Engineering calculators

Low Pass Filter Calculator

Updated Aug 29, 2026 By Jehan Wadia
Rate Formulas
RC Low Pass Filter (Passive)
Circuit Topology
RC low pass filter schematic R C Vin Vout signal flow →
Series R, shunt C. The output is taken across the capacitor, so high frequencies are shunted to ground.
Inputs — enter any two, leave one blank
Type SI shorthand (10k, 4.7M) and the unit box follows.
Left blank here — this is the value being solved.
Fill exactly two of the three fields.
Results
Solved value
Cutoff Frequency fc (Hz)
Angular Frequency ω0 (rad/s)
Time Constant τ = RC (s)
Impedance at fc, Z (Ω)
Phase Shift θ at fc (°)
Step-by-Step Solution
Attenuation at a Specific Frequency
Gain |H(f)|
Phase θ(f)
Attenuation vs. passband
Frequency Analysis
Plots
Second Bode subplot (choose one)
Blank = auto range from fc/100 to fc×100.
Magnitude response |H(f)| in dB vs. frequency (log scale)
Phase response θ(f) in degrees vs. frequency (log scale)
Pole-zero map in the complex s-plane
Transient Analysis
Outputs
Values
Blank = auto (5τ, a practical settling time).
Final value of step response
Step response: output / input vs. time

Introduction

A low pass filter lets low frequency signals through and blocks high frequency ones. This calculator helps you design one fast. Pick your filter type, type in the parts you know, and leave the unknown box blank. The tool solves for it and shows the work.

You can work with four filter types:

  • RC low pass — a resistor and a capacitor. The most common passive filter. See also our dedicated RC Filter Calculator.
  • RL low pass — a resistor and an inductor.
  • Inverting op-amp low pass — an active filter that also adds gain and flips the signal.
  • Non-inverting op-amp low pass — an active filter with gain that keeps the signal polarity.

The calculator gives you the cutoff frequency, time constant, phase shift, and more. It also draws Bode plots, pole-zero maps, Nyquist diagrams, and step and impulse responses. You can check how much the filter cuts a signal at any frequency you choose, like 60 Hz hum or switching noise. If you need to work back from a wavelength or period, the Frequency Calculator and Wavelength Calculator pair well with this tool.

Real parts do not come in every value, so the tool snaps your answer to the nearest standard resistor and capacitor sizes. Pick an E6, E12, E24, or E96 series and see the new cutoff frequency and the error. This makes it easy to move from math to a real circuit you can build. Our Resistor Color Code Calculator helps you identify the bands once you have the part in hand.

How to use our Low Pass Filter Calculator

Pick a filter type, type in the values you know, and press Calculate. The tool finds the missing part value, shows the cutoff frequency, time constant, phase shift, step-by-step math, and Bode plots.

Filter type tabs: Choose RC Low Pass, RL Low Pass, Inverting Op-Amp, or Non-Inverting Op-Amp. Each tab shows its own circuit diagram and its own input boxes.

Resistance (R): Type the resistor value and pick Ω, kΩ, or MΩ. You can also type shorthand like 10k or 4.7M. If your resistor is actually a network of parts, work out the total first with the Parallel Resistor Calculator or the general Resistance Calculator.

Capacitance (C): Type the capacitor value and pick pF, nF, µF, mF, or F. Leave it blank if you want the calculator to find it. For series and parallel capacitor combinations, use the Capacitor Calculator.

Inductance (L): On the RL tab, type the coil value and pick pH, nH, µH, mH, or H. Leave it blank to solve for it.

Cutoff Frequency (fc): Type the −3 dB point you want and pick Hz, kHz, or MHz. On the RC and RL tabs, fill in only two of the three boxes and leave one blank.

Desired Gain (Av): On the op-amp tabs, type the passband gain as a plain number, like 10. The non-inverting circuit needs a gain of 1 or more. To convert that gain into decibels, try the dB Calculator.

Anchor resistor (R2, R, or R1): On the op-amp tabs, set one resistor value to lock the design. 10 kΩ works well for most circuits.

Resistor E-Series: Pick E6, E12, E24, or E96 to see the closest real-world part values and how much they shift the cutoff. The Percent Error Calculator is handy if you want to check tolerance stack-ups by hand.

Evaluate at Frequency: Type any frequency, like 50 Hz hum or 100 kHz ripple, then press Evaluate to see the gain, phase, and attenuation there.

Plot and subplot options: Tick the boxes for the magnitude Bode plot, pole-zero map, or Nyquist diagram, and choose phase or group delay for the second plot.

Custom frequency range: Type a start and end frequency for the graphs. Leave both blank to use the auto range of fc/100 to fc×100.

Transient options: Tick the step response, impulse response, final value, or rise time to add them to the results.

