LC Resonant Frequency Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/6/2026
The resonant frequency of an LC circuit is calculated with Thomson's formula: f = 1 ÷ (2π√(L×C)). For an inductance of 1 mH and a capacitance of 1 µF, the resonant frequency is about 5,033 Hz.
Explanation
An LC circuit, made up of a coil (inductance L) and a capacitor (capacitance C), has a resonant frequency at which energy naturally oscillates between the coil's magnetic field and the capacitor's electric field, with minimal losses. This frequency, given by Thomson's formula, is central to the design of many electronic circuits: filters (to let only a given band of frequencies through), oscillators (to generate a periodic signal at a precise frequency), and tuning circuits (to select one radio frequency among several, as in a classic radio receiver). The relationship shows that increasing the inductance or the capacitance lowers the resonant frequency, and vice versa: a circuit intended for a high frequency generally uses low values of L and C, while a low-frequency circuit uses higher values. This model assumes an ideal LC circuit, with no internal resistance (and therefore no energy losses); a real circuit always has some parasitic resistance that progressively damps the oscillation.
Example: an inductance of 1 mH and a capacitance of 1 µF
Inputs
Inductance: 0.001 H (1 mH). Capacitance: 0.000001 F (1 µF).
Calculation
Frequency = 1 ÷ (2π × √(0.001 × 0.000001)) = 1 ÷ (2π × √(10⁻⁹)) ≈ 1 ÷ 0.0001987 ≈ 5,032.92 Hz.
Result
This LC circuit has a resonant frequency of about 5,033 Hz.
Frequently asked questions
How do I convert µH, nF or pF into base units (H and F)?
1 µH (microhenry) = 0.000001 H, 1 mH (millihenry) = 0.001 H. For capacitance, 1 mF = 0.001 F, 1 µF = 0.000001 F, 1 nF = 0.000000001 F, 1 pF = 0.000000000001 F. Component values (often given in µH and nF on schematics) need to be converted into these base units before entering them into this calculator.
Why doesn't this circuit oscillate indefinitely in reality?
Because a real LC circuit always has some parasitic resistance (in the wires, the coil, the connections) that progressively dissipates energy as heat, which damps the oscillation over time. An ideal LC circuit, with no resistance, would oscillate indefinitely at the resonant frequency calculated by this formula.
What is the resonant frequency of an LC circuit actually used for?
It is used to design filters that isolate a precise band of frequencies (essential in radio, telecommunications, and signal processing), oscillators that generate a stable periodic signal at a given frequency, and tuning circuits that let you select a station or channel among several available frequencies.