LC Resonant Frequency Calculator

LC resonance

An inductor and capacitor together resonate at the frequency where their reactances are equal and cancel. At that point the LC pair stores energy, swapping it back and forth between the magnetic and electric fields.

f₀ = 1 / (2π·√(L·C))

Characteristic impedance: Z₀ = √(L / C)

Rearranged, L = 1 / ((2π·f₀)²·C) and C = 1 / ((2π·f₀)²·L), which is what this calculator solves when you leave L or C blank. Z₀ is the reactance of either component at resonance (Xₗ = X_c = Z₀).

Worked example: tuning to 7 MHz

To resonate at 7 MHz (the 40 m amateur band) with a 1 µH coil, leave capacitance blank and enter the inductance and frequency: the calculator solves C = 1 / ((2π·f)²·L) = 516.9 pF. The characteristic impedance √(L/C) comes out around 44 Ω.

Where it's used

LC resonance sets the tuning of radio filters, oscillators, and matching networks. See the reactance calculatorfor Xₗ and X_c at any frequency, or theRC time constant calculator for first-order RC cutoff.

Real components resonate less cleanly

This assumes a pure inductance and a pure capacitance, which sets the resonant frequency but says nothing about how sharp the peak is. Real inductors have winding resistance and a self-resonant frequency of their own, above which they behave capacitively; real capacitors have series inductance and their own self-resonance. Both effects limit the achievable Q and shift the measured frequency slightly below the calculated one. For anything near a component's self-resonant frequency, the datasheet curve matters more than this formula does.