RC filter cutoff frequency calculator
The cutoff is where the output has fallen to 70.7% of the input — 3 dB down, and half the power.
ohm
nanofarad
Hz
Cutoff frequency
159.1549Hz
- Time constant
- 0.001 s
- Low-pass gain at the test frequency
- 0.157 177
- Same gain
- -16.0722 dB
- Phase shift
- -80.957 degrees
Show the working
- Resistance = 10 000
- Capacitance = 100
- Frequency to evaluate = 1000
- c_f = 100 * 1e-9 = 0.000 000 1
- Time constant = 10 000 * 0.000 000 1 = 0.001
- Cutoff frequency = 1 / (2 * pi * 0.001) = 159.155
- ratio = 1000 / 159.155 = 6.283 19
- Low-pass gain at the test frequency = 1 / sqrt(1 + 6.283 19^2) = 0.157 177
- Same gain = 20 * log10(0.157 177) = -16.0722
- Phase shift = -deg(atan(6.283 19)) = -80.9569
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
Scenarios & local history
Compare a saved scenario
Recent calculations
The formula
- f_c = 1 / (2 pi R C)
- low-pass gain = 1 / sqrt(1 + (f/f_c)^2)
- first-order roll-off is 20 dB per decade above cutoff.