The -3dB Point: Where "Cutoff" Actually Means Half Power
An RC filter's cutoff frequency isn't the point where the signal disappears — it's the frequency at which output power has dropped to half its original value, corresponding to about 70.7% of the original voltage amplitude. This "-3dB point" convention (since 10log10(0.5) is approximately -3dB) is a specific, standard definition, not an arbitrary rule of thumb, and it's exactly what the formula f = 1/(2piRC) calculates.
Below the cutoff frequency, a low-pass RC filter passes the signal largely unchanged; above it, output amplitude falls off at a fixed rate (roughly 20dB per decade for this simple single-pole filter) — a gradual roll-off, not a sharp wall, which is an important distinction from how "filter" sometimes gets imagined. A high-pass configuration (swapping resistor and capacitor positions) produces the mirror-image behavior, passing high frequencies and attenuating low ones.
This simple two-component filter is everywhere in real circuits — as a basic noise filter, an anti-aliasing stage before an ADC, or a DC-blocking coupling stage — precisely because it's cheap, requires no active components, and its cutoff behavior is fully predictable from just two values.