Lc Filter Calculator - Cutoff, L, and C Solver

An LC filter calculator is a tool that solves the cutoff frequency of a second-order inductor–capacitor filter, or sizes the inductor and capacitor that hit a target cutoff, for low-pass, high-pass, and band-pass filter topologies built from a single L and a single C.

• • Audio and speaker crossover design: Pick L and C so a tweeter crossover attenuates frequencies below the audio band with a 40 dB/decade slope.
• • RF and ham radio tank circuits: Tune a resonant LC tank to a band frequency, or check whether a salvaged inductor pairs with the trimmer capacitor on a vintage receiver.
• • Switch-mode power supply input filters: Verify that the LC input filter on a buck or boost converter falls below the switching frequency with enough margin to attenuate ripple.
• • EMI suppression and DC bias removal: Pick an LC corner that blocks conducted EMI on a power line while letting the DC supply reach the load.

An LC filter is the simplest second-order passive filter: an inductor and a capacitor connected so that one is in series with the signal path and the other is in parallel with the load. Because both reactances depend on frequency, the LC network rejects frequencies far from its cutoff twice as fast as a first-order RC filter.

The cutoff is set by fc = 1/(2π√LC), the same identity as the resonant frequency of an L and C alone. The lc filter calculator on this page does all three rearrangements so you do not have to solve for L or C by hand.

When you need to decode a printed capacitor or check that two in series still meet the LC filter design, the Capacitor Calculator handles the same units and codes.

The calculator converts every input to base SI units, applies the resonant frequency equation fc = 1/(2π√LC) for the chosen solver mode, and reports the cutoff in hertz, the angular frequency in rad/s, and the characteristic reactance √(L/C) in ohms.

• L: Inductance in henries. 1 mH = 0.001 H, 1 µH = 1e-6 H.
• C: Capacitance in farads. 1 nF = 1e-9 F, 1 µF = 1e-6 F.
• fc: Cutoff frequency in hertz. The -3 dB point of the filter response.
• ω0: Angular resonant frequency in rad/s. Equal to 2π · fc.

For the cutoff mode the tool multiplies L and C in base SI units, takes the square root, multiplies by 2π, and takes the reciprocal. The angular frequency ω0 = 1/√(L·C) rad/s and the characteristic reactance XL0 = XC0 = √(L/C) Ω fall out as side calculations and confirm that the inductor and capacitor see equal and opposite reactance at fc.

For the inductance and capacitance modes the same identity is rearranged. With fc and C fixed, L = 1/((2π·fc)² · C); with fc and L fixed, C = 1/((2π·fc)² · L). Both forms trace to the same derivation from Kirchhoff's voltage law applied to the series or parallel LC branch.

The fc = 1/(2π√LC) identity also fixes the -3 dB cutoff and the roll-off slope. At fc the gain has dropped to 3 dB below the passband level, and because two reactive elements contribute to the response, the LC network attenuates high frequencies at 40 dB per decade, twice as steep as a first-order RC filter.

According to Wikipedia, LC circuit, the resonant frequency of an LC circuit is f0 = 1/(2π√LC) and this identity is the standard cutoff used for second-order LC low-pass and high-pass filters.

According to Wikipedia, Low-pass filter, at the cutoff frequency of any low-pass filter the gain has dropped to -3 dB and a second-order filter attenuates at 40 dB per decade.

For the capacitive half of the reactance budget at any single frequency, the Capacitive Reactance returns XC directly without re-doing the LC product.

Four ideas explain why an LC filter behaves the way it does and why it cuts off more steeply than a simple RC filter.

These concepts connect directly to the rest of the page. The cutoff frequency in the next section is just the frequency at which the first two reactances cancel, and the limitations later in this article come from real components only approximating the ideal behavior described here.

Whenever you need the rad/s value to match a Laplace-domain transfer function, the Angular Frequency Calculator converts between fc, period, and ω0 directly.

Pick what you know about the filter, enter the values in base SI units or the prefixes the form accepts, and read the cutoff or the missing L or C straight off the result panel.

1. 1 Choose what to solve for: Use the dropdown to pick cutoff frequency, inductance, or capacitance.
2. 2 Enter inductance and capacitance: Type L in henries and C in farads. Common substitutes are 1e-3 for 1 mH, 1e-6 for 1 µH, 1e-9 for 1 nF, and 1e-12 for 1 pF.
3. 3 Enter the target cutoff when solving for L or C: Provide fc in hertz. Use 1e3 for 1 kHz, 1e6 for 1 MHz, and 1e9 for 1 GHz.
4. 4 Read the cutoff or the missing component: The result panel shows the cutoff, angular frequency, and characteristic reactance. For solveL and solveC modes the missing L or C is shown directly.
5. 5 Pick a real part within tolerance: Match the calculated value to the nearest E12 or E24 standard value, then re-enter that real value to confirm the as-built cutoff.

Suppose you want a 10.7 MHz IF tank with a 1 µH inductor. Set Solve for to Capacitance, enter fc = 1.07e7 and L = 1e-6, and the result panel reports the required C as about 2.21 × 10⁻¹⁰ F (≈ 221 pF), which is a common trimmer range for that frequency.

When the required C does not exist as a single part, the Capacitors in Series Calculator helps you combine two or three standard capacitors to land on the target value.

Five concrete ways this tool saves time when you design or troubleshoot an LC filter.

• • Three solvers in one place: Cutoff, missing inductance, and missing capacitance share the same form and units, so you can iterate without switching calculators.
• • Cuts design iteration time: Each solver returns the result instantly, so you can sweep fc or L and watch the rest of the filter re-tune.
• • Matches classroom and lab practice: The fc = 1/(2π√LC) identity appears in electronics textbooks and exam problems, so the result lines up with lecture notes and lab worksheets.
• • Exposes the angular frequency: Side results include ω0 in rad/s and the characteristic reactance, the values used in Bode plots, Laplace-domain transfer functions, and SPICE.
• • Reduces errors from unit drift: Every input is interpreted in base SI, so you do not have to remember whether 1 nF means 1e-9 F or 1e-12 F.

Once the LC filter values are settled, the Impedance Matching Calculator helps you design the L-section that drives a real load without reflecting power back to the source.

Four practical factors shift the cutoff you measure on the bench away from the value the formula predicts.

• • This calculator models an ideal lossless LC network. It does not predict insertion loss, group delay, or the exact Bode magnitude that a SPICE simulation produces, and very low-Q filters can show a rounded cutoff on the bench.
• • Band-pass results assume the low-pass and high-pass stages are isolated. In a real cascaded design the second stage loads the first, so the simulated passband is a starting point and the measured passband is the source of truth.

These factors do not make the formula wrong; they make the boundary conditions on the formula stricter than they look in a first-pass design. Most LC filter problems on the bench trace back to one of these four items rather than to the math itself.

According to Omni Calculator, LC Filter, an LC low-pass places the inductor in series with the load and the capacitor in parallel, while a 1 kHz cutoff with a 47 nF capacitor requires an inductor near 0.539 H.