Resonant Frequency Calculator: f = 1 / (2 pi sqrt(LC))

The frequency at which an inductor and a capacitor resonate.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • f_0 = \frac{1}{2\pi\sqrt{LC}}
  • L = \frac{1}{4\pi^2f_0^2C}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the frequency of the lc circuit: frequency of the lc circuit = (1/(2 pi)) / (inductance^0.5 x capacitance^0.5)
  2. Put the values in (every value in its SI unit): frequency of the lc circuit = (1/(2 pi)) / (0.01^0.5 x 1.0e-6^0.5)
  3. The answer: frequency of the lc circuit: 1591.55 Hz
  4. The same answer in other units: 1.59155 kHz; 0.00159155 MHz

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Inductance; Frequency of the LC circuit (leave it as it is if this is what you are finding) 1591.549 Hz; Capacitance (leave it as it is if this is what you are finding) 1.0E-6 F.

  1. The formula, arranged to find the inductance: inductance = ((1/(2 pi)) / (frequency of the lc circuit x capacitance^0.5))^2
  2. Put the values in (every value in its SI unit): inductance = ((1/(2 pi)) / (1591.55 x 1.0e-6^0.5))^2
  3. The answer: inductance: 0.01 H
  4. The same answer in other units: 10 mH; 10000 uH

Common questions

What is the resonant frequency of an LC circuit?

One over two pi times the square root of the inductance times the capacitance. 10 mH with 1 uF resonates at about 1592 Hz.

What happens at resonance?

The inductive and capacitive reactances are equal and cancel. In a series circuit the current is largest.

How do I tune a circuit to a lower frequency?

Increase the inductance or the capacitance.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any electrical text (resonance in LC circuits).

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