LC Filter Calculator
Design an LC filter from its components. Enter the inductance (H, mH, µH or nH) and the capacitance (F, µF, nF or pF) to get the cutoff or resonant frequency and the characteristic impedance Z0.
Example: with Inductance 100 · Inductance unit µH · Capacitance 100 · Capacitance unit nF → Cutoff / resonant frequency: 50.3292 kHz (50,329 Hz).
- Characteristic impedance Z031.6228 Ω
- Design noteBelow the cutoff a low-pass LC passes signals; above it, attenuation rises. Z0 = √(L/C) is the impedance the filter is matched to.
Computed by the calculator below using its default values. Change any input to see your own numbers.
An LC filter's corner frequency is f = 1/(2π√(LC)) — the same LC resonance. Its characteristic impedance is Z0 = √(L/C), the load it is designed to match.
Cutoff and impedance from L and C
An LC filter uses an inductor and a capacitor to pass some frequencies and block others. Its corner or cutoff frequency — where it starts to roll off — is set by the same LC resonance as a tuned circuit: f = 1/(2π√(LC)). A low-pass LC filter passes signals below that frequency and attenuates those above; a high-pass does the reverse. Because two reactive components are involved, the roll-off is steeper than a single RC stage.
The second number that matters is the characteristic impedance, Z0 = √(L/C). It is the source and load impedance the filter is designed to work between — commonly 50 or 75 ohms in radio work. Two LC pairs can share a cutoff frequency but present very different impedances: swapping a bigger inductor for a smaller capacitor raises Z0 while leaving the corner frequency put.
How it’s calculated
Cutoff/resonant frequency f = 1/(2π√(LC)) and characteristic impedance Z0 = √(L/C), with L in henries and C in farads. Prefixes convert as µH = 1e-6, mH = 1e-3, nH = 1e-9 H and µF = 1e-6, nF = 1e-9, pF = 1e-12 F.
An ideal lossless LC section. The 1/(2π√(LC)) point is the resonant corner; a real filter's response also depends on topology (L-, T- or pi-section) and the source and load impedances.
LC filter cutoff and impedance
| Inductance | Capacitance | Cutoff f | Z0 |
|---|---|---|---|
| 100 µH | 100 nF | 50.33 kHz | 31.6 Ω |
| 1 mH | 1 µF | 5.033 kHz | 31.6 Ω |
| 47 µH | 470 pF | 1.071 MHz | 316 Ω |
| 10 mH | 100 nF | 5.033 kHz | 316 Ω |
Computed with f = 1/(2π√(LC)) and Z0 = √(L/C); rounded.
Common mistakes
- Using L/C instead of L·C inside the frequency square root — the cutoff uses the product, Z0 uses the ratio.
- Forgetting prefix conversions for µH, nF and pF before computing.
- Assuming the cutoff alone defines the filter; the impedance Z0 and the topology matter for the real response.
- Expecting a first-order roll-off; an LC section falls off faster than a single RC stage.
Frequently asked questions
What is the LC filter cutoff frequency formula?
f = 1/(2π√(LC)), the same as LC resonance. With L in henries and C in farads, the cutoff comes out in hertz.
What is the characteristic impedance of an LC filter?
Z0 = √(L/C). It is the source and load impedance the filter is matched to, often 50 or 75 ohms in RF designs.
How is an LC filter different from an RC filter?
An LC filter uses two reactive parts, so it rolls off more steeply (about 40 dB per decade for a second-order section) than a single-stage RC filter's 20 dB per decade.
Can two different LC pairs have the same cutoff?
Yes. Any L and C with the same product share a cutoff frequency, but their ratio sets Z0, so they present different impedances.