LC Resonant Frequency Calculator

Resonant frequency of an LC tank from the inductance and capacitance — or the capacitor you need for a frequency you already have — with the characteristic impedance, Q, bandwidth and the frequency band your component tolerances really allow.

Resonance in an LC tank

What component tolerance does to the resonant frequency

Resonance, impedance and Q

An inductor’s reactance rises with frequency, X_L = 2πfL; a capacitor’s falls, X_C = 1/(2πfC). Put the two together and there is exactly one frequency where they are equal, and because they are opposite in sign they cancel there. Setting 2πfL = 1/(2πfC) and solving gives f₀ = 1 ÷ (2π√(LC)) — 50.33 kHz for 100 µH and 100 nF. Nothing in that depends on whether the two are in series or in parallel, which is why one formula covers both; what changes is what happens at resonance.

Series or parallel. In a series tank the cancelling reactances leave only the resistance, so the impedance collapses to R and the current peaks — that is why a series tank is used as a trap to short an unwanted frequency to ground. In a parallel tank the two branch currents cancel instead, so the impedance rises to R and the voltage peaks — which is why a parallel tank is the tuned load of an oscillator or an RF amplifier. The chart shows the two reactances crossing and the impedance doing whichever of those two things your choice implies.

The characteristic impedance. At resonance each component’s reactance is √(L/C), 31.62 Ω in the example. It is worth knowing because it sets everything else: Q is √(L/C) divided by the series resistance, or the parallel resistance divided by √(L/C). Same L·C product, different ratio — 1 mH with 10 nF resonates at the same frequency as 100 µH with 100 nF but has ten times the characteristic impedance, so with the same coil resistance it would have ten times the Q. Here Q is 15.81 and the −3 dB bandwidth is f₀ ÷ Q = 3.183 kHz.

Tolerance is the number that matters in practice. Because f₀ goes as the inverse square root of the product LC, a tolerance of x% on one component moves the frequency by roughly x/2 %. Prove it with the capacitor alone: a −10% capacitor gives 1/√0.9 = 5.41% high and a +10% one gives 1/√1.1 = -4.65% low — about 5% either way, not 10%, and not symmetric. Add a ±5% coil and the band widens to -6.95% … 8.15%, which at 50.33 kHz is roughly 7.599 kHz of uncertainty — far wider than the tank’s own bandwidth. That is why tuned circuits are trimmed, not calculated: use a C0G/NP0 or film capacitor, keep the tolerance on the capacitor tighter than on the coil, and leave a trimmer if the frequency has to be right.

What the model leaves out. Ideal components. A real inductor has winding resistance (put it in the R box), core losses that rise with frequency, and a self-capacitance that gives it its own self-resonance — above which it behaves as a capacitor. A real capacitor has series inductance and ESR and does the same thing in reverse. Wiring adds a few picofarads that matter at VHF, and a nearby hand or board changes them. Treat the answer as the starting point.

For the reactance of a single component at any frequency, use the reactance calculator; for a filter with a defined −3 dB corner rather than a resonance, the RC and RLC filter calculator; and to convert the capacitor value you have into the units this page wants, the capacitance converter.

Frequently asked questions

Related calculators

References

1. Horowitz P, Hill W. The Art of Electronics, 3rd ed. Cambridge University Press, 2015. Chapter 1 (resistors in series and parallel, reactance, resonance, zener regulators) and Chapter 9 (voltage regulators).
2. IEC 60063:2015. Preferred number series for resistors and capacitors (the E6, E12, E24, E48, E96 and E192 series). International Electrotechnical Commission.