Low Pass Filter Calculator
Enter any two component values and this calculator solves for the -3 dB cutoff frequency of your low-pass filter. It supports passive RC, RL and LC circuits as well as inverting and non-inverting op-amp active filters. You also get the time constant, the phase shift and output attenuation at any signal frequency you choose, plus a worked step-by-step breakdown and a frequency-response chart. All results update instantly as you type.
Formula
Worked example
For a 1 kohm resistor and 159 nF capacitor: tau = 1000 x 0.000000159 = 0.000159 s. fc = 1/(2 x pi x 0.000159) = 1000 Hz. At a 500 Hz signal: ratio = 500/1000 = 0.5, gain = 1/sqrt(1+0.25) = 0.894, attenuation = 20 x log10(0.894) = -0.97 dB, phase shift = -arctan(0.5) = -26.6 degrees.
What is a low-pass filter?
A low-pass filter (LPF) passes frequencies below a chosen threshold, called the cutoff frequency, while progressively attenuating frequencies above it. The transition is gradual, not a brick wall: at the cutoff itself the output power is exactly half the input power (-3 dB). Audio subwoofer crossovers, power-supply ripple rejection, anti-aliasing before analog-to-digital conversion, and sensor signal conditioning all rely on low-pass filters. The simplest passive implementation is a resistor paired with a capacitor (RC) or an inductor (RL). Adding a second reactive component (LC) or an operational amplifier produces steeper roll-off or gain.
How to use this calculator
Select your filter topology from the dropdown, then enter the component values. For RC: enter R in ohms and C in farads (e.g. 159 nF = 0.000000159 F). For RL: enter R and L in henries. For LC: enter L and C. For op-amp types: enter the resistor and capacitor values for the feedback or input network. The cutoff frequency, time constant, DC gain and the filter order all update instantly. To see how the filter treats a specific signal, enter that signal frequency in the bottom field and the calculator shows you the gain, attenuation in dB and phase lag at that frequency. The frequency-response chart below the results gives you the full Bode magnitude plot from fc/100 to 100 x fc.
Cutoff frequency, time constant and the -3 dB point
The cutoff frequency is defined as the point where the filter output voltage falls to 1/sqrt(2) (about 70.7%) of the input, which corresponds to an output power of exactly 50% (-3 dB). For an RC circuit this is fc = 1/(2 x pi x R x C). The time constant tau = RC tells you how quickly the circuit responds in the time domain: after one time constant a step input has charged the capacitor to 63.2%, after five time constants it is over 99%. The cutoff frequency and time constant are reciprocals of each other scaled by 2 x pi: fc = 1/(2 x pi x tau).
First-order versus second-order filters
A first-order filter (RC or RL) rolls off at -20 dB per decade, meaning the output falls to about 10% of the passband level for every tenfold increase in frequency beyond the cutoff. An LC filter is second-order and rolls off at -40 dB per decade, so it attenuates high frequencies far more sharply. In audio work this translates to a subjective difference of 6 dB/octave for first-order and 12 dB/octave for second-order designs. Op-amp Sallen-Key or multiple-feedback topologies can achieve second, third or higher orders while keeping the circuit entirely active, but this calculator covers only first-order active designs.
Active versus passive low-pass filters
Passive RC and RL filters use only resistors and reactive components, so they draw no power from a supply. Their disadvantage is insertion loss: the filter loads the signal source. An active filter adds an op-amp, which isolates the source (high input impedance) and can provide gain, so the useful signal is not weakened. The inverting configuration flips the output phase by 180 degrees and sets gain as -Rf/Ri; the non-inverting configuration preserves phase and sets gain as 1 + Rf/Rg. The cutoff frequency is set by the RC network in the feedback path (inverting) or at the input (non-inverting), independently of the gain setting resistors.
Low-pass filter types at a glance
| Filter type | Order | Roll-off | Cutoff formula | Key feature |
|---|---|---|---|---|
| RC passive | 1st | -20 dB/decade | fc = 1 / (2 x pi x RC) | Simplest; lossy (loads signal source) |
| RL passive | 1st | -20 dB/decade | fc = R / (2 x pi x L) | Good at high current; inductors are bulky |
| LC passive | 2nd | -40 dB/decade | fc = 1 / (2 x pi x sqrt(LC)) | Sharper roll-off; no power supply needed |
| Inverting op-amp | 1st | -20 dB/decade | fc = 1 / (2 x pi x Rf x Cf) | Gain + filtering; output inverted |
| Non-inverting op-amp | 1st | -20 dB/decade | fc = 1 / (2 x pi x Ri x Ci) | High input impedance; no signal inversion |
Comparison of common low-pass filter topologies. "Order" determines the roll-off slope in the stopband.
Frequently asked questions
What does the -3 dB cutoff frequency mean?
The -3 dB point is the frequency at which output power falls to exactly half the input power (voltage falls to about 70.7%). It marks the boundary between the passband, where signals are passed with minimal loss, and the stopband, where they are increasingly attenuated. The formula for an RC filter is fc = 1/(2 x pi x R x C).
How do I choose R and C values for a target cutoff frequency?
Rearrange the cutoff formula: R = 1/(2 x pi x fc x C). In practice, choose a capacitor first because capacitor values come in fewer standard increments (E6 or E12 series) than resistors, then calculate the exact resistance and pick the nearest standard E96 resistor. Aim for impedance levels between 1 kohm and 100 kohm for typical signal-conditioning applications.
What is the phase shift of a low-pass filter?
A first-order RC or RL filter introduces a phase lag of phi = -arctan(f/fc) degrees at frequency f. At the cutoff frequency itself the lag is exactly -45 degrees. Deep in the passband (f much less than fc) the phase lag approaches 0 degrees; deep in the stopband (f much greater than fc) it approaches -90 degrees. The phase shift matters in feedback control loops and audio applications because it changes the timing relationship between input and output signals.
Why does an LC filter roll off more steeply than an RC filter?
An LC filter is second-order because it has two reactive components, each contributing -20 dB/decade of roll-off beyond the cutoff, for a total of -40 dB/decade. An RC filter is first-order with only one reactive component. In audio terms this is the difference between a 6 dB/octave slope (RC) and a 12 dB/octave slope (LC). More reactive stages cascade to give even steeper slopes.
What is the difference between an inverting and a non-inverting op-amp low-pass filter?
Both perform the same low-pass filtering but differ in phase and gain. The inverting configuration adds 180 degrees of phase inversion on top of the RC phase shift, and its DC gain is -Rf/Ri (negative). The non-inverting configuration preserves the signal polarity and has a DC gain of 1 + Rf/Rg (always 1 or greater). Choose inverting when signal polarity is not important and you need a specific gain; choose non-inverting for buffered unity-gain or fixed-amplification applications.
What is the time constant and why does it matter?
The time constant (tau) is the product RC for an RC filter, or L/R for an RL filter. It represents how quickly the circuit responds to a step change: after one time constant the output reaches 63.2% of its final value. The cutoff frequency is directly linked to the time constant by fc = 1/(2 x pi x tau). Longer time constants mean lower cutoff frequencies and slower response; shorter time constants mean higher cutoff frequencies and faster response.
How many dB is -3 dB in plain terms?
-3 dB means the output power is exactly half the input power, because 10 x log10(0.5) = -3.01 dB. For voltage this corresponds to a ratio of 1/sqrt(2) or about 70.7%. It is the conventional definition of the cutoff because it represents a meaningful and easily measurable reduction without completely blocking the signal.