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 a single resistor and capacitor. Enter the component values to see the cutoff frequency, roll-off rate, and complete frequency response table with gain (in dB and %), phase shift, and output voltage at each frequency.
This tool supports **multi-stage cascading** (1-4 identical stages) for steeper roll-off. A single stage provides -20 dB/decade; four stages give -80 dB/decade. The frequency response table spans five decades around the cutoff frequency, and you can also analyze attenuation at any specific target frequency.
Whether you''re designing an **audio treble cut filter**, an **ADC anti-aliasing filter**, a **power supply ripple filter**, or an **RF signal coupling network**, this calculator provides the complete frequency-domain picture. The built-in design helper suggests component values when you specify a target cutoff frequency. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case.
RC filters are the simplest and most commonly used analog filters. Every signal chain — from audio equipment to instrumentation to RF communications — uses RC filtering at some stage. This calculator provides the complete frequency response in one view, making it easy to verify that your filter design meets requirements.
The multi-stage support is particularly useful because real applications often need steeper roll-off than a single stage provides. The design helper feature saves time by computing ideal component values for any target frequency. And the application reference table helps engineers quickly identify typical component ranges for common use cases.
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.
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.