RC Filter Frequency Response Calculator
Gain in dB, output-to-input ratio and phase shift of a first-order RC low-pass or high-pass filter at any frequency, with its response curve drawn.
Results
Gain at that frequency
-16.07
dB
Cut-off frequency
159.15
Hz
Output ÷ input voltage
0.1572
Phase shift
-80.96
°
The dashed line marks the value you entered.
What this tool does
At the cut-off frequency 1 ÷ 2πRC the output is down 3 dB — about 71 % of the input voltage — and the phase has shifted 45°. Beyond it a single RC stage falls off by only 20 dB per decade, a gentle slope, which is why real filters often cascade several stages or use active designs. The figures assume the source has negligible resistance and the next stage draws no current; a load that does changes the cut-off.
Formula
f_c = 1 ÷ (2πRC) · low-pass |H| = 1 ÷ √(1 + (f/f_c)²) · high-pass |H| = (f/f_c) ÷ √(1 + (f/f_c)²)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
rk | Resistance | kΩ |
cn | Capacitance | nF |
f | Signal frequency | Hz |
ty | Filter type | — |
G | Gain at that frequency | dB |
FC | Cut-off frequency | Hz |
H | Output ÷ input voltage | — |
PH | Phase shift | ° |
Worked example
- Resistance10 kΩ
- Capacitance100 nF
- Signal frequency1000 Hz
- Filter type1
- Gain at that frequency-16.07 dB
- Cut-off frequency159.15 Hz
- Output ÷ input voltage0.1572
- Phase shift-80.96 °
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.