RC Low-Pass Filter Calculator
Find the cutoff frequency of a simple RC low-pass filter from the resistor and capacitor, plus its time constant and −3 dB point.
How it works
f_c = 1 ÷ (2π·R·C) · τ = R·C · roll-off = −20 dB/decade · phase at f_c = −45°
An RC low-pass filter passes slow (low-frequency) signals and attenuates fast ones, because the capacitor’s impedance falls as frequency rises and shorts high frequencies to ground. The cutoff frequency is where the output has dropped to −3 dB (about 71% of the input) and the phase has shifted 45°. Above the cutoff the response rolls off at 20 dB per decade — a factor of ten in frequency for every factor of ten in attenuation.
Worked example
With R = 10 kΩ and C = 0.1 µF, f_c = 1 ÷ (2π × 10,000 × 0.0000001) = 159.2 Hz. The time constant is 10,000 × 0.0000001 = 1 ms.
Frequently asked questions
What is the difference between the cutoff frequency and the time constant?
They describe the same filter two ways. The time constant τ = RC is how fast it responds in the time domain; the cutoff f_c = 1/(2πRC) is where it rolls off in the frequency domain. They are linked by f_c = 1/(2πτ).
How steep is the roll-off?
A single RC stage rolls off at 20 dB per decade (6 dB per octave) — fairly gentle. Cascading stages or using an active filter gives a sharper transition, at the cost of more parts.
How do I turn it into a high-pass filter?
Swap the resistor and capacitor positions: take the output across the resistor instead of the capacitor. The same f_c formula applies, but now low frequencies are blocked and high ones pass.
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This calculator is for educational purposes. Double-check important results before acting on them.