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LC Resonant Frequency Calculator

Find the resonant frequency of an LC circuit.

How it is calculated

An LC circuit resonates at f = 1 / (2π × √(L × C)). In this tool, L is entered in millihenries (mH) and C in microfarads (µF); the tool converts them to henries (× 10⁻³) and farads (× 10⁻⁶) before applying the formula, and returns the frequency in hertz (Hz) and kilohertz (kHz). Both values must be greater than zero. This is the ideal resonance of a lossless inductor and capacitor: real coils have resistance and stray capacitance, and real capacitors have tolerances, so the measured frequency will be slightly different. Quadrupling either L or C halves the frequency.

Worked example

Take an inductor of 10 mH and a capacitor of 0.1 µF. Convert: L = 0.01 H, C = 1 × 10⁻⁷ F. Product: L × C = 1 × 10⁻⁹. Its square root is 3.162 × 10⁻⁵. Then f = 1 / (2π × 3.162 × 10⁻⁵) = 5,032.92 Hz, which is 5.033 kHz.

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Common mistakes

  • Entering the inductance in henries or microhenries when the field is in millihenries, which shifts the answer by a factor of √1000 or more.
  • Entering capacitance in nanofarads or picofarads as if it were microfarads.
  • Forgetting the square root, so that doubling the capacitance appears to halve the frequency instead of dividing it by about 1.41.
  • Expecting a real circuit to match exactly, ignoring coil resistance, stray capacitance and component tolerance.
  • Confusing frequency f in hertz with angular frequency ω = 2πf in radians per second.

About this calculator

This calculator applies Thomson's formula, f = 1 / (2π√(LC)), to find the frequency at which an inductor-capacitor circuit naturally oscillates — the point where inductive and capacitive reactance cancel each other out.

It's used by electronics hobbyists tuning radio receiver circuits, RF engineers designing filters and impedance-matching networks for antennas, and students verifying lab measurements of a tank circuit's resonant frequency against the theoretical value.

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Comments (1)

  • Editorial team

    For a check, 10 mH with 1 µF resonates at about 1,591.55 Hz. If your circuit has several parts, combine them first: capacitors in parallel add up, as do inductors in series, and you enter the totals. The tool gives only the resonant frequency, so to find a capacitor for a target frequency you have to rearrange the formula yourself. What are you building, a filter, a radio tuner or something else?

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