# RC Filter Calculator

Calculate RC filter cutoff frequency, time constant, gain, and phase shift. Design low-pass and high-pass filters with resistor and capacitor values.

## What this calculates

RC filters are the simplest analog filters, built from just a resistor and a capacitor. The cutoff frequency fc = 1/(2piRC) is where the output drops to 70.7% of the input (-3 dB). Below cutoff a low-pass filter passes signals through; above cutoff it attenuates them at 20 dB per decade.

## Inputs

- **Resistance (R)** (Ω) — min 0
- **Capacitance (C)** (nF) — min 0
- **Signal Frequency (optional)** (Hz) — min 0 — Leave at 0 to skip gain calculation.

## Outputs

- **Cutoff Frequency (fc)** (Hz) — The -3 dB point where output is 70.7% of input
- **Cutoff Frequency** (kHz) — Cutoff frequency in kilohertz
- **Time Constant (τ)** (ms) — τ = RC in milliseconds
- **Gain at Signal Frequency** (dB) — Attenuation of a low-pass filter at the signal frequency
- **Phase Shift at Signal Frequency** (°) — Phase angle of a low-pass filter at the signal frequency

## Details

An RC filter's behavior depends entirely on the relationship between the signal frequency and the cutoff frequency. The transfer function for a low-pass RC filter is:

|H(f)| = 1 / sqrt(1 + (f/fc)^2)

For a high-pass filter (swap R and C), the transfer function is:

|H(f)| = (f/fc) / sqrt(1 + (f/fc)^2)

  - At f = fc: gain is -3 dB (70.7% voltage), phase is -45 degrees

  - At f = 10 x fc: gain is about -20 dB (10% voltage) for low-pass

  - At f = 0.1 x fc: gain is about -20 dB (10% voltage) for high-pass

The same R and C values set the time constant tau = RC, which governs the step response. A low-pass RC filter with a 1 kHz cutoff has a time constant of about 0.16 ms. This dual interpretation (frequency domain vs time domain) makes RC filters useful for both signal filtering and timing applications.

Common uses include smoothing power supplies, filtering ADC inputs, debouncing switches, coupling audio signals, and building anti-aliasing filters. For steeper rolloff, cascade multiple stages or use active filter topologies.

## Frequently Asked Questions

**Q: What is the difference between low-pass and high-pass RC filters?**

A: In a low-pass RC filter, the output is taken across the capacitor, so low frequencies pass through and high frequencies are attenuated. In a high-pass filter, the output is taken across the resistor, so high frequencies pass and low frequencies are blocked. The same R and C values give the same cutoff frequency for both configurations.

**Q: Why is the cutoff at -3 dB?**

A: The -3 dB point is where the output power is half of the input power. In voltage terms, the output is 1/sqrt(2) or about 70.7% of the input. This is a natural mathematical result of the transfer function at f = fc, and it has become the standard definition of bandwidth for filters and amplifiers.

**Q: Can I cascade RC filters for steeper rolloff?**

A: Yes, but each additional stage adds only 20 dB/decade of rolloff, and they interact unless separated by buffer amplifiers. Two unbuffered stages do not give exactly -40 dB/decade because the second stage loads the first. For precise multi-pole filtering, use active filter designs like Sallen-Key or state-variable topologies.

**Q: How does an RC filter compare to an RL filter?**

A: Both achieve the same filtering function. RC filters use a capacitor and are preferred at lower frequencies and in compact circuits because capacitors are cheap and small. RL filters use an inductor and are sometimes preferred at higher frequencies or in power applications where inductors handle current better. The cutoff for an RL filter is fc = R/(2piL).

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Source: https://vastcalc.com/calculators/physics/rc-filter
Category: Physics
Last updated: 2026-04-08