Filter Response

The corner frequency is where the output is −3 dB and 45° shifted — not where the filter stops working. Attenuation only really arrives a decade further out, which is why an anti-alias filter placed at the Nyquist frequency does almost nothing. The order sizing at the bottom answers the question that actually matters: how many poles do I need?

Single-pole results are exact for an unloaded filter; loading the output with anything comparable to R shifts the corner, so buffer it. The LC case assumes the Q you enter — real damping comes from winding resistance and the load, and a high-Q LC peaks at its corner rather than rolling off, amplifying exactly the ringing it was fitted to suppress. Order sizing assumes ideal asymptotic roll-off; real filters need a margin. See also RC / RL Time Constant and Sampling & Aliasing.