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Ideal LC Natural Resonance Frequency

Calculate the natural frequency of an ideal inductor-capacitor model and solve for either component.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

An ideal 1 H inductor and 1 μF capacitor have natural frequency about 159.155 Hz, or 0.159155 kHz. A practical filter’s cutoff also depends on its circuit and loading.

Natural frequency f₀ = 1 / (2π√(LC))

Worked example

Enter these known values and leave the other values blank.

Inductance
1 H
Capacitance
1 μF
Ideal natural frequency
0.15915 kHz

Assumptions and limitations

  • Inductance, capacitance and frequency must be positive. The formula uses henries and farads internally and returns ordinary frequency in cycles per second.
  • This is an ideal LC natural-frequency calculation. It ignores resistance, component losses, parasitics, nonlinearities and tolerance.
  • It is not a universal −3 dB cutoff formula for every LC filter. Transfer response and cutoff depend on topology, source and load impedances and damping.
  • The RPM frequency option represents cycles per minute. It does not imply that the circuit contains a rotating component.

Common questions

Is natural frequency always the filter cutoff?

No. Natural frequency follows from L and C, while a specified gain cutoff depends on the complete loaded circuit response.

What happens if capacitance is multiplied by four?

With inductance fixed, natural frequency is halved because frequency varies inversely with the square root of capacitance.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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