Low Pass / High Pass Filter Calculator
-3 dB cutoff for RC and RL filters
Required Parameters
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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).
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
Knowledge Base
Qu'est-ce que la fréquence de coupure à −3 dB ?
C'est la fréquence à laquelle la puissance de sortie est réduite de moitié (tension à 70,7 % de l'entrée). Au-delà, le filtre atténue le signal à raison de −20 dB/décade pour un premier ordre.
Quelle est la formule de coupure d'un filtre RC ?
fc = 1 / (2π × R × C). Exemple : R = 10 kΩ, C = 100 nF → fc = 159 Hz. C'est la formule de base pour les filtres passe-bas et passe-haut de premier ordre.
Quelle différence entre passe-bas et passe-haut ?
Passe-bas : laisse passer les basses fréquences, atténue les hautes (le condensateur est vers la masse). Passe-haut : laisse passer les hautes fréquences (le condensateur est en série avec le signal). Même formule de coupure dans les deux cas.
Comment cascader des filtres pour une pente plus raide ?
Deux filtres RC identiques en cascade donnent −40 dB/décade, mais attention à l'interaction entre étages. Pour des performances optimales, utilisez des topologies actives (Sallen-Key, Butterworth) avec des ampli-ops.
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