About the LC Resonant Frequency
Every inductor-capacitor pair has a natural frequency at which it "rings," and this calculator finds that resonant frequency directly from the inductance and capacitance values you provide. It's the same relationship used to tune radio receivers, design filters, and set the operating point of oscillator circuits.
How It Works
Enter the circuit's inductance in millihenries and its capacitance in microfarads. The calculator converts both to base SI units (henries and farads), then applies the standard LC resonance formula to return the resonant frequency in hertz.
Formula & Methodology
The calculator first converts the entered millihenry value to henries (multiplying by 1e-3) and the entered microfarad value to farads (multiplying by 1e-6). It multiplies those two SI values together, takes the square root, multiplies by 2 pi, and inverts the result to get frequency in hertz. Because L and C sit under a square root in the denominator, resonant frequency drops off relatively slowly as either component is increased; doubling either one lowers the resonant frequency by a factor of about 1.41 rather than by half.
Examples
Audio-range LC pair
A 10 mH inductor paired with a 100 µF capacitor gives a resonant frequency of about 159.15 Hz, from 1/(2 x pi x sqrt(0.01 x 0.0001)).
Smaller RF-range components
A much smaller 1 mH inductor with a 1 µF capacitor resonates at a far higher frequency of roughly 5,032.9 Hz.
Advantages
- Handles the millihenry and microfarad unit conversions automatically so component datasheet values can be entered directly.
- Gives an instant answer for a formula that's tedious to compute by hand due to the nested square root.
- Useful for iterating quickly on component choices when targeting a specific resonant frequency.
Common Mistakes
- Entering inductance or capacitance in the wrong unit scale (henries instead of millihenries, or farads instead of microfarads), which throws the frequency off by orders of magnitude.
- Assuming resonant frequency scales linearly with component value, when it actually scales with the inverse square root.
- Ignoring real-world parasitic resistance in the inductor or capacitor, which broadens and slightly shifts the resonance peak compared to the ideal calculated value.
Edge Cases to Watch For
- An inductance or capacitance of zero or less returns an error, since the square root and division would otherwise be undefined or produce a nonsensical result.
- Extremely small inductance or capacitance values push the resonant frequency into the megahertz or gigahertz range, which is mathematically valid but well beyond what many real LC components are rated for.
- The formula assumes an ideal, lossless LC pair; real inductors and capacitors have parasitic resistance that shifts and damps the actual resonance peak in a physical circuit.
Common Use Cases
- Radio and RF hobbyists selecting L and C values to tune a receiver or transmitter circuit to a target frequency.
- Electronics students checking LC resonance homework problems.
- Filter designers estimating the center frequency of a tank circuit before prototyping.