Resonant Frequency Calculator (LC and RLC)
Find the resonant frequency of an LC or RLC circuit, the frequency at which inductive and capacitive reactance cancel. Solve for frequency, or reverse the math to find the inductance or capacitance you need. Add a resistance to get the quality factor (Q), bandwidth, reactances, and series or parallel impedance, with every step shown.
Formula
Worked example
L = 1 mH and C = 220 pF: L·C = 1e-3 × 220e-12 = 2.2e-13. √(2.2e-13) = 4.69e-7. f = 1 / (2π × 4.69e-7) ≈ 339,318 Hz ≈ 339.32 kHz. With R = 10 Ω, Q = (1/10)·√(1e-3 / 220e-12) ≈ 213, so the bandwidth is about 339.32 kHz / 213 ≈ 1.59 kHz.
What the resonant frequency means
An LC circuit pairs an inductor (L) with a capacitor (C). Energy sloshes back and forth between the magnetic field of the coil and the electric field of the capacitor, like a swinging pendulum. The resonant frequency is the natural rate of that oscillation. At this exact frequency the inductive reactance, which grows with frequency, equals the capacitive reactance, which shrinks with frequency, so the two cancel. In a series circuit that leaves only the resistance, so current peaks; in a parallel (tank) circuit the impedance peaks instead. This is why tank circuits are the heart of radio tuners, oscillators, and band-pass filters.
Three solve modes: frequency, inductance, capacitance
Most calculators only go one way. This one reverses the math too. Leave the mode on "Resonant frequency" to enter L and C and read off f. Switch to "Inductance" or "Capacitance" to enter a target frequency plus the one component you already have, and the calculator rearranges f = 1 / (2π√LC) to give the coil or capacitor value you need to hit that frequency. This is exactly the step you take when designing a tuner or oscillator: you fix the band you want, choose a standard capacitor, and back out the inductance (or the other way round). Every component value is converted to base SI units first, then the answer is scaled back to a readable unit (nH to H, pF to F, Hz to GHz).
Adding resistance: Q factor, bandwidth and impedance
A real coil has resistance, and that resistance sets how sharp the resonance is. Toggle on "Add resistance" to enter R and pick series or parallel topology. The quality factor Q = (1/R)·√(L/C) measures sharpness: a high Q (small R, or a large L/C ratio) gives a tall, narrow peak that rejects everything except a thin band around the resonant frequency, while a low Q gives a broad, gentle peak. The bandwidth between the half-power (-3 dB) points is simply f / Q, so doubling Q halves the bandwidth. At resonance the reactances cancel, so a series RLC presents an impedance equal to just R, while a parallel tank presents a high impedance of about L/(R·C). Resistance barely moves the center frequency for typical high-Q designs, it mainly changes the width and height of the peak.
Quality factor (Q) and what it means
| Q range | Resonance | Typical use |
|---|---|---|
| Below 1 | Overdamped, no real peak | Damping, snubbers |
| 1 to 10 | Broad, gentle peak | Wideband filters, power circuits |
| 10 to 50 | Selective peak | Audio and RF band-pass filters |
| 50 to 200+ | Very sharp, narrow band | Radio tuners, oscillators, crystals |
Q sets how selective the circuit is. Bandwidth at the half-power points is f divided by Q.
Frequently asked questions
What is the formula for resonant frequency?
For an LC circuit the resonant frequency is f = 1 / (2π√(L·C)), where L is inductance in henries and C is capacitance in farads. The result is in hertz. The same value as an angular frequency is ω₀ = 2πf = 1/√(L·C).
How do I find the inductance or capacitance for a target frequency?
Rearrange the resonance formula. To find the coil for a chosen frequency and capacitor, use L = 1 / ((2πf)²·C). To find the capacitor for a chosen frequency and coil, use C = 1 / ((2πf)²·L). Switch the "Solve for" mode at the top of this calculator and it does the rearranging for you, returning the value in a readable unit.
What is the Q factor and how does it relate to bandwidth?
The quality factor Q = (1/R)·√(L/C) measures how sharp the resonance is. The -3 dB bandwidth around the resonant frequency is BW = f / Q, so a higher Q means a narrower, more selective band. Add a resistance in this calculator to see both Q and the bandwidth for your circuit.
Does resistance change the resonant frequency?
For an ideal series RLC circuit, resistance does not change the resonant frequency, it only affects how sharp and tall the resonance peak is (the Q factor and bandwidth). In real parallel tank circuits, large losses can shift the peak slightly, but for most practical, high-Q designs the LC formula is accurate.
How do I get a higher resonant frequency?
Use a smaller inductance or a smaller capacitance. Because both sit under a square root, you must cut the product L·C by a factor of four to double the frequency. To tune lower, increase L or C instead.