LC Resonance Calculator
Where the reactances cancel, and how sharply.
Where the reactances cancel, and how sharply. Resonant frequency of an LC circuit, with the characteristic impedance, Q factor and bandwidth.
Resonant frequency
5.033 kHz
Q = 3.16 · bandwidth 1.592 kHz
At resonance the inductive and capacitive reactances are equal and opposite, so they cancel and the circuit looks purely resistive. The frequency where that happens is 1/(2π√LC), and neither component's value matters on its own — only the product. The Q factor says how sharp the resonance is. High Q means a narrow, selective response, which is what a radio tuner wants; low Q means a broad one, which is what a crossover in a loudspeaker wants. Bandwidth is simply the resonant frequency divided by Q. Because the frequency depends on the square root of the product, quadrupling either component halves the frequency. That square root is why tuning circuits need such wide-ranging variable capacitors to cover a modest frequency band.
How the LC Resonance Calculator works
Resonant frequency of an LC circuit, with the characteristic impedance, Q factor and bandwidth. At resonance the two reactances cancel exactly and the circuit looks purely resistive.
Also known as: resonant frequency of lc circuit · tank circuit frequency · what capacitor for this frequency · q factor of a resonant circuit
Where to go next
The LC Resonance question rarely arrives on its own. These are the ones that usually come with it:
- Impedance Calculator — Magnitude and phase — they do not simply add.
- Inductor Calculator — Reactance, energy and the L/R time constant.
- Resistor Series & Parallel Calculator — Parallel is always below the smallest. That is the check.
- Speed Distance Time Calculator — Any one of the three from the other two, in four units.
Frequently asked questions
What is the resonant frequency formula?
One over 2π times the square root of LC. Only the product of the two matters — halving the inductance and doubling the capacitance leaves the frequency unchanged.
What happens at resonance?
Inductive and capacitive reactance are equal and opposite, so they cancel. A series circuit then presents only its resistance and current peaks; a parallel one presents maximum impedance and current is minimum.
What does the Q factor mean?
How sharp the resonance is. High Q gives a narrow, selective response — what a radio tuner needs — and low Q gives a broad one, which is what a loudspeaker crossover needs. Bandwidth is the resonant frequency divided by Q.
Why does quadrupling the capacitance halve the frequency?
Because the frequency depends on the square root of the product. That square root is why tuning circuits need such wide-ranging variable capacitors to cover a modest band of frequencies.
What is a tank circuit?
A parallel LC circuit, so called because energy sloshes back and forth between the magnetic field of the inductor and the electric field of the capacitor. Resistance is what eventually drains it.
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Related calculators
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Open