About the LC Resonant Frequency Calculator
This LC resonant frequency calculator works out the frequency at which an inductor and a capacitor resonate — the point where their reactances are equal and cancel. Enter L in microhenries and C in picofarads to get the resonant frequency, or switch modes to solve for the capacitance or inductance needed to hit a target frequency, which is how radio tuning circuits, crystal-less oscillators and RF filters are designed.
It is useful for radio amateurs building antenna tuners, traps and VFOs, students studying tank circuits, and engineers designing Colpitts/Hartley oscillators, wireless power coils, induction heaters and EMI filters. The tool also reports the characteristic impedance √(L/C), the reactance at resonance and — if you enter the series resistance of the coil — the quality factor Q and −3 dB bandwidth.
Values assume ideal components. Real inductors have winding resistance and self-capacitance, capacitors have tolerance, and stray PCB capacitance of a few picofarads can noticeably lower the resonant frequency at VHF, so leave tuning range in your design.
With the default inputs, the resonant frequency is 5,032,921.21 Hz. Change any value above to recalculate instantly.
How to use the lc resonant frequency calculator
- 1Choose what to solve for: frequency, capacitance or inductance.
- 2Enter the known values — L in µH, C in pF, target frequency in kHz.
- 3Optionally enter the coil’s series resistance to get Q and bandwidth.
- 4Read the resonant frequency and the component values.
- 5Use the reactance chart to see how far off-resonance your signal is.
Formula and method
An inductor’s reactance XL = 2πfL rises with frequency and a capacitor’s XC = 1/(2πfC) falls. Setting them equal and solving for f gives the resonant frequency f₀ = 1/(2π√(LC)). Rearranging the same equation gives the capacitance or inductance needed to resonate at a chosen frequency.
At resonance each reactance equals the characteristic impedance √(L/C). For a series RLC circuit the quality factor is Q = √(L/C)/R, the ratio of reactance to resistance, and the −3 dB bandwidth is f₀/Q — a higher Q means a sharper, more selective tuned circuit. Ideal components are assumed.
- f₀
- Resonant frequency (Hz)
- L
- Inductance (H; entered in µH)
- C
- Capacitance (F; entered in pF)
- R
- Series resistance of the circuit (Ω)
- Q
- Quality factor
- BW
- −3 dB bandwidth (Hz)
Worked examples
10 µH coil with a 100 pF capacitor
f₀ = 1 ÷ (2π√(10 µH × 100 pF)) ≈ 5.033 MHz. Both reactances equal √(10 µH ÷ 100 pF) ≈ 316 Ω there. With 5 Ω of coil resistance, Q ≈ 63 and the bandwidth is about 79.6 kHz.
Capacitor to tune a 2 µH coil to 7.1 MHz (40 m band)
C = 1 ÷ ((2π × 7.1 MHz)² × 2 µH) ≈ 251.2 pF. A 250 pF variable capacitor plus a small trimmer would cover it, allowing for a few pF of stray capacitance.
Inductor for a 455 kHz IF transformer with 1,000 pF
L = 1 ÷ ((2π × 455 kHz)² × 1 nF) ≈ 122.35 µH, the classic AM radio intermediate frequency. At resonance each reactance is about 350 Ω.
Frequently asked questions
What is the formula for LC resonant frequency?+
f = 1 / (2π√(LC)) with L in henries and C in farads. For example 10 µH and 100 pF give 1 / (2π√(10⁻⁵ × 10⁻¹⁰)) ≈ 5.03 MHz.
What happens at resonance in an LC circuit?+
The inductive and capacitive reactances become equal. In a series circuit they cancel, so impedance drops to the resistance alone and current peaks; in a parallel tank the impedance becomes very high and energy swings back and forth between L and C.
How does changing L or C affect the frequency?+
Frequency is inversely proportional to the square root of L × C. Quadrupling the capacitance or the inductance halves the resonant frequency, while doubling either lowers it by about 29%.
What is the Q factor of a tank circuit?+
Q is the ratio of reactance to resistance at resonance, Q = √(L/C)/R for a series circuit. A high Q (often 50–300 for good RF coils) gives a narrow bandwidth, f₀/Q, and a sharper response.
Why does my measured frequency differ from the calculation?+
Stray capacitance from wiring and the PCB, the coil’s own self-capacitance and component tolerances (often ±5–20%) all shift resonance. At RF, a few extra picofarads can lower the frequency noticeably.