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

For both first‑order RC low‑pass and high‑pass filters, the cutoff frequency is f_c = 1 / (2πRC). At this frequency the output magnitude is 1/√2 of the pass‑band value, which corresponds to −3 dB.

What resistor and capacitor values should I choose?

Choose R and C so that their product RC gives the desired cutoff frequency via f_c = 1 / (2πRC). In practice you also consider noise, loading, and component availability. For audio filters, R between 1 kΩ and 100 kΩ and C between 1 nF and 1 µF are common starting points.

What is the phase shift of an RC filter?

A first‑order RC filter introduces a frequency‑dependent phase shift. For a low‑pass filter the phase goes from 0° at very low frequency to −90° at very high frequency. For a high‑pass filter it goes from +90° at very low frequency to 0° at very high frequency. At the cutoff frequency the magnitude is −3 dB and the phase shift is ±45°.

RC Filter Calculator – Low‑Pass & High‑Pass Cutoff, Gain & Phase

Q: What is an RC filter?

An RC filter is a simple analog filter made from one resistor (R) and one capacitor (C). Depending on how they are connected, it can act as a low‑pass filter that passes low frequencies and attenuates high frequencies, or as a high‑pass filter that does the opposite.

What is an RC filter?

An RC filter is the simplest analog filter you can build: it uses one resistor (R) and one capacitor (C). Depending on how you connect them, the circuit behaves as:

RC low‑pass filter – passes low frequencies, attenuates high frequencies.
RC high‑pass filter – passes high frequencies, attenuates low frequencies.

Both are first‑order filters: their magnitude response rolls off at approximately 20 dB/decade (6 dB per octave) beyond the cutoff frequency.

RC low‑pass and high‑pass formulas

Cutoff frequency and time constant

For both low‑pass and high‑pass RC filters:

Time constant: \(\tau = R C\)

Cutoff (−3 dB) frequency: \[ f_c = \frac{1}{2\pi R C} \]

At \(f = f_c\), the output magnitude is \(1/\sqrt{2} \approx 0.707\) of the pass‑band value, which corresponds to −3 dB.

Low‑pass RC filter transfer function

Standard low‑pass topology: resistor in series, capacitor to ground, output across the capacitor.

Transfer function: \[ H_{LP}(j\omega) = \frac{1}{1 + j\omega R C} \] Magnitude: \[ |H_{LP}(j\omega)| = \frac{1}{\sqrt{1 + (\omega R C)^2}} \] Phase: \[ \phi_{LP}(\omega) = -\arctan(\omega R C) \]

High‑pass RC filter transfer function

Standard high‑pass topology: capacitor in series, resistor to ground, output across the resistor.

Transfer function: \[ H_{HP}(j\omega) = \frac{j\omega R C}{1 + j\omega R C} \] Magnitude: \[ |H_{HP}(j\omega)| = \frac{\omega R C}{\sqrt{1 + (\omega R C)^2}} \] Phase: \[ \phi_{HP}(\omega) = \frac{\pi}{2} - \arctan(\omega R C) \]

How to choose R and C for a desired cutoff

If you know the desired cutoff frequency \(f_c\), you can choose any convenient R or C and solve for the other:

From \(f_c = \dfrac{1}{2\pi R C}\): \[ R = \frac{1}{2\pi f_c C} \quad\text{or}\quad C = \frac{1}{2\pi f_c R} \]

Practical guidelines:

For audio filters, R between 1 kΩ and 100 kΩ is typical.
Very large R increases noise and sensitivity to input bias currents.
Very large C is bulky and may be more expensive or leaky (electrolytics).
Pick standard E‑series values that are easy to source.

Example: audio low‑pass at 1.6 kHz

Suppose you want a simple low‑pass filter with \(f_c \approx 1.6\ \text{kHz}\) for audio.

Choose \(R = 10\ \text{k}\Omega\).
Compute \(C\): \[ C = \frac{1}{2\pi f_c R} = \frac{1}{2\pi \cdot 1600 \cdot 10\,000} \approx 9.95 \times 10^{-9}\ \text{F} \approx 10\ \text{nF} \]
Use standard values R = 10 kΩ, C = 10 nF.

Enter these values in the calculator and you will see \(f_c \approx 1.59\ \text{kHz}\), magnitude ≈ 0.707 (−3 dB) and phase ≈ −45° at that frequency.

Common pitfalls and design tips

Loading effects: The formulas assume the filter is not significantly loaded. If the next stage has a low input impedance, it will change the effective R and shift \(f_c\).
Source impedance: A non‑ideal source resistance adds to R in a low‑pass or forms a divider in a high‑pass, again shifting the response.
Tolerance: Real components have tolerances (e.g., ±5%). Expect the actual cutoff to vary accordingly.
Noise: Higher resistance values increase thermal noise. For low‑noise designs, prefer smaller R and larger C.

FAQ

Is the cutoff frequency the same for low‑pass and high‑pass RC filters?

Yes. For a given R and C, both first‑order RC low‑pass and high‑pass filters have the same cutoff frequency \(f_c = 1/(2\pi R C)\). What changes is which side of that frequency is passed.

Can I cascade RC filters to get a steeper slope?

Yes. Cascading two identical RC low‑pass filters gives a second‑order response with approximately 40 dB/decade roll‑off. However, the exact response depends on how the stages load each other; for precise control, active filters with op‑amps are often used.

What happens at DC and very high frequency?

Low‑pass: At DC (0 Hz) the capacitor is open‑circuit, so the output equals the input (gain ≈ 1). At very high frequency the capacitor shorts to ground, so the output tends to 0.
High‑pass: At DC the capacitor blocks, so the output is 0. At very high frequency the capacitor behaves like a short, so the output tends to the input (gain ≈ 1).

RC Filter Calculator (Low‑Pass & High‑Pass)