resonant frequency and bandwidth of a series RLC circuit, so you can see how sharp and selective the tuned response will be. You enter three values: the resistance R in ohms, the inductance L in henries and the capacitance C in farads. From these the calculator returns the quality factor Q, the resonant frequency in hertz, and the bandwidth, which is the resonant frequency divided by Q. Q describes how much energy the circuit stores compared with how much it loses each cycle: a high Q gives a narrow, tall resonance peak and a selective, low-loss response, while a low Q gives a broad, heavily damped one. It depends on the ratio of reactance to resistance, so lowering the resistance or increasing the inductance-to-capacitance ratio raises Q. This is useful for anyone designing or checking tuned circuits, oscillators and filters, including electronics students, hobbyists and engineers who need a quick check of resonant behaviour before building or simulating a circuit. Enter your own R, L and C values, or try the worked example of 10 ohms, 1 millihenry and 0.1 microfarad, which gives a resonant frequency of about 15.9 kHz and a Q of 10. The calculator assumes ideal components and rounds results for display, so treat the figures as a close estimate rather than an exact lab measurement.
The formula
For a series RLC circuit, the resonant frequency is f0 = 1 / (2 pi times the square root of L C), and the quality factor is Q = (1/R) times the square root of (L/C). The bandwidth is f0 divided by Q.
Worked example
With R = 10 ohms, L = 1 mH and C = 0.1 microfarad, the resonant frequency is about 15.9 kHz and Q = (1/10) times the square root of (0.001/0.0000001) = 0.1 times 100 = 10. Enter 10, 0.001, 1e-7 to confirm.
Frequently asked questions
What is the quality factor?
A measure of how sharp a resonance is and how little energy is lost per cycle. Higher Q means a narrower, more selective response.
How is Q related to bandwidth?
Q equals the resonant frequency divided by the bandwidth, so a high Q gives a narrow bandwidth.
What gives a high Q?
A large reactance compared with the resistance: a high inductance-to-capacitance ratio and low resistance.
Who this calculator is for
This calculator is for electronics students, hobbyists and engineers.
What this calculator assumes
- You enter values in the units shown.
- Ideal components are assumed.
- Results are rounded for display.
Formula and sources
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