RC Low-pass Filter Calculator
This RC Low-pass Filter Calculator determines cutoff frequency, time constant, angular frequency, voltage ratio, gain, attenuation, and phase shift for an ideal first-order passive filter.
Enter resistance, capacitance, and an analysis frequency to check how strongly the filter passes or attenuates that frequency. The results support noise filtering, sensor conditioning, ADC input networks, debouncing, and simple anti-alias design estimates.
The model assumes an unloaded filter driven by an ideal low- impedance source. Real circuits require source resistance, load impedance, capacitor parasitics, tolerance, and settling time to be included in the final design review.
RC Low-pass Filter Calculator
Calculate cutoff frequency, time constant, voltage gain, attenuation, and phase for an ideal first-order RC low-pass filter.
Series resistance between Vin and Vout.
Shunt capacitance from Vout to ground.
Frequency used for gain and phase calculation.
Cutoff frequency (fc)
159.155 Hz
fc = 1 / (2πRC)
- Time constant (τ)
- 1ms
- Angular frequency (ω)
- 6,283.185rad/s
- Output voltage ratio |H|
- 0.157177V/V
- Gain
- -16.072dB
- Attenuation
- 16.072dB
- Phase shift
- -80.957°
At the selected analysis frequency, the ideal output amplitude is 15.72% of Vin with -80.957° of phase lag.
RC Low-pass Filter Diagram
The resistor connects Vin to Vout, while the capacitor shunts higher-frequency energy from Vout to ground.
RC Low-pass Filter Formulas
At cutoff, |H| equals 1/√2 or approximately 0.707, gain is about -3.01 dB, and phase shift is -45 degrees.
Time constant: τ = RCCutoff: fc = 1 / (2πRC)Angular frequency: ω = 2πfVoltage gain: |H| = 1 / √(1 + (f / fc)²)Gain: 20 log10(|H|)Phase: -atan(f / fc)- τ = Time constant in seconds (s)
- fc = Cutoff frequency in hertz (Hz)
- f = Analysis frequency in hertz (Hz)
- |H| = Output-to-input voltage magnitude ratio
- Gain = Signed amplitude response in decibels (dB)
- Phase = Output phase relative to input in degrees
How to Use This Calculator
- Enter the series resistance and choose Ω, kΩ, or MΩ.
- Enter the shunt capacitance and choose pF, nF, µF, mF, or F.
- Enter the frequency where gain and phase should be evaluated using Hz, kHz, or MHz.
- Select Calculate and compare the analysis frequency with fc, then review voltage ratio, dB attenuation, and phase lag.
Worked Example
10 kΩ and 100 nF Filter
R = 10 kΩ = 10,000 Ω
C = 100 nF = 100 × 10⁻⁹ F
τ = RC = 0.001 s = 1 ms
fc = 1 / (2π × 10,000 × 100 × 10⁻⁹)
fc ≈ 159.15 Hz
At 1 kHz, |H| ≈ 0.157, gain ≈ -16.07 dB, and phase shift ≈ -80.96°.
Engineering Notes
RC filter basics
A first-order passive low-pass filter passes frequencies well below fc and rolls off at approximately 20 dB per decade above cutoff.
Noise filtering
Choose fc above the highest wanted signal content but below dominant unwanted noise. Broadband noise may require a higher-order filter.
ADC input filtering
RC networks can limit high-frequency noise at ADC inputs, but resistor value and capacitor settling must satisfy acquisition-time and source-impedance limits.
Anti-alias filtering
A simple RC stage provides limited attenuation near Nyquist. Confirm the complete analog response and use additional filter order when alias rejection is critical.
Sensor filtering
Low-pass filtering can smooth sensor noise and PWM ripple, but excessive RC values add delay and may suppress legitimate transient behavior.
Common Mistakes
- Ignoring source resistance that adds to the intended series resistor.
- Allowing load impedance to shift the ideal transfer function.
- Confusing -3 dB voltage gain with zero output or complete rejection.
- Using nominal capacitance without checking tolerance and DC bias.
- Assuming one RC pole provides sufficient anti-alias attenuation.
FAQ
What is an RC low-pass filter?
An RC low-pass filter uses a series resistor and a capacitor to ground to pass lower frequencies while progressively attenuating frequencies above its cutoff.
How is cutoff frequency calculated?
For an ideal first-order RC low-pass filter, cutoff frequency is fc = 1 / (2πRC), with resistance in ohms and capacitance in farads.
What happens above cutoff?
Above cutoff, output amplitude falls at approximately 20 dB per decade for an ideal first-order filter, while phase approaches -90 degrees.
Why use 0.707 at the cutoff frequency?
At cutoff, the output voltage ratio is 1 / √2, approximately 0.707. This corresponds to -3.01 dB amplitude gain and half the input power for equal impedances.
How do you choose RC values?
Choose an available resistor or capacitor, calculate the other from C = 1 / (2πRfc) or R = 1 / (2πCfc), then check source impedance, loading, tolerance, noise, and settling requirements.
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This calculator provides an ideal unloaded first-order RC response for engineering reference. Verify source and load impedance, capacitor parasitics, tolerance, ADC settling, noise spectrum, sampling rate, and measured frequency response before using the result in production.