Last updated: 2026-06-16

RC Filter Cutoff Frequency

A first-order RC filter is a resistor and a capacitor in series. It is the simplest frequency-selective circuit, and its single defining number is the cutoff frequency — the boundary between the band it passes and the band it attenuates. This calculator takes the resistance $R$ and the capacitance $C$ and returns the cutoff frequency $f_c$ along with the time constant $\tau$.

Formula

The cutoff is the −3 dB point: the frequency at which the capacitor's reactance equals the resistance, the output power has fallen to half the input power, and the amplitude has dropped to about 70.7% of its passband value. It is the reciprocal of the time constant scaled by $2\pi$, since $\tau = RC$ gives $f_c = 1 / (2\pi\tau)$.

Worked example

A filter uses a $1\ \text{k}\Omega$ resistor and a $100\ \text{nF}$ capacitor.

The time constant is $\tau = RC = 1000 \times 100 \times 10^{-9} = 1 \times 10^{-4}\ \text{s} = 0.1\ \text{ms}$.

Cutoff for a 100 nF capacitor

Why it matters

The same resistor and capacitor define both a low-pass and a high-pass filter; they share the cutoff $f_c = 1 / (2\pi RC)$ and differ only in where the output is taken. A low-pass filter passes frequencies below $f_c$ and is used to smooth signals and remove high-frequency noise; a high-pass filter passes frequencies above $f_c$ and is used to block DC offsets and couple AC signals. Beyond the cutoff a single RC stage rolls off at 20 dB per decade, so cascading stages or moving to a higher-order topology gives a sharper transition when one stage is not selective enough.