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First-Order RC Low-Pass Filter — result sheet
Calculate the cutoff frequency, time constant, gain, phase shift, and output amplitude of a simple RC low-pass filter.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: f꜀ = 1/(2πRC); τ = RC; |H(f)| = 1/√(1 + (f/f꜀)²); phase = −atan(f/f꜀).
A single-pole RC low-pass filter passes slow voltage changes more readily than fast ones when the output is taken across the capacitor. The cutoff is the frequency where the magnitude is 1/√2 of the low-frequency gain.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Resistance — Ω; minimum 1.0E-6; maximum 1000000000
- Capacitance — µF; minimum 1.0E-9; maximum 1000000
- Signal frequency — Hz; minimum 0; maximum 1000000000
- Input amplitude — V; minimum 0; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Resistance | 1000 |
| Capacitance | 0.1 |
| Signal frequency | 100 |
| Input amplitude | 1 |
1,591.55 Hz cutoff and 0.998 V output amplitude
Assumptions and limits
- The circuit is a passive first-order RC network with output measured across the capacitor.
- The source and load do not materially change the stated resistance or capacitance.
- The result is a small-signal frequency response and does not model component parasitics, distortion, noise, or power limits.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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