Low Pass / High Pass Filter Calculator

-3 dB cutoff for RC and RL filters

Operating Mode

Required Parameters

Resistance

Ohm

Capacitance

Waiting for input data...

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Quick Answer

The -3dB cutoff frequency (fc) is where the signal power drops by half. For RC filters: fc = 1 / (2πRC). For RL filters: fc = R / (2πL).

Documentation

Filter Cutoff Frequency Calculator

Calculate the -3dB cutoff frequency of passive RC and LC filters. Design low-pass, high-pass, band-pass, and band-stop filter networks.

RC Filter Cutoff

fc = 1 / (2pi x R x C)

Where:

fc = Cutoff frequency (Hz)
R = Resistance (Ohms)
C = Capacitance (Farads)

LC Filter Cutoff

fc = 1 / (2pi x sqrt(L x C))

Filter Types

Type	Passes	Blocks	Order
Low-pass	Below fc	Above fc	1st: -20dB/dec
High-pass	Above fc	Below fc	1st: -20dB/dec
Band-pass	f1 to f2	Outside band	2nd order
Band-stop	Outside band	f1 to f2	2nd order

Design Example

Low-pass filter at 1 kHz:

Choose C = 100 nF
R = 1/(2pi x 1000 x 100n) = 1.59 kOhm
Nearest standard: 1.5 kOhm -> fc = 1.06 kHz

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Design Notes

First-order passive filters only roll off at -20dB per decade. They are great for simple noise filtering, anti-aliasing before a slow ADC, or debounce circuits, but inadequate for separating close frequencies. When designing RC filters, avoid using extremely large resistors (e.g., >1MΩ) because the input bias current of the next stage (like an Op-Amp or ADC) will cause a DC voltage error. Conversely, avoiding extremely small resistors (<100Ω) will save power and prevent overloading the driving source.

Common Mistakes

1
Expecting a sharp cutoff from a simple RC filter. It's a gentle curve, not a brick wall.
2
Not balancing the source impedance. If your signal source already has 10kΩ output impedance, and you use a 1kΩ series resistor for your filter, your effective R is 11kΩ.
3
Ignoring capacitor tolerances. Cheap Y5V or Z5U ceramic capacitors can vary by +20%/-80% with temperature and DC bias, completely ruining your cutoff frequency.

Engineering Handbox

1. Identify variables: R = 10,000, C = 0.0000001 2. Multiply R × C = 0.001 seconds (Time Constant τ) 3. Multiply by 2π: 0.001 × 6.283 = 0.006283 4. Divide 1 by result: 1 / 0.006283 = 159.15 Hz

VerificationThe cutoff frequency is approximately 159.15 Hz.

Knowledge Base

What is the -3dB cutoff frequency?

The -3dB point is where output power drops to half (-3.01 dB) of the input, or voltage drops to 70.7% (1/√2). This is the standard definition of 'cutoff' for passive filters and is used universally in electronics, audio, and RF engineering.

Does a higher capacitance lower the cutoff frequency?

Yes. In an RC filter, fc = 1/(2πRC). Doubling either R or C halves the cutoff frequency. For example, changing from 10nF to 100nF with a 10k resistor moves the cutoff from 1.59 kHz down to 159 Hz.

What is the formula for RC low pass filter cutoff?

fc = 1 / (2π × R × C), where fc is in Hz, R in ohms, and C in farads. Example: R = 10k, C = 100nF gives fc = 1 / (6.283 × 10000 × 0.0000001) = 159.15 Hz.

What is the difference between low pass and high pass?

A low pass filter passes frequencies below the cutoff and blocks higher frequencies. A high pass filter does the opposite — it passes frequencies above the cutoff and blocks lower ones. Both use the same formula for the -3dB point, just with swapped component positions.

How steep is the rolloff of a first-order filter?

A single RC or RL filter rolls off at -20 dB/decade (or -6 dB/octave). This means every 10x increase in frequency above cutoff reduces the signal by 20 dB. For steeper rolloff, cascade multiple stages: 2nd order = -40 dB/decade, 3rd order = -60 dB/decade. Use active filter topologies (Sallen-Key, Butterworth) for multi-order designs.

What is the difference between RC and RL filters?

RC filters use a resistor and capacitor: fc = 1/(2πRC). RL filters use a resistor and inductor: fc = R/(2πL). RC filters are far more common because capacitors are smaller, cheaper, and more precise. RL filters are used mainly in power applications and at very low frequencies where the required capacitor would be impractically large.

How do I filter noise from a power supply?

Place a low pass RC filter on the supply rail. For typical switching noise (100 kHz-1 MHz), use R = 10-100 ohm with C = 100nF-10uF. A 10 ohm + 100nF filter has fc = 159 kHz, attenuating switcher harmonics. For sensitive analog circuits, add a ferrite bead instead of a resistor for better high-frequency rejection.

What is an anti-aliasing filter?

An anti-aliasing filter is a low pass filter placed before an ADC (analog-to-digital converter) to remove frequencies above half the sampling rate (Nyquist frequency). Without it, high-frequency signals fold back as spurious low-frequency artifacts. Set the filter cutoff at or below fs/2 (e.g., 5 kHz for a 10 kS/s ADC).

Which capacitor type should I use for a filter?

For precision filters: C0G/NP0 ceramic (tight tolerance, stable with temperature/voltage). For general filtering: X7R ceramic (good up to 10uF but value drops with DC bias). Avoid Y5V/Z5U ceramics for filtering — their capacitance can drop by 80% with temperature and applied voltage, completely shifting your cutoff frequency.

Can I use a filter calculator for audio crossovers?

Yes, but single RC stages give only -6 dB/octave rolloff which is too gentle for speaker crossovers. Most audio crossovers use 2nd order (-12 dB/octave) or higher, with Butterworth (flat passband) or Linkwitz-Riley (flat summed response) alignments. Use this calculator for the individual stage cutoff, then cascade.

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