LC Filter Calculator

An LC filter is a frequency-selective circuit built from an inductor (L) and a capacitor (C). Unlike RC or RL filters, which use a resistor and roll off at 20 dB/decade, an LC filter exploits resonance: at the resonant frequency f₀ = 1/(2π√(LC)) the inductive and capacitive reactances cancel, so the circuit passes (or blocks) that frequency very sharply. A second-order LC stage rolls off at 40 dB/decade — roughly twice as steep as a first-order RC/RL stage.

f₀ = 1 / (2π√(LC)), with L in henries and C in farads. Worked example: L = 10 µH and C = 100 nF gives L·C = 1×10⁻¹², √(LC) = 1 µs, so f₀ = 1/(2π × 10⁻⁶) ≈ 159.155 kHz. The frequency is the same for series and parallel LC arrangements; what changes is the impedance behaviour (minimum in series, maximum in parallel) and the Q-factor formula.

Rearrange the resonance formula: L = 1/((2πf₀)²·C) and C = 1/((2πf₀)²·L). Pick one component first — usually the inductor, since fewer standard values exist — enter your target f₀, and this calculator solves for the other. Then use the E12/E24 picker below to snap both parts to real, buyable standard values and see the actual resulting f₀ and its error.

Q = f₀/BW measures how sharp the resonance is. For a series LC with series resistance R: Q = (1/R)·√(L/C). For a parallel LC tank with parallel (load) resistance R: Q = R·√(C/L). Example with 1 mH + 220 pF: R = 10 Ω in series gives Q ≈ 213 and BW ≈ 1.59 kHz; the same tank with a 10 kΩ parallel load gives Q ≈ 4.69 and BW ≈ 72.3 kHz. Less loss (smaller series R, larger parallel R) means higher Q and a narrower, sharper response.

For a maximally flat (Butterworth) second-order response, design for Q ≈ 0.7071. Q above 0.7071 produces peaking near cutoff — steeper, but with ripple and ringing (Chebyshev-like). Q below 0.7071 is overdamped and rolls off more gently. For band-pass or notch selectivity the rule is simpler: higher Q means a narrower pass/stop band, since BW = f₀/Q.

Real inductors and capacitors are sold in E12 (12 values per decade) or E24 (24 values per decade) series. Enter your ideal L or C and the picker returns the nearest standard value plus its percentage error. Even better, use “pick pair”: it searches every standard L/C combination and returns the pair whose actual resonant frequency lands closest to your target.

RC and RL are first-order filters (one reactive element plus a resistor): gentle 20 dB/decade roll-off, no resonance, no Q peaking. LC filters are second-order (two reactive elements): 40 dB/decade roll-off and a resonant peak whose sharpness is set by Q. LC needs no resistor, so losses are lower — good for power and RF — but inductors are bulkier, costlier, and have parasitics. For RC/RL cutoff math, use our cutoff-frequency calculator.

Same f₀ formula, different wiring. Low-pass: series L feeding a shunt C (passes below f₀). High-pass: series C feeding a shunt L (passes above f₀). Band-pass: series LC in the signal path — impedance is minimum at f₀, so only f₀ gets through. Notch/band-stop: a parallel LC tank in the signal path — impedance is maximum at f₀, so f₀ is blocked. The schematic above updates with your choice.

Three usual suspects. (1) Component tolerance: ±5–10% on L or C shifts f₀ by roughly half the combined tolerance. (2) Parasitics: every real inductor has winding capacitance (its self-resonant frequency) and DC resistance; every capacitor has ESR and ESL. (3) Loading: the source and load impedances become part of the circuit and change Q (and slightly f₀). Always measure with the actual source and load connected, and keep lead lengths short at RF.

Yes — both are classic uses. Loudspeaker crossovers are LC low-pass/high-pass networks (a 2nd-order Linkwitz-Riley crossover is just two cascaded Butterworth Q = 0.7071 sections). Switch-mode power supplies use an LC low-pass to smooth switching ripple. At RF, LC tanks tune receivers and match antennas — for example, 1 mH with 220 pF resonates at ≈ 339.319 kHz, in the range used by many tuned RF stages.