What is the frequency above which a low-pass filter’s output power is less than half the input power?

In filter design, the "cutoff frequency" (also known as the half-power point or -3 dB point) is the specific frequency where the output power drops to exactly 50% of the input power. For a low-pass filter, this is the frequency above which the filter begins to significantly attenuate the signal. Frequencies below the cutoff pass through with minimal loss, while frequencies above it are blocked. Distractors such as "rolloff" refer to the steepness of the attenuation slope after the cutoff, not the half-power frequency itself, while a "notch" refers to a completely different type of filter that attenuates a very narrow band of frequencies.