What is the frequency above which a low-pass filter's output power is less than half the input power?
Why A filter's cutoff frequency is defined as the point where output power drops to half the input power, which is -3 dB in decibels (10 log 0.5 = -3 dB). For a low-pass filter, signals below cutoff pass with little loss, and above cutoff attenuation increases steadily. That -3 dB half-power point is the standard reference used to specify any filter's passband edge.
Watch out Rolloff sounds plausible but it describes how fast attenuation increases beyond cutoff (dB per octave or decade), not a single frequency; a notch frequency is the deep rejection point of a band-stop filter, and the neper is just a unit of attenuation ratio based on natural logs.
Cutoff = half power = -3 dB. Rolloff is the slope, cutoff is the spot.