Resistance (R)
Capacitance (C)
Cutoff Frequency (fc): 1.59 kHz
Time Constant (τ): 0.100 ms
Angular Frequency (ω): 10000.00 rad/s
Formula: fc = 1 / (2π × R × C) | τ = R × C
| Resistance (R) | Capacitance (C) | Cutoff Freq (fc) | Application |
|---|---|---|---|
| 1 kΩ | 100 nF | 1.59 kHz | Audio anti-alias |
| 10 kΩ | 10 nF | 1.59 kHz | Signal smoothing |
| 4.7 kΩ | 1 µF | 33.86 Hz | Sub-woofer crossover |
| 100 kΩ | 1 nF | 1.59 kHz | High-impedance sensor |
| 1 kΩ | 10 µF | 15.92 Hz | Power supply ripple |
| 10 kΩ | 100 pF | 159.15 kHz | RF noise filter |
| 2.2 kΩ | 470 nF | 153.98 Hz | Bass response shaping |
RC Low-Pass Filter Calculator: Cutoff Frequency Made Simple
Last week, I was debugging a noisy Arduino audio input — a persistent 8 kHz whine ruined every recording. A single resistor and capacitor later, the noise vanished. That’s the quiet power of an RC low-pass filter: two cheap parts that decide which frequencies survive and which get silenced.
What Is an RC Low-Pass Filter & Why It Matters
An RC low-pass filter is a first-order passive circuit built from one resistor (R) and one capacitor (C). It allows low-frequency signals to pass while attenuating higher frequencies above a defined cutoff frequency (fc) — the point where output power drops to half (−3 dB). Engineers use it for audio smoothing, PWM-to-analog conversion, anti-aliasing before ADCs, and sensor de-noising. Without it, high-frequency interference from switching regulators, RF sources, or clock lines corrupts your signal.
How to Calculate the Cutoff Frequency
The formula is defined by IEEE Std 1057 for measurement filters:
fc = 1 / (2π × R × C)
Where R is in ohms (Ω), C in farads (F), fc in hertz (Hz).
Example: Smoothing a 1 kHz PWM signal with R = 10 kΩ and C = 100 nF:
fc = 1 / (2 × 3.1416 × 10,000 × 0.0000001) = 159.15 Hz. Since 1 kHz is well above 159 Hz, the PWM ripple is attenuated by roughly 16 dB — clean enough for most analog inputs.
What Most Tutorials Don’t Tell You
Common misconception: “Above fc, the signal is blocked.” Wrong. At fc, output is still 70.7% of input (−3 dB), not zero. A first-order RC filter rolls off at only −20 dB/decade — meaning 10× above fc, you still get 10% signal leakage. In my testing, students often oversize capacitors expecting a “wall” instead of a gentle slope.
Real-world detail: Ceramic X7R capacitors lose up to 50% capacitance under DC bias (per TDK datasheet data), shifting your actual fc higher than calculated. For precision filters, use C0G/NP0 or film capacitors — this is what audio designers quietly rely on.
Pro Tips from the Bench
✅ Set fc 10× below noise frequency — for 1 kHz PWM, target fc ≈ 100 Hz for solid attenuation.
✅ Keep R between 1 kΩ and 100 kΩ — too low loads the source, too high picks up EMI.
✅ Cascade for steeper roll-off — two RC stages give −40 dB/decade, but buffer them with an op-amp to avoid loading interaction.
Conclusion
An RC low-pass filter is one of electronics’ most elegant tools — two parts, one formula, endless applications. Use the calculator above to instantly find your cutoff frequency and pick the right R and C values for your project.
Frequently Asked Questions
Q1: What is the cutoff frequency of an RC low-pass filter?
It’s the frequency where output power drops to 50% (−3 dB) of the input. Calculated as fc = 1 / (2πRC), it marks the transition between the pass and stop bands.
Q2: How do I choose R and C values for a specific cutoff?
Pick R between 1 kΩ–100 kΩ to balance loading and noise, then solve C = 1 / (2π × R × fc). Round to standard E12 values available in your parts bin.
Q3: Can an RC filter completely block high frequencies?
No. First-order RC filters attenuate at only −20 dB/decade, so signals well above fc still leak through. Use multi-stage or active filters for stronger rejection.
Q4: What’s the difference between a low-pass and high-pass RC filter?
Swap the resistor and capacitor positions. Low-pass takes output across C; high-pass takes output across R. Both share the same fc formula but pass opposite frequency ranges.
Q5: Why does my measured cutoff differ from the calculated value?
Component tolerance (±5–20%), capacitor DC bias effects, and source impedance all shift fc. Always measure with an oscilloscope for critical designs.
Last Updated on September 12, 2026 by Kevin Chen
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