Resonant Frequency Calculator

The resonant frequency of a circuit with an inductor (L) and a capacitor (C) is the frequency at which their reactances are equal and cancel out. An LC circuit tuned to it picks out that one frequency, which is how radios tune to a station and how filters and oscillators are built.

f = 1 / (2 * π * √(L * C))

with f in hertz, L in henries and C in farads. Enter any two of the three, and the calculator finds the third:

• C = 1 / (L * (2 * π * f)²)
• L = 1 / (C * (2 * π * f)²)

Examples

1. A 10 mH coil with a 100 nF capacitor: 10 mH is 0.01 H, and 100 nF is 0.0000001 F.

   f = 1 / (2 * π * √(0.01 * 0.0000001)) = 5,033 Hz

2. The capacitor to tune a 10 µH coil to 1 MHz:

   C = 1 / (0.00001 * (2 * π * 1000000)²) = 2.533 nF

Each field has its own unit menu, so values can be entered in mH, µH, nF, pF, kHz or MHz directly.

Series and parallel resonance

The frequency is the same either way, but the circuit behaves oppositely:

• Series LC: the impedance drops to a minimum, ideally just the wires' resistance, so the most current flows at resonance.
• Parallel LC (a tank circuit): the impedance rises to a maximum, so the least current flows from the source.

Real components have tolerances, often 5–10% for capacitors, so the actual frequency can differ from the calculated one.

Frequently asked questions

How do I find the resonant frequency from the reactances?

If the inductor and capacitor have reactances XL and Xc at a frequency f, the resonant frequency is f0 = f * √(Xc / XL). For XL = 35 Ω and Xc = 23 Ω at 60 Hz: f0 = 60 * √(23 / 35) = 48.64 Hz.

What happens below and above resonance?

Below it, the capacitor's reactance is larger, and above it the inductor's. So a series circuit acts as a capacitor below resonance and as an inductor above it, and a parallel circuit does the opposite. See the Capacitive Reactance Calculator and the Inductive Reactance Calculator.