Custom simulation time: Type how long the transient plot should run and pick ns, µs, ms, or s. Leave it blank for the auto 5τ window.

What Is a Low Pass Filter?

A low pass filter is a circuit that lets low frequency signals pass through and blocks high frequency signals. Think of it like a screen door: air (low frequencies) gets through, but bugs (high frequencies) do not. Engineers use low pass filters to clean up noise, smooth out signals, and protect audio and sensor circuits from unwanted hiss and buzz.

The Cutoff Frequency

Every low pass filter has a cutoff frequency, written as fc. This is the point where the output signal drops to about 70.7% of the input signal. In decibels, that is a drop of 3 dB, so it is often called the "−3 dB point." Below the cutoff, signals pass almost untouched. Above it, they get weaker and weaker. For a simple one-part (first-order) filter, the signal drops by 20 dB for every 10× jump in frequency.

The Four Filter Types

  • RC low pass (passive): A resistor in series with a capacitor to ground. The capacitor shorts high frequencies to ground. Formula: fc = 1 / (2πRC). This is the most common and cheapest low pass filter. It behaves like a frequency-dependent voltage divider.
  • RL low pass (passive): An inductor in series with a resistor to ground. The inductor fights fast changes in current, so it blocks high frequencies. Formula: fc = R / (2πL). Used more in power and radio circuits. The Impedance Calculator shows how reactance climbs with frequency.
  • Inverting op-amp (active): Adds an amplifier chip. It filters and boosts the signal, but flips it upside down (180° phase shift). Gain = −R2 / R, and fc = 1 / (2πR2C).
  • Non-inverting op-amp (active): Also filters and boosts, but keeps the signal right side up. Gain = 1 + R2/R1, and the cutoff comes only from the input R and C.

Passive vs. Active Filters

Passive filters (RC and RL) use only resistors, capacitors, and inductors. They need no power supply and never make the signal bigger — only smaller. Active filters use an op-amp and a power supply. They can boost the signal, and they do not get thrown off when you connect them to another circuit. Basic current and voltage relationships in either case follow from Ohm's Law.

Time Constant, Phase, and Step Response

The time constant (τ) tells you how fast the filter reacts. For RC it is τ = R × C; for RL it is τ = L / R. After one time constant, the output has climbed to 63.2% of its final value. After about five time constants, it is basically done. The phase shift is how much the output lags behind the input in time. At the cutoff frequency, a first-order low pass filter lags by 45°, and far above cutoff it settles near 90°.

Where Low Pass Filters Are Used

  • Removing hiss and static from audio signals
  • Anti-aliasing filters before an analog-to-digital converter
  • Smoothing noisy readings from temperature, pressure, and other sensors
  • Cleaning ripple off power supply outputs — size the supply itself with the PSU Calculator
  • Blocking radio interference on long cables, where the Wire Resistance Calculator and Voltage Drop Calculator also matter

Picking Real Parts

Math gives you an exact value, but stores only sell certain sizes. These are called E-series values (E6, E12, E24, E96). E24 parts have ±5% tolerance and E96 parts have ±1%. After you round to a real part, your cutoff frequency shifts a little. A good rule: keep resistors between about 1 kΩ and 100 kΩ, then solve for the capacitor. Very small resistors waste power, and very large ones pick up noise. Use the Resistor Calculator to explore combinations, the LED Resistor Calculator for indicator circuits, and the Trace Width Calculator when you lay the design out on a board.


Formulas used

RC low pass cutoff frequency
f_c = \frac{1}{2\pi R C}
RL low pass cutoff frequency
f_c = \frac{R}{2\pi L}
Time constant (RC and RL)
\tau = R C \qquad \tau = \frac{L}{R}
Magnitude response of a first-order low pass filter
\left|H(f)\right| = \frac{1}{\sqrt{1 + \left(\frac{f}{f_c}\right)^2}}, \qquad |H|_{dB} = 20\log_{10}|H(f)|
Phase shift of a first-order low pass filter
\theta(f) = -\arctan\!\left(\frac{f}{f_c}\right)
Group delay
\tau_g(\omega) = \frac{\tau}{1 + (\omega\tau)^2}, \qquad \omega = 2\pi f
Step, impulse response and 10%-90% rise time
v(t) = 1 - e^{-t/\tau}, \qquad h(t) = \frac{1}{\tau}e^{-t/\tau}, \qquad t_r = \tau\ln 9 \approx 2.197\,\tau
Active op-amp low pass design (inverting and non-inverting)
C = \frac{1}{2\pi f_c R_2},\; R = \frac{R_2}{|A_v|},\; A_v = -\frac{R_2}{R} \qquad C = \frac{1}{2\pi f_c R},\; R_2 = R_1(A_v-1),\; A_v = 1 + \frac{R_2}{R_1}

Frequently asked questions

Why do I need to leave one box blank on the RC tab?

