LC Resonant Frequency Calculator determines the natural oscillation frequency of an inductor-capacitor circuit, along with impedance, wavelength, and the resulting tank energy.
Calculate LC Resonant Frequency and Required Inductance for Tuned Circuits
This calculator finds the natural oscillation frequency of an inductor-capacitor tank circuit, or works backward to size the inductor needed to hit a target frequency. RF and analog design engineers, ham radio operators, and electronics students use it to tune oscillators, filters, and antenna matching networks.
LC Circuit Inputs and Calculated Outputs
Enter inductance (H, mH, µH, or nH) and capacitance (F, µF, nF, or pF) to find resonant frequency, or enter capacitance and a target frequency to solve for the required inductance. Results include angular frequency, signal period, characteristic impedance, free-space wavelength, and peak tank energy at 1V.
LC Resonant Frequency and Impedance Formulas
The resonant frequency of an LC tank is given by Thomson’s resonance formula, named for Lord Kelvin (William Thomson):
$$f_0 = \frac{1}{2\pi\sqrt{LC}}$$
Solved for the required inductance at a target frequency — the same rearrangement used in the All About Circuits LC Resonance Calculator reference:
$$L = \frac{1}{C(2\pi f_0)^2}$$
Angular frequency and period follow directly:
$$\omega_0 = 2\pi f_0 = \frac{1}{\sqrt{LC}} \qquad T_0 = \frac{1}{f_0}$$
At resonance the inductive and capacitive reactances are equal in magnitude, so the phase angle is exactly 0° and the tank is purely resistive. The characteristic (surge) impedance of the tank is:
$$Z_0 = \sqrt{\frac{L}{C}}$$
Peak current at a given peak voltage follows Ohm’s law using $Z_0$ in place of resistance: $I_{peak} = V_{peak}/Z_0$. Free-space wavelength follows the standard wave relation $\lambda = c/f_0$, using $c = 2.998 \times 10^8$ m/s. Maximum stored tank energy at a given peak voltage:
$$E = \frac{1}{2}CV_{peak}^2$$
Most common input mistake: confusing angular frequency ($\omega$, rad/s) with frequency ($f$, Hz) — dividing by $2\pi$ is required to convert between them, and skipping that step gives a resonant frequency off by a factor of about 6.28. Example: with C = 10 pF and a target $f_0$ = 5.03 MHz, $L = 1/(10\times10^{-12} \times (2\pi \times 5.03\times10^6)^2) \approx 100.12\ \mu\text{H}$.
LC Tank Reactance vs. Frequency Diagram
LC Resonant Frequency Calculator FAQs
What Does It Mean for an LC Circuit to Be “At Resonance”?
Resonance is the single frequency at which inductive reactance ($X_L = \omega L$) and capacitive reactance ($X_C = 1/\omega C$) are equal in magnitude. Their effects cancel, leaving a purely resistive, zero-phase-angle circuit — that’s $f_0 = 1/(2\pi\sqrt{LC})$.
Why Is the Characteristic Impedance $Z_0 = \sqrt{L/C}$ Important?
$Z_0$ is the reactance magnitude of both L and C at resonance, and sets the peak circulating current for a given peak voltage ($I = V/Z_0$). It also determines the tank’s Q factor relative to any resistive losses present.
Why Might the Required Inductance Result Not Work in a Real Circuit?
The formula assumes an ideal, lossless inductor. Real inductors have a self-resonant frequency where parasitic winding capacitance makes them act capacitive instead of inductive — if the target frequency is close to that limit, the calculated L may not be physically realizable.
What Are the Most Common Mistakes When Calculating LC Resonance?
Confusing angular frequency ($\omega$, rad/s) with frequency ($f$, Hz) and forgetting the $2\pi$ conversion; mixing unit prefixes between L and C (mH with pF instead of matching base units); and assuming the 0° phase angle holds at frequencies other than exactly $f_0$.
Is Real Power Consumed by an Ideal LC Tank at Resonance?
No — an ideal LC tank with no resistance dissipates zero real power at any frequency, including resonance. Energy oscillates losslessly between the inductor’s magnetic field and the capacitor’s electric field; real circuits lose some to parasitic resistance.