RC Low-Pass Filter Gain Calculator

About this calculator

For a first-order RC low-pass filter, the voltage gain magnitude at frequency f is |H(f)| = 1 / √(1 + (f/fc)²), where the cutoff frequency fc = 1/(2πRC). Expressed logarithmically, that's gain(dB) = 20 log₁₀|H(f)| — at the cutoff itself the gain is always 0.707 (−3 dB), and it falls off at roughly 20 dB per decade beyond that.

Audio engineers use this exact math to design tone controls and anti-aliasing filters, electronics hobbyists use it to pick R and C values that tame high-frequency noise on a signal line, and it's a staple circuit-analysis exercise because it shows so clearly how a filter's response depends on both the component values and the signal frequency.