LC Resonant Frequency Calculator
Calculate the resonant frequency of an LC circuit using inductance (L) and capacitance (C). Useful for RF design, filters, oscillators, and tuning circuits.
What the LC resonant frequency calculator does
The LC resonant frequency calculator finds the frequency at which an inductor and a capacitor resonate. Enter the inductance in henries and the capacitance in farads, press Calculate, and the tool returns the resonant frequency in hertz together with the angular frequency in radians per second. The same figure applies whether the two parts are wired in series or in parallel.
The formula
f0 = 1 / (2π √(LC)), and ω0 = 2π f0 = 1 / √(LC)
Resonance occurs where the inductive reactance XL = 2πfL and the capacitive reactance XC = 1 / (2πfC) are equal. Solving XL = XC for f gives the formula. With the default 1 mH and 1 µF, f0 = 1 / (2π × √(10−9)) = 5,033 Hz.
Worked examples
| Application | L | C | f0 |
|---|---|---|---|
| Crossover for a loudspeaker | 2.2 mH | 4.7 µF | 1.57 kHz |
| Switching converter output filter | 10 µH | 100 µF | 5.03 kHz |
| Wireless charging coil (Qi) | 24 µH | 100 nF | 103 kHz |
| Crystal-radio tuner | 250 µH | 200 pF | 712 kHz |
| RFID tag | 2.5 µH | 74 pF | 11.7 MHz |
| 2.4 GHz matching network | 2.2 nH | 2 pF | 2.40 GHz |
Solving for L or C
Most design work runs the formula backwards: the frequency is fixed and one component must be chosen.
- C = 1 / (4π² f0² L)
- L = 1 / (4π² f0² C)
For a 13.56 MHz RFID reader with a 1 µH antenna coil, C = 1 / (4π² × (13.56 × 106)² × 10−6) = 138 pF. In practice a fixed 120 pF plus a 30 pF trimmer covers component tolerance and stray capacitance.
Series and parallel behaviour
| Series LC | Parallel LC (tank) | |
|---|---|---|
| Impedance at f0 | Minimum (only the loss resistance) | Maximum |
| Below f0 | Capacitive | Inductive |
| Above f0 | Inductive | Capacitive |
| Typical use | Band-pass in series, notch across a line | Tuned load, oscillator frequency setting |
The tank circuit resonance calculator goes into the parallel case in more detail.
Sharpness of the resonance
The quality factor Q sets how selective the circuit is: bandwidth = f0 / Q. For a series circuit Q = (1/R) × √(L/C), where R is the total series resistance. The 712 kHz crystal-radio tank with a coil resistance of 5 Ω has Q = (1/5) × √(250 × 10−6 / 200 × 10−12) = 224 and a bandwidth of about 3.2 kHz, narrow enough to separate AM stations 9 or 10 kHz apart. The characteristic impedance √(L/C) also equals the reactance of each component at resonance, here 1,118 Ω.
Energy and voltage at resonance
In a series circuit driven at f0, the voltage across the inductor and the capacitor is Q times the source voltage. A 1 V drive into the Q = 224 tuner puts 224 V across the capacitor. This voltage magnification is useful in induction heating and wireless power but can destroy capacitors with too low a voltage rating.
Common mistakes
- Unit errors. Both fields want base SI units: 47 µH is 4.7e-5 H, 22 pF is 2.2e-11 F.
- Ignoring stray capacitance. At radio frequencies a few picofarads from wiring can shift f0 by tens of percent.
- Ignoring the inductor’s self-resonant frequency. Above it the part is no longer an inductor.
- Using a lossy capacitor. Electrolytics have high ESR and are unusable in resonant circuits; use film or C0G ceramic types.
Related tools
The inductive reactance calculator and the inductance calculator help choose or wind the coil, and the inductance unit converter and frequency converter handle unit changes. The impedance converter covers the impedance side of the design.
External references
Frequently asked questions
Is the resonant frequency the same for series and parallel LC?
Yes, for ideal components. Only the impedance behaviour differs.
How do I enter 100 pF?
As 1e-10 or 0.0000000001. Scientific notation is easier and less error-prone.
What happens if I double both L and C?
The frequency halves, because the product LC quadruples and the square root doubles.
Why does my measured frequency come out lower than calculated?
Stray capacitance and lead inductance add to the nominal values, and inductors are often above their marked value at low frequencies. Trim C to correct.
Can I use this for an LC filter’s cutoff?
The resonant frequency is the corner of a second-order LC low-pass filter. Its damping and peaking depend on the load resistance, which the calculator does not model.