What the LC Resonance Calculator does
This calculator finds the resonant frequency of an inductor and capacitor, or works backwards to the inductance or capacitance needed for a frequency you choose. It also gives the Q factor and bandwidth for both the series and the parallel case, the characteristic impedance sqrt(L/C), and a table of how each part's reactance changes around resonance.
Resonance is the frequency at which the inductor's reactance and the capacitor's reactance are equal and opposite, so they cancel. What happens then depends entirely on how they are connected: in series the impedance collapses to the loss resistance, and in parallel it rises to a peak.
How to use it
- Choose what to solve for: the frequency from a known L and C, or the capacitance or inductance needed for a target frequency.
- Enter the two values you know. Shorthand is understood: 100u, 4n7, 455k.
- Enter the resistance for the Q calculation - the coil's series loss resistance for a series circuit, or the damping resistance across a parallel tank.
- Read the Q and bandwidth for whichever arrangement you are building; the calculator gives both because the same parts behave oppositely in each.
- Use the reactance table to see how quickly the circuit loses its balance either side of resonance - that is what the bandwidth figure means in practice.
Reading the results
Q is a ratio, so it has no units: it is the reactance at resonance divided by the loss resistance in a series circuit, and the other way up in a parallel one. High Q means a narrow, sharp response; low Q means a broad, damped one.
Bandwidth is f0 / Q, measured between the -3 dB points. A 10 MHz tank with a Q of 100 has a 100 kHz bandwidth, which is why Q is the figure that decides whether a filter can separate two adjacent channels.
The characteristic impedance sqrt(L/C) is the reactance of each component at resonance. Two pairs that resonate at the same frequency can have very different impedances, and that is what decides how the tank couples to the circuit around it.
Worked example: 100 uH with 100 nF
f0 = 1 / (2 pi sqrt(L C)) = 1 / (2 pi sqrt(1e-4 x 1e-7)) = 1 / (2 pi x 3.1623e-6) = 50.33 kHz. At that frequency the inductor's reactance is 2 pi x 50,329 x 1e-4 = 31.62 ohms, and the capacitor's is exactly the same - which is sqrt(L/C) = sqrt(1000) = 31.62 ohms.
With 5 ohms of series loss resistance the series Q is 31.62 / 5 = 6.32, giving a bandwidth of 50,329 / 6.32 = 7.96 kHz - a broad response, useful for a supply filter and useless for tuning a radio.
For a 455 kHz IF transformer with a 1 mH coil the calculator works the other way: C = 1 / ((2 pi x 455,000)^2 x 1e-3) = 122.4 pF. In practice you would fit 100 pF and trim with the coil's slug, because stray capacitance in the circuit adds perhaps 10 pF of its own.
Formulas and scoring rules
- Resonant frequency
f0 = 1 / (2 pi sqrt(L x C))- Component for a frequency
C = 1 / ((2 pi f0)^2 L), L = 1 / ((2 pi f0)^2 C)- Characteristic impedance
Z0 = sqrt(L / C)Equal to XL and to XC at resonance.- Q, series
Q = sqrt(L/C) / R = (1/R) sqrt(L/C)R is the loss resistance in series with the loop.- Q, parallel
Q = R / sqrt(L/C) = R sqrt(C/L)R is the damping resistance across the tank.- Bandwidth
BW = f0 / QBetween the -3 dB points, centred on f0.- Reactances
XL = 2 pi f L, XC = 1 / (2 pi f C)Equal at f0; XL dominates above it and XC below.
Series and parallel are not variations, they are opposites
A series LC at resonance is a short circuit apart from its loss resistance. Put it across a signal path and it is a notch filter; put it in series with the path and it is a band-pass. The current through it at resonance is limited only by R, and the voltage across each reactive component is Q times the applied voltage - which is how a modest signal can produce hundreds of volts across the capacitor in a high-Q series circuit.
