Design low-pass and high-pass RC filters with cutoff frequency, frequency response table, gain/phase analysis, and multi-stage cascading support.
The **RC Filter Calculator** designs first-order passive low-pass and high-pass filters using one resistor and one capacitor. Enter the component values to see the cutoff frequency, roll-off rate, and a frequency response table with gain, phase shift, and output voltage at each frequency.
This tool also supports **multi-stage cascading** for steeper roll-off. A single stage gives the standard first-order response, while two to four identical stages increase attenuation more aggressively. The response table spans a wide frequency range so you can see how the filter behaves below, at, and above the cutoff point.
That makes it useful for audio tone shaping, anti-aliasing, ripple reduction, and general signal conditioning. The built-in design helper also suggests component values when you start from a target cutoff frequency.
RC filters are the simplest analog filters, which also makes them the easiest to misestimate when you only look at the cutoff formula. The actual response depends on the component values, the stage count, and any loading effects from the next circuit.
This calculator keeps the cutoff, gain, phase, and component suggestions on the same page so you can check whether a design will behave the way you expect before you build it.
Cutoff Frequency: f_c = 1 / (2πRC) Low-Pass Gain: |H(f)| = 1 / √(1 + (f/f_c)²) High-Pass Gain: |H(f)| = (f/f_c) / √(1 + (f/f_c)²) Multi-stage gain: |H(f)|^n for n cascaded stages Phase (low-pass): φ = −arctan(f/f_c) Phase (high-pass): φ = 90° − arctan(f/f_c) Roll-off: −20n dB/decade (n = number of stages)
Result: f_c = 15.92 kHz, roll-off = -20 dB/decade
f_c = 1/(2π × 1000 × 10e-9) = 15,915 Hz ≈ 15.92 kHz. At f_c, the gain is -3 dB (70.7%), so V_out = 0.707V. At 10× f_c (159.2 kHz), gain drops to -20 dB (10%), V_out = 0.1V. Phase shift at f_c is -45°.
The only difference between an RC low-pass and high-pass filter is which component the output is taken across. **Low-pass**: output across C (the capacitor integrates the signal, smoothing high frequencies). **High-pass**: output across R (the capacitor differentiates the signal, blocking DC and low frequencies). Both use identical components and share the same cutoff frequency — they are exact complements.
Real capacitors and resistors have parasitic properties that affect high-frequency performance. Ceramic capacitors have low ESR and ESL, making them ideal for RF filters. Electrolytic capacitors have significant ESR, limiting their usefulness above a few kHz. Carbon film resistors can have parasitic inductance at RF frequencies. For precision filters, choose metal film resistors and C0G/NP0 ceramic or film capacitors.
When a single RC stage doesn't provide enough attenuation, engineers have several options: cascade buffered RC stages, use higher-order passive LC filters, or switch to active filters (Sallen-Key, multiple feedback). Active filters using op-amps offer adjustable Q factor, gain, and sharper roll-off without the loading problems of passive cascades. For critical applications, consider Butterworth (maximally flat), Chebyshev (steepest roll-off), or Bessel (best phase response) filter designs.
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The cutoff frequency (f_c) is where the filter's output power drops to half (-3 dB) of the input. For a low-pass filter, frequencies below f_c pass through with minimal attenuation; frequencies above f_c are progressively reduced. At f_c, the capacitor's reactance equals R.
In a low-pass filter, the output is taken across the capacitor — at low frequencies C has high impedance (passes signal), at high frequencies C has low impedance (shorts signal to ground). In a high-pass filter, the output is across the resistor — C blocks DC but passes AC above f_c.
It means the output drops by a factor of 10 (20 dB) for every factor of 10 increase in frequency beyond f_c. Two cascaded stages give -40 dB/decade, three give -60 dB/decade. This rate, also expressed as -6 dB/octave per stage, determines how sharply the filter rejects unwanted frequencies.
A single RC stage provides gentle -20 dB/decade roll-off, which may not adequately reject unwanted frequencies. Cascading stages steepens the roll-off. However, each stage loads the previous one (unless buffered with an op-amp), causing the actual -3dB point to shift. Buffered stages maintain the ideal response.
Start with your required cutoff frequency and choose R in a practical range (1kΩ-100kΩ for most applications). Then C = 1/(2πf_c R). The design helper in this calculator shows suggested C for your R (or R for your C) at any target frequency.
The filter's output impedance affects the load. For a low-pass RC filter, output impedance at low frequencies approaches 0 (good), but for a high-pass filter, it approaches R. If the load impedance is comparable to R, the filter characteristics change. Use a buffer (op-amp follower) to isolate the filter from the load.