LC Resonant Frequency Calculator Formula

Understand the math behind the lc resonant frequency calculator. Each variable explained with a worked example.

Formulas Used

Resonant Frequency

resonant_freq = 1 / (2 * pi * sqrt(inductance * 1e-3 * capacitance * 1e-6))

Angular Frequency

angular_freq = 1 / sqrt(inductance * 1e-3 * capacitance * 1e-6)

Variables

VariableDescriptionDefault
inductanceInductance(mH)10
capacitanceCapacitance(μF)100

How It Works

LC Resonant Frequency

An LC circuit oscillates at a natural frequency determined by the inductance and capacitance.

Formula

f = 1 / (2*pi*sqrt(L*C))

At resonance, the inductive and capacitive reactances are equal and cancel, leaving only resistance to limit current.

Worked Example

An LC circuit with L = 10 mH and C = 100 μF.

inductance = 10capacitance = 100
  1. 01f = 1 / (2*pi*sqrt(L*C))
  2. 02f = 1 / (2*pi*sqrt(10e-3 * 100e-6))
  3. 03f = 1 / (2*pi*sqrt(1e-6))
  4. 04f = 1 / (2*pi*0.001)
  5. 05f = 1 / 0.006283 = 159.15 Hz

Frequently Asked Questions

What is resonance in an LC circuit?

Resonance occurs when the inductor and capacitor exchange energy back and forth at a natural frequency, like a pendulum swinging.

Where are LC circuits used?

In radio tuners (selecting a station frequency), oscillators, filters, and impedance matching networks.

What limits the oscillation in a real LC circuit?

Resistance in the wire and components gradually converts the oscillating energy to heat, causing the oscillation to decay (damped oscillation).

Ready to run the numbers?

Open LC Resonant Frequency Calculator