An RC filter is nothing more than a resistor and a capacitor in series, with the output taken from across one of the two parts. Because a capacitor's impedance (XC=1/(2πfC)) falls as frequency rises, the R-C pair forms a frequency-dependent voltage divider: at low frequencies the capacitor's impedance is huge (it looks like an open circuit), and at high frequencies its impedance shrinks toward zero (it looks like a short). Which frequencies get passed through depends entirely on where you take the output from:
Both configurations use the exact same formula for the transition point, the cutoff frequency: fc = 1/(2πRC). This is also, not coincidentally, the reciprocal of 2π times the familiar RC time constant (τ=RC) used for charge/discharge calculations — the same R and C values govern both the filter's frequency response and its step-response speed.
| Quantity | Formula |
|---|---|
| Cutoff (−3 dB) frequency | fc = 1/(2πRC) |
| Low-pass magnitude | |H(f)| = 1/√(1+(f/fc)²) → dB = −20log₁₀√(1+(f/fc)²) |
| High-pass magnitude | |H(f)| = (f/fc)/√(1+(f/fc)²) |
| Roll-off rate (past cutoff) | −20 dB/decade (−6 dB/octave) — a "first-order" or "single-pole" filter |
| Phase shift at fc | −45° (low-pass) or +45° (high-pass) |
Because this is only a first-order filter (one reactive element), the roll-off is gentle: one decade past fc, the signal is down by only about 20 dB (a factor of 10 in amplitude) — not a sharp cliff. Applications needing a steeper cutoff use a second-order filter instead; see the LC Filter calculator (two reactive elements, −40 dB/decade) or the Sallen-Key active filter calculator for op-amp-based second-order designs with a tunable Q.
It is the frequency at which the filter's output is attenuated by exactly −3.01 dB (about 70.7% of the input amplitude), calculated as fc = 1/(2πRC). This is true for both low-pass and high-pass RC filters using the same R and C.
They use the identical resistor and capacitor and the identical cutoff-frequency formula — the only difference is which component the output is taken across. Output across the capacitor gives a low-pass filter (passes low frequencies); output across the resistor gives a high-pass filter (passes high frequencies).
A single RC stage is a first-order (one-pole) filter with a roll-off of −20 dB per decade (−6 dB per octave) past the cutoff frequency — a gentle slope. Steeper roll-offs need a second-order filter, such as an LC filter or an active Sallen-Key filter.
Exactly −3.01 dB, which corresponds to the output amplitude being 1/√2 ≈ 70.7% of the input amplitude, and a phase shift of 45° (negative for low-pass, positive for high-pass).
Pick a convenient, commonly-available capacitor value first, then solve R = 1/(2πfcC); or pick a resistor value first and solve C = 1/(2πfcR). Use the "Design for Target fc" tab above to compute either one directly.
A high-pass (DC-blocking) filter passes the audio-frequency signal of interest while blocking DC offset and very low "subsonic" frequencies (rumble, thumps) that could otherwise saturate later amplifier stages or waste headroom.
Yes — fc = 1/(2πRC) is simply 1/(2π) times the reciprocal of the time constant τ=RC used for charge/discharge calculations. The same R and C values simultaneously set both the filter's frequency response and how fast it responds to a step change.
For a low-pass filter the phase shift is −atan(f/fc), ranging from 0° at very low frequencies to −90° at very high frequencies (with −45° exactly at fc). A high-pass filter's phase is the complement of this, from +90° down to 0°.
You can, but a naive cascade of two identical RC stages does not simply double the roll-off to −40 dB/decade at the same fc unless the stages are buffered (e.g. with an op-amp) to prevent the second stage from loading the first — otherwise the combined response shifts and the math gets more involved. A proper 2nd-order design (LC or Sallen-Key) is the standard way to get a clean −40 dB/decade.
For cutoffs in the 20 Hz–20 kHz audio range, common combinations use resistors from a few hundred ohms to tens of kilohms paired with capacitors from a few nanofarads to a few microfarads — the calculator above will show you the exact pairing for your target.
Yes, in a real circuit the driving source's output impedance and the following stage's input impedance add to (or divide) the effective R, which can shift the actual cutoff away from the ideal formula's prediction. For critical designs, buffer the filter with an op-amp or account for the surrounding impedances.
A low-pass filter is the standard choice, since switching noise (e.g. from a PWM signal or switching regulator) is high-frequency and a low-pass filter passes the low-frequency signal of interest while attenuating the noise above the chosen cutoff.
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