LC Circuit Resonant Frequency Calculator
Calculate the resonant frequency of an LC circuit (inductor-capacitor tank circuit).
Essential for radio tuning, filter design, and oscillator circuits.
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:
| Inductance | Value |
|---|---|
| 1 H | 1 Henry |
| 1 mH | 0.001 H |
| 1 µH | 0.000001 H |
| 1 nH | 0.000000001 H |
| Capacitance | Value |
|---|---|
| 1 F | 1 Farad |
| 1 mF | 0.001 F |
| 1 µF | 0.000001 F |
| 1 nF | 0.000000001 F |
| 1 pF | 0.000000000001 F |
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:
| Application | Frequency | Typical Component Values |
|---|---|---|
| AM Radio Tuning | 535–1,605 kHz | L=250µH, C=25–350pF |
| FM Radio Tuning | 88–108 MHz | L=100nH, C=2–5pF |
| Wi-Fi 2.4 GHz | 2,400 MHz | L=1nH, C=4.4pF |
| Power factor correction | 50–60 Hz | L=10mH, C=100µF |
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 × 0.0000000031623) ≈ 1.592 MHz This is in the AM broadcast band, a classic tuning circuit value.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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