A parallel LC at resonance is nearly an open circuit. Energy circulates between the inductor and the capacitor, and the current in the loop is Q times the current supplied from outside. That circulating current is real: it heats the coil, and it is why a tank's components must be rated for far more than the external current suggests.
What limits Q in practice
Q is set by losses, and in most LC circuits the inductor is the lossy part. Its winding resistance rises with frequency because of skin and proximity effects, and the core adds hysteresis and eddy-current losses on top. Air-cored coils are lower-loss at high frequency; ferrite cores give more inductance for the size and more loss with it.
The capacitor contributes too, through its equivalent series resistance and dielectric losses - which is why a Class 2 ceramic is a poor choice in a tuned circuit and a C0G or film part is a good one. Everything else connected to the tank damps it as well: the input resistance of the next stage often sets the loaded Q, which can be far below the components' own.
Limitations: what the result does not prove
- This is the ideal lossless resonance formula with a single lumped resistance for Q. It does not model frequency-dependent coil losses, core losses or dielectric losses, all of which reduce Q as frequency rises.
- Stray capacitance is not included. Board, coil self-capacitance and the next stage's input capacitance all add to C and lower the frequency, often by several per cent.
- Component tolerances of 5-20% are normal, so a tuned circuit is trimmed, not calculated once. A calculated value is a starting point for a slug or a trimmer.
- Above an inductor's self-resonant frequency the model breaks down entirely: the part is a capacitor there, and no LC formula applies.
Privacy: where your data goes
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Standards and sources
- Texas Instruments - Op amps for everyone design reference - checked 19 Sep 2026
- Coilcraft - Inductor Q, self-resonance and loss mechanisms
- Wurth Elektronik - Trilogy of magnetic components
Frequently asked questions
How do I calculate LC resonant frequency?
f0 = 1 / (2 pi sqrt(L x C)), with L in henries and C in farads. 100 uH with 100 nF gives 50.33 kHz. The formula is the same for series and parallel circuits - what differs is what the circuit does at that frequency.
What is the Q factor of a resonant circuit?
The ratio of reactance to loss: in a series circuit Q = sqrt(L/C) / R, and in a parallel one Q = R x sqrt(C/L). It is dimensionless, and it decides how sharp the response is - bandwidth is simply f0 divided by Q.
What is the difference between series and parallel resonance?
At resonance a series LC has minimum impedance, equal to its loss resistance, so it passes current freely. A parallel LC has maximum impedance and blocks it. The same two components make a notch or a peak depending only on how they are wired.
How do I find the capacitor for a given resonant frequency?
C = 1 / ((2 pi f0)^2 L). For 455 kHz with a 1 mH coil that is 122 pF. Allow for stray capacitance - typically 5-15 pF on a board - and use a trimmer or an adjustable coil to bring it exactly on frequency.
Why does my tuned circuit resonate below the calculated frequency?
Almost always extra capacitance: the coil's own self-capacitance, board capacitance and the input capacitance of whatever the tank drives all add to C, and frequency falls with the square root of the total. Tolerance on both parts adds to the spread.
Can the voltage in an LC circuit be higher than the supply?
Yes, and this surprises people. In a series resonant circuit the voltage across the inductor and across the capacitor is Q times the applied voltage. With a Q of 50, ten volts in gives five hundred volts across each component - which the parts must be rated for.
What limits how high a Q I can get?
Losses, mostly in the inductor: winding resistance that rises with frequency, and core losses. The capacitor's ESR and dielectric matter too. And whatever loads the tank damps it, so the loaded Q in a circuit is often a fraction of the components' unloaded Q.
Does resistance change the resonant frequency?
Only slightly, and only at low Q. The classic formula ignores it, which is accurate to within a fraction of a per cent for any Q above about 10. Below that the peak shifts and broadens until, at very low Q, there is no meaningful peak at all.
Last reviewed by the A2Z.Tools team against the sources listed above.
