LC Tank Circuit Calculator - Frequency and Impedance

How It Works

An LC circuit (also called a tank circuit or tuned circuit) consists of an inductor (L) and a capacitor (C) connected together. At a specific frequency called the resonant frequency, the circuit oscillates: energy swings back and forth between the magnetic field of the inductor and the electric field of the capacitor.

The resonant frequency formula:

f = 1 / (2π × √(L × C))

Where:

• f = resonant frequency in Hertz (Hz)
• L = inductance in Henries (H)
• C = capacitance in Farads (F)
• π ≈ 3.14159

Angular (radian) frequency:

ω₀ = 1 / √(L × C) (in radians per second)

Characteristic impedance:

Z₀ = √(L / C) (in Ohms)

Unit conversions used in this calculator:

Series vs. Parallel LC circuits:

In a series LC circuit, impedance is minimum at resonance (close to zero); the circuit passes the resonant frequency easily. Used in bandpass filters and series resonant traps.

In a parallel LC circuit (tank circuit), impedance is maximum at resonance; the circuit blocks the resonant frequency from passing through. Used in oscillators, AM radio tuning circuits, and bandstop filters.

Real-world applications by frequency band:

Every row is a real pair rather than a plausible-looking one. Put the components into the calculator and the frequency that comes back lands inside the band beside them, both ends of it. Tables like this are worth checking, because the components and the band often drift apart once someone rounds one of them.

Quality Factor (Q): The Q factor describes how sharp the resonance peak is. High Q = narrow, sharp resonance (selective filters). Low Q = broad, gentle resonance (wideband). Q is determined by the resistance in the circuit. This calculator assumes an ideal lossless LC circuit (Q = ∞); in real circuits, inductor winding resistance and capacitor ESR reduce Q.

Worked example: L = 100 µH, C = 100 pF f = 1 / (2π × √(0.0001 × 0.0000000001)) = 1 / (2π × 0.0000001) ≈ 1.592 MHz This is in the AM broadcast band, a classic tuning circuit value.

If you know the frequency and need the part

This page works one way: give it L and C, get the frequency. To go backwards, to find the capacitor that pairs with a coil you already have or the coil for a capacitor you already have, use the LC Resonant Frequency Calculator, which solves for any of the three.