RC Cutoff Frequency

The corner frequency of an RC filter is where the capacitor's reactance $1/2\pi f C$ has fallen to equal the resistance. There the output is 0.707 of the input — half the power, hence "−3 dB" — and the phase has shifted 45°. A 1 kΩ resistor with 0.1 µF gives $1/(2\pi \times 10^{-4}) \approx 1592$ Hz. Above that corner a low-pass output rolls off at 6 dB per octave and keeps rolling forever.

The name "cutoff" is the misleading part: nothing is cut off. At the corner you still have 71% of the signal, and one octave above you still have about half. A single RC section is a gentle slope, not a wall, which is why anti-aliasing filters ahead of an ADC use multiple poles and why putting a filter corner right at the edge of the wanted band always disappoints. Set the corner well clear of what you want to keep.

The other trap is loading. This formula assumes nothing draws current from the output; a following stage with an impedance comparable to R shifts the corner and shrinks the passband gain. And note the same components in the time domain give the time constant $\tau = RC$, so $f_c = 1/2\pi\tau$ — the corner frequency and the 63% charging time are the same fact told twice. Swap which component the output is taken across and the identical corner becomes a high-pass instead.