Low Pass Filter Calculator — RC & RL Cutoff Frequency

Calculate fc from R and C — or solve for any two of R, C, L, fc

Operating Mode

Target Variable

Required Parameters

Resistance

Ohm

Capacitance

Waiting for input data...

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Quick Answer

A first-order low pass filter passes frequencies below the cutoff fc and attenuates higher frequencies at -20 dB/decade. RC: fc = 1/(2πRC). RL: fc = R/(2πL). The -3 dB point is where output voltage drops to 70.7% of the input.

Documentation

Low Pass Filter Calculator

Design a first-order passive low pass filter and compute the -3 dB cutoff frequency from resistor and capacitor (or inductor) values — or enter any two of R, C, L, fc to solve for the third.

Quick start: Select RC Low Pass, enter R and C → instant fc. Switch Target Variable to find C for a desired cutoff.

RC low pass filter formula

fc = 1 / (2π × R × C)

Symbol	Meaning
fc	Cutoff frequency (Hz) — -3 dB point
R	Series resistance (Ω)
C	Shunt capacitance (F)

Rearranged:

C = 1 / (2π fc R) — pick C when you know target fc and R
R = 1 / (2π fc C) — pick R when fc and C are fixed

Time constant: τ = RC = 1 / (2π fc)

RL low pass filter formula

fc = R / (2π × L)

Use RL when inductors are preferred (e.g. power-line filtering). Capacitors dominate most signal-level designs because they are smaller and cheaper.

What a low pass filter does

A low pass filter passes low frequencies and attenuates high frequencies. Above fc, response drops -20 dB per decade (first order). Applications:

Anti-aliasing before an ADC (set fc ≤ fs/2)
Power-supply noise filtering on analog rails
Audio / sensor conditioning — remove high-frequency noise
Debounce and slow edge shaping (RC time constant)

Worked example — 1 kHz RC low pass

Target fc = 1 kHz, choose C = 47 nF:

R = 1 / (2π × 1000 × 47×10⁻⁹) ≈ 3.39 kΩ
Nearest E24: 3.3 kΩ → actual fc ≈ 1.03 kHz
Verify capacitor tolerance — use C0G/NP0 for precision

Use Target Variable → Find capacitance (C) in the calculator above with R = 3.3 kΩ and fc = 1 kHz.

RC vs RL — when to use which

Type	Formula	Typical use
RC	fc = 1/(2πRC)	ADC anti-aliasing, audio, GPIO debounce, supply filtering
RL	fc = R/(2πL)	Power inductor filters, low-frequency networks

Common mistakes

Reading fc as a brick wall — first-order filters roll off gently; expect -20 dB/decade, not instant blocking.
Ignoring source impedance — if the driver already has 10 kΩ output Z, your effective R is higher than the printed resistor value.
Y5V/Z5U capacitors — capacitance can collapse under DC bias; cutoff shifts badly. Prefer C0G/NP0 for filters.
Wrong topology — this calculator covers passive first-order RC/RL low pass. Active op-amp filters need different design rules.

Related tools

RC/LC Filter Cutoff Calculator — includes high-pass modes
RC Filter Calculator — RC low pass & high pass only
Reactance Calculator — Xc and XL at any frequency
RC Time Constant Calculator — τ = RC step response
Capacitor Network Calculator — combine caps for target values

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 a low pass filter?

A low pass filter passes frequencies below the cutoff frequency and blocks (attenuates) higher frequencies. A simple RC or RL network rolls off at -20 dB per decade above fc — the standard -3 dB cutoff where power is halved.

How do I calculate low pass filter cutoff frequency?

For an RC low pass filter: fc = 1 / (2π × R × C). Example: R = 10 kΩ, C = 100 nF → fc = 159 Hz. For RL: fc = R / (2π × L). Enter any two values in the calculator to solve for the third.

What is the RC low pass filter formula?

fc = 1/(2πRC), where R is in ohms, C in farads, and fc in hertz. Rearranged: C = 1/(2πfcR) or R = 1/(2πfcC). The time constant τ = RC equals 1/(2πfc).

What is the difference between RC and RL low pass filters?

RC filters use a resistor and capacitor (fc = 1/2πRC) and dominate hobby, audio, and ADC anti-aliasing designs. RL filters use a resistor and inductor (fc = R/2πL) and appear in power filtering where large capacitors would be impractical.

How do I calculate capacitance for a target cutoff frequency?

C = 1 / (2π × fc × R). Example: target fc = 1 kHz with R = 3.3 kΩ → C ≈ 48 nF (use standard 47 nF). Select C0G/NP0 capacitors for precision filters.

What does the -3 dB cutoff mean?

At fc the output voltage is 1/√2 ≈ 70.7% of the input — a 3 dB power reduction. This is the industry-standard definition of filter cutoff for RC, RL, and active filters.

Can I use this for anti-aliasing before an ADC?

Yes. Set fc at or below half your sampling rate (Nyquist). Example: 10 kS/s ADC → fc ≤ 5 kHz. Use the calculator to pick R and C, then verify with a precision capacitor (C0G/NP0).

How steep is a first-order low pass filter?

A single RC or RL stage rolls off at -20 dB/decade (-6 dB/octave). For sharper separation, cascade stages or use active topologies (Sallen-Key, Butterworth). See our RC/LC filter cutoff calculator for high-pass modes too.

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