Low Pass Filter Calculator

What the low pass filter calculator does

A low-pass filter lets low-frequency signals through while blocking high-frequency ones, and its cutoff frequency marks the boundary. This calculator finds that cutoff frequency for RC and RL low-pass filters, as well as active op-amp versions, from the component values.

Below is what a low-pass filter is, the equations behind it, how it favours low frequencies, and a worked example.

How to use it

1. Choose the filter type: RC, RL, or an active op-amp version.
2. Enter the component values, such as the resistance and capacitance.
3. Press Calculate for the cutoff frequency, or Reset to clear it.

What a low-pass filter is

A low-pass filter is a circuit that allows signals below a certain frequency to pass through while reducing signals above it. The dividing line is the cutoff frequency: frequencies well below it come through largely intact, while frequencies well above it are attenuated, fading away the higher they go. The name says it directly, it passes the low frequencies. It is one of the most common and useful circuits in electronics and signal processing, used wherever the high-frequency part of a signal needs to be removed.

The simplest low-pass filters use just two components, a resistor and a capacitor, or a resistor and an inductor, arranged so that the high frequencies are diverted or blocked while the low frequencies reach the output. More elaborate active versions add an operational amplifier for gain and a sharper response, but the principle is unchanged. This calculator finds the cutoff frequency that separates the passed lows from the blocked highs, for the common RC and RL designs and for active op-amp filters.

The equations it uses

For a resistor-capacitor low-pass filter, the cutoff frequency is:

f_c = 1 ÷ (2πRC)

and for a resistor-inductor low-pass filter it is:

f_c = R ÷ (2πL)

where R is the resistance, C is the capacitance, and L is the inductance. These are the same cutoff relationships that govern simple filters in general, since the cutoff is set by the resistor working against the reactance of the capacitor or inductor. For the active op-amp versions, the cutoff is likewise set by a resistor and capacitor, while the amplifier provides gain. The calculator applies the appropriate relationship for the filter type you select.

How it lets the lows through

The way a low-pass filter works follows from how a capacitor responds to frequency. A capacitor has low reactance at high frequencies and high reactance at low ones, so in the common low-pass arrangement the capacitor is placed across the output, where it short-circuits the high frequencies to ground while leaving the low frequencies untouched. The low frequencies pass on to the output, and the high frequencies are bled away, which is exactly the filtering wanted.

As with its high-pass counterpart, a low-pass and a high-pass RC filter use the very same components and the same cutoff formula; what makes one low-pass is that the output is taken across the capacitor rather than the resistor. This is why the cutoff frequency formula is identical to the high-pass case. At the cutoff frequency itself, the output has fallen to about 70 percent of the input, and above it the signal fades away increasingly, which is the behaviour the calculator's cutoff frequency identifies. Below the cutoff, signals pass through with little change.

Where low-pass filters are used

Low-pass filters are extremely common. In audio, they remove unwanted high-frequency hiss and noise, and they route the lower frequencies to a woofer in a loudspeaker crossover, keeping treble out of a speaker meant for bass. They smooth out rapid fluctuations in a signal, which is why they are used to clean up the output of power supplies and to average out noisy measurements, leaving the slow, meaningful part behind.

In digital systems, a low-pass filter is essential before an analogue signal is sampled, removing high frequencies that would otherwise cause errors known as aliasing. They also pair with high-pass filters to build band-pass filters that isolate a chosen range of frequencies. Wherever the high end of a signal is unwanted, whether it is noise, interference, or detail that must be smoothed, a low-pass filter is the tool, and choosing the right cutoff frequency sets exactly where the smoothing begins. This calculator provides that cutoff for the filter you are designing.

Units and precision

The calculator takes resistance in ohms and its multiples, capacitance in farads and its smaller multiples, and inductance in henries and its smaller multiples, returning the cutoff frequency in hertz. It applies the exact cutoff relationship for the RC, RL, or active filter type chosen. For the simple RC and RL filters the cutoff is the half-power point where the response has dropped to about 70 percent. The active op-amp options also involve the amplifier's gain, which depends on the resistor values in those designs.

A worked example

Suppose a resistor-capacitor low-pass filter uses a 10-kilohm resistor and a 10-nanofarad capacitor.

The cutoff frequency is f_c = 1 ÷ (2πRC) = 1 ÷ (2π × 10000 × 0.00000001) ≈ 1,592 hertz. Signals well below about 1.6 kilohertz pass through this filter, while those well above it are attenuated, with the transition centred on the cutoff. Choosing different component values shifts the cutoff, moving the boundary between the passed lows and the blocked highs.

Questions people ask

How do you calculate a low-pass filter's cutoff?

For an RC filter, use f_c = 1 ÷ (2πRC); for an RL filter, use f_c = R ÷ (2πL), from the component values.

How does a low-pass filter work?

A capacitor across the output short-circuits high frequencies to ground while passing low ones to the output. The lows come through while the highs are bled away.

Why use a low-pass filter before sampling?

To remove high frequencies that would otherwise cause aliasing, a kind of error, when an analogue signal is converted to digital. It is called an anti-aliasing filter.

What are low-pass filters used for?

Removing high-frequency hiss and noise from audio, smoothing power-supply output, averaging noisy measurements, routing bass to woofers, and preventing aliasing before sampling.

References

A quick note on where the physics comes from. Low-pass filters and their cutoff frequency are standard physics and electronics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The HyperPhysics link is worth a quick click to confirm it lands where you expect.

1. OpenStax, University Physics Volume 2, Section 15.3, RLC Series Circuits with AC. https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac
2. HyperPhysics, RC Filter Circuits. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/filter.html
3. National Institute of Standards and Technology (NIST), SP 811, Guide for the Use of the International System of Units. https://www.nist.gov/pml/special-publication-811