LC Resonant Frequency Calculator (Inductor-Capacitor Circuit)

Calculate the resonant frequency of an LC circuit made of an inductor (L) and a capacitor (C). Solve for frequency, inductance, or capacitance from the other two values, plus characteristic impedance.

Usage Tips

  • Switch "Value to solve for" to derive resonant frequency, inductance, or capacitance from the other two values — handy for radio tuning circuits or filter design.
  • Real circuits have parasitic elements such as coil winding resistance and a capacitor's equivalent series resistance (ESR), so the actual resonant frequency can differ slightly from the ideal formula's result.
  • Characteristic impedance (Z₀) is a useful reference when designing RF filters or antenna matching networks, to check how well it matches the load impedance.
  • Choose units from H/mH/µH/nH, F/mF/µF/nF/pF, and Hz/kHz/MHz/GHz so you can enter values exactly as printed on the component (e.g. 100µH, 220pF).

Frequently Asked Questions

They are widely used wherever a specific frequency needs to be selectively passed or rejected, such as radio tuning circuits, wireless communication filters, and oscillators. Early radio receivers used a variable capacitor to shift the LC circuit's resonant frequency in order to tune in the desired station.

The angular frequency of an LC circuit is ω = 1/√(LC); converting this to frequency via f = ω/(2π) gives f = 1/(2π√(LC)). It is called Thomson's formula after William Thomson (Lord Kelvin), who published it in 1853.

Increasing either L or C lowers the resonant frequency. Since the formula's denominator contains the square root of the product of L and C, the two are inversely related — a larger LC product means a lower frequency.

Z₀ = √(L/C) represents the ratio of voltage to current as an LC circuit exchanges energy. It is used as a reference value when checking how well a circuit matches the load impedance in filter design and RF matching.
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Side Note — LC Resonant Circuits and the History of Radio

The principle of the LC resonant circuit was established in the late 19th century and underpinned the practical development of radio broadcasting in the early 20th century. Early radio receivers had to pick out only the desired station's frequency from the faint radio waves picked up by the antenna, which they did by varying a capacitor's capacitance to shift the resonant frequency to match the target station — an operation known as "tuning."

William Thomson (later Lord Kelvin), whose name is attached to the formula, published a theory of electrical oscillation circuits in 1853, mathematically describing how an LC circuit resonates at a particular frequency. This formula is still used today not only in radio and television tuners, but across a wide range of fields including wireless transmit/receive circuits, noise-rejection filters, and metal detectors.

Modern tuning methods rely mainly on digital signal processing and PLLs (phase-locked loops), but the LC resonant circuit as an analog building block remains one of the first topics taught in electrical engineering curricula, still foundational to high-frequency circuit design today.