LC Filter Calculator
Enter any two of inductance (L), capacitance (C), or cutoff frequency to solve for the third. Choose your filter type and whether to solve for frequency, inductance, or capacitance. You also get the characteristic impedance, Q factor, and bandwidth for band-pass and band-stop designs. All values update instantly as you type.
What is an LC filter?
An LC filter is a passive electronic circuit built from an inductor (L) and a capacitor (C). Because an inductor resists changes in current and a capacitor resists changes in voltage, their combined reactances cancel at one specific frequency called the resonant or cutoff frequency. Below that frequency an inductor looks like a short circuit and a capacitor looks like an open circuit; above it, the roles reverse. Arranging these two components in different series-parallel topologies gives you the four basic filter types: a low-pass that passes signals below the cutoff, a high-pass that passes signals above it, a band-pass that passes a narrow window of frequencies around the resonance, and a band-stop (notch) that blocks that same narrow window.
The resonant frequency formula
All four filter types share one fundamental equation: fc = 1 / (2 * pi * sqrt(L * C)). Rearranging it gives you the other two useful forms: L = 1 / ((2 * pi * fc)^2 * C) when you know the target frequency and capacitance, and C = 1 / ((2 * pi * fc)^2 * L) when you know the target frequency and inductance. The angular frequency omega = 2 * pi * fc is often more convenient in circuit analysis because it removes the 2*pi factor from many equations. The characteristic impedance Z0 = sqrt(L / C) tells you the impedance the filter presents at resonance; matching your source and load to Z0 minimises signal reflections and maximises power transfer.
Q factor, bandwidth, and filter selectivity
The quality factor Q describes how selective (narrow) a filter is. For a band-pass or band-stop filter, Q = fc / BW, where BW is the -3 dB bandwidth. A Q of 1 gives a broad, gentle response; a Q of 100 gives a razor-sharp resonance. In a physical LC tank circuit, Q is also Q = (1 / R) * sqrt(L / C), so lower series resistance means higher Q. In practice, inductor winding resistance and core losses limit achievable Q. For a standard second-order low-pass or high-pass filter, Q = 0.707 (1 / sqrt(2)) gives the maximally flat (Butterworth) response with no passband ripple, while Q = 0.577 gives a Bessel response optimised for constant group delay. Higher Q produces a resonant peak before the rolloff, which can be useful in some equalisation applications.
How to read the Bode plot
The chart below the results shows the magnitude response of your filter across two decades below and two decades above the cutoff frequency. The vertical axis is gain in decibels (dB); 0 dB means the signal passes unchanged, -3 dB means it is attenuated to about 70.7 percent of its original amplitude (the standard "cutoff" criterion), and -40 dB means it is reduced to 1 percent. For a second-order LC filter the rolloff outside the passband is -40 dB per decade (compared with only -20 dB/decade for a first-order RC or RL filter), which is why LC filters are preferred when a steeper rolloff is needed without active components. You can see the Q factor influence: higher Q sharpens the transition but can introduce a resonant peak just inside the passband.
Common LC filter frequency bands and applications
| Frequency range | Application | Typical L range | Typical C range |
|---|---|---|---|
| 1 Hz - 20 Hz | Sub-audio, seismic sensing | 10 H - 1000 H | 1 uF - 100 uF |
| 20 Hz - 20 kHz | Audio crossovers, power supply filtering | 1 mH - 10 H | 1 nF - 1 uF |
| 20 kHz - 1 MHz | Switching power supplies (EMI filters) | 1 uH - 1 mH | 1 nF - 100 nF |
| 1 MHz - 30 MHz | AM radio, HF communications | 100 nH - 10 uH | 1 pF - 1 nF |
| 30 MHz - 300 MHz | FM radio, VHF TV, two-way radio | 10 nH - 1 uH | 1 pF - 100 pF |
| 300 MHz - 3 GHz | UHF, WiFi, Bluetooth, cellular | 1 nH - 100 nH | 0.1 pF - 10 pF |
| 3 GHz+ | Microwave, radar, satellite | Stripline / waveguide | Stripline / waveguide |
Typical resonant frequency ranges used in electronics design.
Frequently asked questions
What is the difference between an LC low-pass and a high-pass filter?
In a low-pass configuration the inductor is in series with the signal path and the capacitor is across (shunt to) the load. The inductor blocks high-frequency current while the capacitor shunts it to ground, so only low frequencies reach the output. A high-pass configuration swaps the positions: the capacitor goes in series (blocking DC and low frequencies) and the inductor is the shunt element. Both share the same resonant frequency formula fc = 1 / (2 * pi * sqrt(LC)), only the circuit topology changes.
How do I choose between inductance and capacitance values?
Start from the characteristic impedance Z0 = sqrt(L / C). For a 50-ohm RF system you want Z0 near 50 ohm, so if fc = 100 MHz and Z0 = 50 ohm, then L = Z0 / (2 * pi * fc) = 79.6 nH and C = 1 / (Z0 * 2 * pi * fc) = 31.8 pF. For audio crossovers, use larger inductors (in the mH range) and capacitors (in the uF range) to hit frequencies in the hundreds of hertz range. Practical inductor values top out around 10 mH for RF work and a few henries for power-line filters.
Why does my calculated inductance seem very large or very small?
The resonant frequency scales as 1 / sqrt(LC), so halving the frequency requires quadrupling the L*C product. At audio frequencies (1 kHz) with a 100 nF capacitor, you need L = 1 / ((2*pi*1000)^2 * 100e-9) = 253 mH, a physically large coil. At 100 MHz with the same capacitor, L collapses to 25 nH, a few turns of wire. If the result seems impractical, adjust the unit: try increasing C by a factor of 100 (to 10 uF) and L shrinks by the same factor.
What is the characteristic impedance and why does it matter?
Z0 = sqrt(L / C) is the impedance the filter presents at resonance, analogous to the characteristic impedance of a transmission line. If your source and load impedances match Z0, reflections are minimised and the filter response matches the ideal shape. Mismatches shift the apparent cutoff frequency and can distort the passband. In RF design (50 ohm or 75 ohm systems) you design L and C to achieve the target Z0; in audio work impedance matching is less critical.
How do I convert between Q factor and damping ratio?
The damping ratio zeta = 1 / (2 * Q). A critically damped system (zeta = 1, Q = 0.5) returns to rest without oscillating. Underdamped (Q greater than 0.5) means the step response rings. The Butterworth (maximally flat) second-order filter has Q = 0.707 (zeta = 0.707), and a Chebyshev or resonant-peaking filter has Q above 1. For band-pass and band-stop filters, Q = fc / BW directly gives the selectivity.