RC Low Pass Filter Calculator
Enter resistance and capacitance to calculate time constant and cutoff frequency. Add an optional test frequency to compute gain and phase shift.
What this RC low pass filter calculator does
This tool computes the key parameters of a first-order passive RC low pass filter: the time constant (τ = RC) and the cutoff frequency (fc = 1 / (2πRC)). If you provide a test frequency, it also calculates the amplitude ratio, attenuation in decibels, and phase shift at that frequency.
In practical terms, an RC low pass filter allows lower-frequency signals to pass while reducing higher-frequency components. That makes it useful for smoothing PWM outputs, reducing sensor noise, anti-aliasing before ADCs, and simple tone shaping in analog circuits.
Core formulas used
- Time constant: τ = R × C
- Cutoff frequency: fc = 1 / (2πRC)
- Magnitude response: |H(jω)| = 1 / √(1 + (f/fc)²)
- Gain in dB: 20 log10(|H|)
- Phase shift: φ = -tan-1(f/fc)
How to use the calculator
1) Enter resistor value and unit
Provide resistance in ohms, kilo-ohms, or mega-ohms. For example, 10 kΩ is entered as value 10 with unit kΩ.
2) Enter capacitor value and unit
Provide capacitance in F, mF, µF, nF, or pF. Example: 100 nF means value 100 with unit nF.
3) Optionally enter a test frequency
If you enter frequency, the calculator returns filter behavior at that point: amplitude ratio, attenuation, and phase lag.
4) Click calculate
You will get the time-domain and frequency-domain results instantly. Use reset to clear all fields.
Quick design intuition
- Larger R or C lowers cutoff frequency.
- Smaller R or C raises cutoff frequency.
- At f = fc, output is about 0.707 of input (−3 dB) and phase is about −45°.
- For frequencies much higher than fc, attenuation increases at roughly −20 dB/decade.
Practical engineering tips
Component tolerance matters
Real resistors and capacitors vary from nominal values. A 5% resistor and a 10% capacitor can shift your actual cutoff noticeably. If precision matters, choose tighter tolerance parts or calibrate in software.
Watch loading effects
If the next stage has low input impedance, it changes the effective resistance and moves cutoff frequency. Buffering with an op-amp follower can preserve intended behavior.
Noise vs response trade-off
Lowering cutoff removes more high-frequency noise, but also slows response time. Tune R and C based on acceptable lag.
Example
Suppose R = 10 kΩ and C = 100 nF. Then τ = 0.001 s (1 ms), and fc is about 159.15 Hz. At 1 kHz, gain drops significantly and phase lag increases, which this calculator shows directly.
Frequently asked questions
Is this for active filters?
No. This is for a first-order passive RC low pass filter. Active filters require additional equations.
Can I use this as a cutoff frequency calculator?
Yes. Enter R and C only, and the tool gives cutoff frequency immediately.
What units should I use?
Use whichever is convenient; the calculator converts units automatically. Just pair numeric value and unit correctly.