RC Low Pass Filter Cutoff Calculator
A first-order RC low pass filter passes low frequencies and attenuates higher ones above its cutoff. The cutoff, or minus-3-dB point, is where the output power falls to half the input power. This calculator returns the cutoff frequency, the RC time constant, and the angular cutoff frequency from a resistor and capacitor value. Low pass filters smooth signals, remove high-frequency noise, and form the building blocks of audio tone controls, sensor conditioning, and anti-aliasing front ends. Enter R in ohms and C in farads to size your filter.
RC low pass formula
time constant tau = R * C
cutoff frequency fc = 1 / (2 * pi * R * C)
angular cutoff omega = 2 * pi * fc = 1 / (R * C)
rolloff above cutoff = 20 dB per decade
At the cutoff the output amplitude is 1 divided by the square root of 2 (about 70.7 percent) of the input, the half-power point. R is in ohms, C in farads.
Filter notes
- Below the cutoff the signal passes nearly unchanged; above it, it is attenuated.
- The single-pole rolloff is 20 dB per decade, or about 6 dB per octave.
- 1 nanofarad equals 0.000000001 farad; 1 microfarad equals 0.000001 farad.
- The time constant sets how quickly the filter responds to a step change.
- For steeper slopes, cascade stages or use an active filter design.
RC low pass filter: frequently asked questions
What is the RC low pass filter cutoff formula?
The minus-3-dB cutoff frequency of a first-order RC low pass filter is fc = 1 / (2 * pi * R * C), with R in ohms and C in farads, giving the cutoff in hertz. At this frequency the output amplitude is about 70.7 percent of the input and the power is halved.
What happens above and below the cutoff?
Below the cutoff, signals pass with little attenuation. Above the cutoff, the filter attenuates at 20 dB per decade (a factor of ten in frequency cuts the amplitude tenfold) for a single-pole RC stage. The cutoff is the transition point.
What is the time constant of the filter?
The time constant is tau = R * C in seconds. It relates to the cutoff by fc = 1 / (2 * pi * tau). The time constant also describes the step response: the output reaches about 63.2 percent of a step input after one time constant.
Why minus 3 dB at the cutoff?
At the cutoff frequency the reactance of the capacitor equals the resistance, so the output is the input divided by the square root of 2 in amplitude. In decibels that is about minus 3.01 dB, and the delivered power is exactly half, which is why it is called the half-power point.
Does this apply to a single-pole filter only?
Yes. This calculator models a first-order, single-pole RC low pass filter with a 20 dB per decade rolloff. Multi-pole or active filters have steeper slopes and different cutoff behaviour that this simple formula does not capture.
Official sources
- NIST: SI units (hertz, ohm, farad).
- NASA Glenn Research Center: RC filter and reactance fundamentals.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.