RC Low-Pass Filter

fc = 1 / (2πRC)

Quick answer

This calculator solves fc = 1 / (2πRC) for Cutoff Frequency. With Resistance 10 kΩ, Capacitance 100 nF, the result is 0.1592 kHz. It solves in 3 directions, so you can enter the values you have and get the one you need.

Calculator

Cutoff Frequency (kHz)
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Formula

fc = 1 / (2πRC)

Description

A first-order RC low-pass filter passes signals below the cutoff frequency and attenuates signals above it. The cutoff frequency (also called the -3dB point or corner frequency) is where the output amplitude drops to 70.7% of the input (half power). Above this frequency, attenuation increases at 20 dB per decade (6 dB per octave). The filter consists of a series resistor followed by a capacitor to ground. At low frequencies, the capacitor impedance is high and most of the signal passes through. At high frequencies, the capacitor becomes a low impedance path to ground, shunting the signal.

Variables

  • fc — Cutoff frequency at -3dB point (Hz)
  • R — Resistance (Ω)
  • C — Capacitance (F)

Practical Notes

First-order RC filters are used for anti-aliasing before ADCs, power supply decoupling, smoothing PWM signals into analog voltages, and removing high-frequency noise from sensor signals. For steeper rolloff, cascade multiple stages or use active filter topologies (Sallen-Key, multiple feedback). The phase shift at fc is -45 degrees.

Symbols and units

Symbol Meaning Default unit Accepted units
fc Cutoff Frequency kHz Hz, kHz, MHz, GHz
R Resistance kΩ mΩ, Ω, kΩ, MΩ
C Capacitance nF pF, nF, µF, mF, F

Step by step

  1. 1. What you know: Resistance 10 kΩ, Capacitance 100 nF
  2. 2. The relation: fc = 1 / (2πRC)
  3. 3. Substitute: R = 10 kΩ, C = 100 nF
  4. 4. Result: Cutoff Frequency = 0.1592 kHz

Worked examples

Minimum range

Given: Resistance 100 Ω, Capacitance 100 pF

Result: Cutoff Frequency = 15.92 MHz

Low range

Given: Resistance 1 kΩ, Capacitance 1 nF

Result: Cutoff Frequency = 0.1592 MHz

Typical

Given: Resistance 10 kΩ, Capacitance 100 nF

Result: Cutoff Frequency = 0.1592 kHz

High range

Given: Resistance 100 kΩ, Capacitance 1 µF

Result: Cutoff Frequency = 1.592 Hz

Maximum range

Given: Resistance 1 MΩ, Capacitance 10 µF

Result: Cutoff Frequency = 0.01592 Hz

Solving for each variable

Solve for Cutoff Frequency

Resistance 100 Ω, Capacitance 100 pF → 15.92 MHz

Solve for Resistance

Cutoff Frequency 100 Hz, Capacitance 100 pF → 15.92 MΩ

Solve for Capacitance

Cutoff Frequency 100 Hz, Resistance 100 Ω → 15.92 µF

How Cutoff Frequency changes with Resistance

Resistance (input) Cutoff Frequency (result)
1 kΩ 1.592 kHz
2.5 kΩ 0.6366 kHz
5 kΩ 0.3183 kHz
7.5 kΩ 0.2122 kHz
10 kΩ 0.1592 kHz
15 kΩ 106.1 Hz
20 kΩ 79.58 Hz
40 kΩ 39.79 Hz
70 kΩ 22.74 Hz
100 kΩ 15.92 Hz

The same result in other units

Unit Value
Hz 159.2
kHz 0.1592
MHz 0.0001592

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Frequently asked questions

How do you calculate RC Low-Pass Filter?

Use fc = 1 / (2πRC). With Resistance 10 kΩ, Capacitance 100 nF, Cutoff Frequency works out to 0.1592 kHz.

What is the formula for RC Low-Pass Filter?

The formula is fc = 1 / (2πRC). A first-order RC low-pass filter passes signals below the cutoff frequency and attenuates signals above it.

How do you find Resistance when you know the other values?

Rearrange for Resistance: with Cutoff Frequency 100 Hz, Capacitance 100 pF, Resistance is 15.92 MΩ.

How do you find Capacitance when you know the other values?

Rearrange for Capacitance: with Cutoff Frequency 100 Hz, Resistance 100 Ω, Capacitance is 15.92 µF.

What units does RC Low-Pass Filter use?

Cutoff Frequency is shown in Hz, kHz, MHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Filters formulas →
RC Low-Pass Filter RC High-Pass Filter Bandpass Bandwidth Filter Rolloff Rate Notch Frequency Butterworth Q Factor Sallen-Key Cutoff Frequency Chebyshev Filter Order

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