Low-Pass & High-Pass Filter Calculator — RC Cutoff Frequency Formula

This low-pass and high-pass filter calculator instantly computes the cutoff frequency ($f_c$) of a passive RC circuit, or finds the resistor and capacitor values you need for a target frequency.

What Is a Low-Pass and High-Pass Filter?

A passive RC filter is a simple two-component circuit — one resistor ($R$) and one capacitor ($C$) — that selectively passes or blocks frequencies.

• Low-Pass Filter (LPF): Passes frequencies below the cutoff ($f_c$) and attenuates those above it. The resistor is in series with the signal; the capacitor shunts to ground at the output.
• High-Pass Filter (HPF): Passes frequencies above the cutoff and attenuates those below it. The capacitor is in series; the resistor shunts to ground.

The cutoff frequency is the frequency at which the output power drops to 50% of the input (a −3 dB attenuation). Below the cutoff, a low-pass filter is essentially transparent; above it, attenuation increases at 20 dB per decade.

RC Filter Cutoff Frequency Formula

Both low-pass and high-pass RC filters share the same formula:

$f_c = \frac{1}{2\pi R C}$

Where:

• $f_c$ — cutoff frequency in hertz (Hz)
• $R$ — resistance in ohms (Ω)
• $C$ — capacitance in farads (F)

Solving for R or C:

$R = \frac{1}{2\pi f_c C} \qquad C = \frac{1}{2\pi f_c R}$

The voltage gain at any frequency:

• Low-pass: $A_v = \dfrac{1}{\sqrt{1 + (f/f_c)^2}}$
• High-pass: $A_v = \dfrac{f/f_c}{\sqrt{1 + (f/f_c)^2}}$

Step-by-Step Calculation Example

Goal: Design a low-pass filter to remove high-frequency noise from an audio signal, with a cutoff at 20 kHz. Available capacitor: 1.5 nF.

1. Known values: $f_c = 20{,}000\,\text{Hz}$, $C = 1.5 \times 10^{-9}\,\text{F}$
2. Solve for $R$: $R = \frac{1}{2\pi \times 20{,}000 \times 1.5 \times 10^{-9}}$
3. Calculate: $R = \frac{1}{0.0001885} \approx 5{,}305\,\Omega$
4. Use the nearest standard value: 5.1 kΩ (E24 series) gives $f_c \approx 20.8\,\text{kHz}$.

Common RC Filter Values Quick Reference

Frequently Asked Questions

What is the roll-off rate of a first-order RC filter?

A first-order RC filter attenuates at −20 dB per decade (or −6 dB per octave) beyond the cutoff. For sharper roll-off, cascade two stages (second order, −40 dB/decade) or use an active filter with an op-amp.

Does the low-pass and high-pass formula change for RL filters?

For RL filters (resistor + inductor), the cutoff formula is $f_c = R / (2\pi L)$, where $L$ is inductance in henries. The behavior is identical — only the components swap roles.

What phase shift does the RC filter introduce?

At exactly $f_c$, the filter introduces a −45° phase shift (low-pass) or +45° phase shift (high-pass). Phase shift is 0° far below $f_c$ for low-pass, and approaches 0° far above $f_c$ for high-pass.

Does the load impedance affect the cutoff frequency?

Yes. If you connect a low-impedance load at the output, it appears in parallel with the output component and shifts $f_c$ higher. To prevent loading effects, buffer the output with a unity-gain op-amp (voltage follower).