The resonant frequency of a circuit containing an inductor (L) and a capacitor (C) is the frequency at which energy oscillates freely between the magnetic field of the inductor and the electric field of the capacitor. At this frequency the inductive reactance and capacitive reactance are exactly equal and cancel, leaving a circuit that behaves purely resistively. The governing equation is f = 1 / (2π√(L×C)). This calculator solves for whichever of L, C or f you leave blank, and adds reactance, Q factor and bandwidth.
Reviewed: June 19, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: Wikipedia: LC circuit, RLC circuit, All About Circuits — resonance.
What is resonant frequency?
When an inductor and capacitor are connected together, the inductor opposes changes in current while the capacitor opposes changes in voltage. At one specific frequency these two effects are perfectly balanced and the circuit "rings" — energy sloshes back and forth between the two components with minimal external input. That frequency is the resonant frequency.
Where f is in hertz (Hz), L is inductance in henries (H), and C is capacitance in farads (F). Rearranged to size a component for a target frequency:
Reactance, Q factor and bandwidth
At resonance the inductive reactance equals the capacitive reactance:
The quality factor Q describes how sharp (selective) the resonance is. For a series RLC circuit:
A high-Q circuit (small R) resonates over a very narrow band of frequencies — ideal for a selective radio tuner. A low-Q circuit (large R) has a broad bandwidth — useful where you want to pass a range of frequencies.
Worked example 1 — tuning an LC tank circuit
Scenario: You have a 10 mH inductor and want a tank circuit that resonates at 5 kHz. What capacitor do you need?
(2π × 5000) = 31,416 rad/s; squared = 9.87×108; × 0.01 = 9.87×106. So C = 1 / 9.87×106 = 101 nF (use a standard 100 nF capacitor, giving 5.03 kHz). This matches the quick-answer example above.
Worked example 2 — Q factor of a radio tuner
Scenario: A series RLC tuner uses L = 100 µH, C = 100 pF and coil resistance R = 5 Ω. Find the resonant frequency, Q factor and bandwidth.
A Q of 200 gives an 8 kHz-wide passband centred on 1.59 MHz — sharp enough to separate AM radio stations spaced 9–10 kHz apart.
Where resonant frequency is used
- Radio & RF tuning — selecting one station or channel from many with an LC tank circuit.
- Oscillators — LC and crystal oscillators generate a stable frequency for clocks and transmitters.
- Filters — band-pass and band-stop (notch) filters built around a resonant LC pair.
- Switch-mode power supplies — resonant (LLC) converters switch at resonance for high efficiency.
- Antenna matching — tuning the feed network so the antenna presents resonance at the operating frequency.
- EMI / EMC — identifying and damping unwanted resonances that cause ringing and emissions.
Sources & further reading
- Wikipedia — LC circuit (energy exchange, resonance derivation).
- Wikipedia — RLC circuit (damping, Q factor, bandwidth).
- All About Circuits — tank-circuit resonance.
Frequently Asked Questions
For an LC or series/parallel RLC circuit, f = 1 / (2π√(L × C)), where L is in henries and C is in farads. At this frequency the inductive and capacitive reactances are equal and cancel.
Multiply L by C, take the square root, multiply by 2π, and take the reciprocal. For L = 10 mH and C = 100 nF: f = 1 / (2π√(0.01 × 1e−7)) ≈ 5.03 kHz.
The inductive reactance XL = 2πfL equals the capacitive reactance XC = 1/(2πfC), so they cancel. A series RLC circuit then has minimum impedance (just R) and maximum current; a parallel RLC circuit has maximum impedance and minimum line current.
Q measures how sharp the resonance is. For a series RLC circuit Q = (1/R)√(L/C) = XL/R. Higher Q means narrower bandwidth and a more selective filter. Bandwidth = resonant frequency ÷ Q.
Rearrange to C = 1 / ((2πf)² × L). Enter the target frequency and known inductance above and the calculator returns the required capacitance and the reactance at that frequency.
The ideal lossless resonant frequency f = 1/(2π√(LC)) is the same for both. Real parallel circuits with significant coil resistance resonate slightly lower, but the standard formula is used for most practical work.