How do I calculate the cutoff frequency of an RC filter?

fc = 1 / (2π × R × C). For R = 10kΩ and C = 100nF: fc = 1 / (2π × 10000 × 100×10⁻⁹) = 159.15 Hz. This is the −3dB point where the output is 70.7% of the input amplitude.

What is the time constant of an RC circuit?

The time constant τ = R × C (in seconds). After one time constant, the capacitor charges to 63.2% of the final voltage. After 5τ, it is considered fully charged (99.3%). The cutoff frequency relates to time constant as fc = 1 / (2π × τ).

What is the difference between a low-pass and high-pass RC filter?

In a low-pass filter, the output is taken across the capacitor — it passes low frequencies and attenuates high ones. In a high-pass filter, the output is taken across the resistor — it passes high frequencies and blocks DC and low frequencies. The cutoff frequency formula is the same for both.

RC Filter Calculator — Cutoff Frequency & Time Constant

How the RC Filter Calculator Works

An RC filter is a first-order passive filter built from one resistor and one capacitor. It is the simplest frequency-selective circuit and is ubiquitous in signal conditioning, anti-aliasing before ADC inputs, debouncing switch signals, power supply decoupling, and audio processing.

Cutoff Frequency

fc = 1 / (2π × R × C)

At the cutoff frequency, the filter output is −3dB below the input (amplitude = 70.7% of input). Below fc, a low-pass filter passes signals with minimal attenuation. Above fc, attenuation increases at −20 dB per decade (6 dB per octave).

Time Constant

τ = R × C

The time constant τ describes how quickly the capacitor charges or discharges. The cutoff frequency and time constant are inversely related: fc = 1 / (2π × τ). In step-response terms: after 1τ the capacitor reaches 63.2% of final voltage, after 5τ it reaches 99.3%.

Low-Pass vs High-Pass

Both topologies use the same R and C — only the output tap changes:

Low-pass: Output across capacitor (C). Passes DC and low frequencies. Used for anti-aliasing, noise filtering on ADC inputs, power rail smoothing.
High-pass: Output across resistor (R). Blocks DC and low frequencies. Used for AC coupling, removing DC offset from audio signals, differentiation circuits.

Design Example: Anti-aliasing for 1 kSPS ADC

Nyquist frequency = 500 Hz → set fc at 200–300 Hz for roll-off margin
Choose C = 100 nF (common value), solve for R: R = 1 / (2π × 200 × 100e-9) = 7.96 kΩ → use 8.2 kΩ (E24)
Actual fc = 1 / (2π × 8200 × 100e-9) = 194 Hz
Attenuation at 500 Hz: −20 log10(500/194) = −8.2 dB

Component Selection Tips

Capacitor type: Use NP0/C0G ceramics for precision applications (stable vs. temperature and voltage). X7R is acceptable for general filtering but capacitance drops under DC bias.
Resistor tolerance: 1% metal film for accuracy. 5% carbon film is sufficient for non-critical filtering.
Source impedance: If the driving source has significant output impedance (Rsource), the effective R is Rsource + R. Account for this in your design, especially with op-amp output stage resistors.

Frequently Asked Questions

How do I get a steeper roll-off?
A first-order RC filter rolls off at −20 dB/decade. For steeper attenuation, cascade multiple RC stages (each adds −20 dB/decade) or use active filters (Sallen-Key, Butterworth, Chebyshev) with op-amps. A second-order active filter gives −40 dB/decade; fourth-order gives −80 dB/decade.

What is the phase shift at cutoff?
At fc, an RC filter introduces a −45° phase shift (low-pass) or +45° (high-pass). Phase shift increases toward −90° well above cutoff for LPF (or toward 0° for HPF). In control systems, phase shift reduces phase margin and can cause instability.

Can I use an RC filter to debounce a mechanical switch?
Yes. A 10kΩ resistor with a 100nF capacitor gives τ = 1ms, which filters most contact bounce (typically 1–20ms). Pair with a Schmitt trigger (e.g., 74HC14) to generate clean digital edges from the filtered analog output.

RC Filter Calculator

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