The calculator solves for the empty box. Fill in exactly two of the three values (R, C, and fc) and leave the third one blank. If you fill all three, or only one, you will see an error message asking you to clear a field.

Should I pick the resistor or the capacitor first?

Pick the resistor first. Capacitors come in fewer sizes than resistors, but a good rule is to choose an R between 1 kΩ and 100 kΩ, then let the tool solve for C. Round C to a real value, then adjust R to fix the cutoff.

Can I type 10k or 4.7u instead of using the unit dropdown?

Yes. Type SI shorthand like 10k, 4.7M, 100n, or 2.2u. When you click away, the calculator moves the number into the right unit box for you.

How much does the filter cut a signal 10 times above the cutoff?

About 20 dB, which is 1/10th of the original size. At 100× the cutoff you get about 40 dB, or 1/100th. Use the Evaluate at Frequency box to get the exact number for your filter.

What is a pole-zero plot showing me?

It marks where the filter's math blows up on a chart called the s-plane. A first-order low pass filter has one pole sitting on the negative real axis at −1/τ. A pole on the left side means the circuit is stable and will not ring or oscillate.

What is group delay and when should I care?

Group delay is how long the filter holds the signal back, measured in time instead of degrees. It matters for audio and data signals, where different parts of a wave arriving at different times can smear the shape. Low frequencies get delayed by about τ seconds.

What does the Nyquist diagram show?

It plots the real part against the imaginary part of the filter response as frequency rises. For a first-order low pass it traces a half circle from 1 down to 0. Engineers use it to check stability in feedback loops.

What is rise time and how is it linked to the cutoff?

Rise time is how long the output takes to climb from 10% to 90% after a sudden jump. It equals about 2.2 × τ. A quick shortcut: rise time ≈ 0.35 / fc. A faster filter has a higher cutoff and a shorter rise time.

Why is the step response final value always 1?

Because DC is a zero-frequency signal, and a low pass filter passes it fully. The output climbs and settles at the same level as the input. For the op-amp tabs, the final value would be scaled by the gain instead.

Can I make the slope steeper than 20 dB per decade?

Not with one filter. This tool covers first-order filters, which always roll off at 20 dB per decade. To get a steeper slope you stack stages, or use a Sallen-Key or Butterworth design. Two stages give 40 dB per decade.

Will connecting a load change my RC filter's cutoff?

Yes. A passive RC filter feeds the next circuit directly, so a low load resistance pulls the cutoff around and cuts the passband level. Feed it into a high impedance input, or use one of the op-amp tabs instead.

Should I use an RC or an RL filter?

Use RC almost every time. Capacitors are cheap, small, and close to ideal. Inductors cost more, take up space, pick up magnetic noise, and have their own resistance. RL filters show up mostly in power and radio work where current handling matters.

Which capacitor type works best in a filter?

Use C0G/NP0 ceramic or film capacitors. They hold their value steady over temperature and voltage. Avoid cheap X7R or Y5V ceramics in tight designs, since their value can drop a lot when voltage is applied.

Why must the non-inverting gain be 1 or more?

Because its gain formula is 1 + R2/R1. Resistors cannot be negative, so the smallest possible gain is 1. If you enter a value below 1 the tool shows an error. Enter exactly 1 to build a unity-gain buffer.

Why does my op-amp filter not work at very high frequencies?

Every op-amp has a gain-bandwidth product (GBW). Divide the GBW by your gain to find the highest frequency the chip can handle. If your cutoff is close to that limit, pick a faster op-amp or lower the gain.

How do I design a filter to kill 60 Hz mains hum?

Set the cutoff well below 60 Hz, such as 6 Hz, so the hum lands a full decade above and gets cut by about 20 dB. Then type 60 Hz into the Evaluate box to check the exact drop. This only works if your wanted signal is slower than the hum.

Why does the cutoff change after I round to standard parts?

Standard E-series parts rarely match the exact math value. The tool shows the new cutoff and the percent error in the table. Picking E96 (±1%) instead of E24 (±5%) gets you much closer, but those parts cost more.

What is the difference between fc and ω0?

They are the same corner shown two ways. fc is in hertz (cycles per second) and ω0 is in radians per second. Convert with ω0 = 2π fc. Formulas and Bode math often use ω0; datasheets usually list fc.

Does the calculator include the inductor's own resistance?

No. It treats the inductor as ideal. Real coils have DC resistance that adds to R and shifts the cutoff up. For accurate results, add the coil's DCR to your R value before you calculate.

Why is the phase shift 45 degrees at the cutoff?

At the cutoff, the reactance equals the resistance, so the two effects are balanced. That makes the output lag the input by exactly 45°. Far below cutoff the lag is near 0°, and far above it settles near 90°.