LC Resonant Frequency Calculator
Enter the inductance and capacitance. You get the resonant frequency, and the quality factor and bandwidth if you add the series resistance.
Worked examples
Audio filter
10 mH and 1 uF
1,591.5 Hz
1 / (2 x pi x sqrt(0.01 x 0.000001)).
With resistance
10 mH, 1 uF and 10 ohms in series
Q of 10
(1 / 10) x sqrt(0.01 / 0.000001).
About LC Resonant Frequency Calculator
An inductor and a capacitor together form a resonant circuit. At one frequency the reactance of the inductor equals the reactance of the capacitor, and energy swings back and forth between them. That frequency is one over 2 pi times the square root of the inductance times the capacitance. Radios use it to pick out a station, and filters use it to pass or block a band of frequencies.
How sharp the resonance is depends on the resistance. The quality factor Q compares the reactance at resonance with the series resistance, and the bandwidth is the resonant frequency divided by Q. A high Q gives a narrow, selective response. Enter a series resistance, such as the wire resistance of the coil, to see both. The page also gives the period and the reactance of each part at resonance.
How to use LC Resonant Frequency Calculator
- Enter the inductance and capacitance, choosing the units.
- Optionally enter the series resistance of the circuit.
- Read the resonant frequency and period.
- If you gave a resistance, read the quality factor and bandwidth.
Common uses
- Tuning a radio receiver or transmitter circuit
- Designing a notch or band pass filter
- Choosing a capacitor to resonate with a coil at a given frequency
- Understanding oscillators in physics and electronics courses
Frequently asked questions
What is the resonant frequency formula?
f0 = 1 / (2 x pi x the square root of L x C), with L in henries and C in farads. A 10 millihenry inductor and a 1 microfarad capacitor resonate at about 1,592 hertz.
What is the Q factor?
Q measures how sharp the resonance is. For a series circuit it is the reactance of the inductor at resonance divided by the resistance. A higher Q means a narrower bandwidth and less energy lost per cycle.
How do I tune the frequency?
Reduce the inductance or capacitance to raise it. Quadrupling either one halves the frequency, because of the square root.
Is the formula the same for series and parallel circuits?
Yes, the resonant frequency of the ideal circuit is the same. The behaviour at resonance differs: a series circuit has minimum impedance and a parallel one has maximum.