Enter values and press Calculate.
Not the same as simple LC resonance: this constant-k filter cutoff fc=1/(π√LC) is exactly 2× the plain resonance formula f0=1/(2π√LC) used for tank/resonant circuits — see the note below for why.
An LC filter section uses one inductor and one capacitor (instead of a resistor and a capacitor) to build a second-order filter: a series inductor followed by a shunt capacitor (low-pass), or a series capacitor followed by a shunt inductor (high-pass). Because it has two reactive elements instead of one, its roll-off past cutoff is −40 dB per decade — twice as steep as the single-element RC filter's −20 dB/decade — while also (ideally) dissipating no power in the passband, since ideal inductors and capacitors don't resist current the way a resistor does.
You may have seen f0=1/(2π√(LC)) before — that is the resonant frequency of an LC tank circuit (see the RLC Resonant Frequency & Q calculator), used for band-pass/band-stop and oscillator design. This calculator answers a different question: given an L and a C wired as a matched filter section (the classic "constant-k image-parameter" filter design from filter theory), where does the passband end? That cutoff works out to fc=1/(π√(LC)) — exactly twice the plain resonance frequency for the same L and C, because a filter section's cutoff condition (image impedance becoming imaginary) is mathematically distinct from a tank circuit's resonance condition (reactances cancelling). Both are valid, well-known formulas — they simply answer two different circuit questions.
| Quantity | Formula |
|---|---|
| Cutoff frequency (constant-k filter section) | fc = 1/(π√(LC)) |
| Characteristic (nominal) impedance | Zo = √(L/C) |
| Design: inductor for target fc, Zo | L = Zo/(πfc) |
| Design: capacitor for target fc, Zo | C = 1/(πfcZo) |
| Roll-off rate | −40 dB/decade (−12 dB/octave), second-order |
The characteristic impedance Zo matters because this style of filter is designed to be driven from, and loaded by, a source/load resistance equal to Zo — exactly like an audio speaker crossover is designed around the speaker's nominal impedance (commonly 4 Ω or 8 Ω), or an RF filter is designed around a 50 Ω system.
For a constant-k (image-parameter) LC filter section, fc = 1/(π√(LC)). This is the frequency at which the filter's passband ends and its stopband begins, with a steep −40 dB/decade roll-off past that point.
They describe different circuit behaviours. f0=1/(2π√(LC)) is where a series or parallel LC tank circuit resonates (reactances cancel). fc=1/(π√(LC)) is where a constant-k filter section's image impedance becomes imaginary, marking the edge of its passband. For the same L and C, the filter cutoff is exactly twice the resonance frequency.
Zo=√(L/C) is the impedance the filter is designed to be driven from and loaded into for its response to match the ideal design equations — for example, a speaker crossover is designed around the speaker's nominal impedance (often 4 Ω or 8 Ω), and an RF filter is designed around 50 Ω.
An LC filter section is second-order (two reactive elements) with a −40 dB/decade roll-off, twice as steep as a first-order RC filter's −20 dB/decade, because it has two reactive elements instead of one.
Use L = Zo/(πfc) and C = 1/(πfcZo). Enter your target cutoff and system impedance in the "Design" tab above to get both values directly.
A low-pass section uses a series inductor followed by a shunt capacitor; a high-pass section swaps them — a series capacitor followed by a shunt inductor. Both use the same fc and Zo formulas for the same L and C values.
In the ideal case, yes — inductors and capacitors don't dissipate power the way resistors do, so an ideal LC filter passes in-band signal with no resistive loss. Real inductors have winding resistance and core losses that introduce some practical loss, especially at high current or high frequency.
Use the driver's nominal impedance rating (commonly 4 Ω, 6 Ω, or 8 Ω for most consumer speakers) as Zo — check the speaker's datasheet, since using the wrong impedance shifts both the actual cutoff frequency and the crossover's intended response shape.
Yes, this is standard practice in filter design (called a multi-section or "ladder" filter) and yields roll-offs of −80 dB/decade or steeper, at the cost of more components and more complex design equations than a single L-section.
That calculator finds a series or parallel RLC tank circuit's resonant frequency and Q/bandwidth — useful for oscillators, tuned amplifiers, and band-pass/notch applications. This calculator is for filter design: sizing a simple L-C section to hit a target low-pass or high-pass cutoff at a specified system impedance.
Yes — the ideal formulas assume the filter is driven and loaded exactly at its designed characteristic impedance Zo. A significant mismatch between the actual source/load impedance and Zo will shift the real-world response away from the ideal calculated curve.
It depends on frequency and current: air-core or powdered-iron toroids are common for RF and moderate-power filters, while ferrite cores suit higher-frequency, lower-current signal filtering; audio crossover inductors are often air-core or laminated-iron-core coils sized for the expected speaker current.
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