RC and RL Filter Calculator: Cut-off Frequency, Gain, Phase and Bode Plot for Low-Pass and High-Pass Filters
First-order RC and RL filters with a Bode plot.
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How this calculator works
Choose an RC or RL circuit and a low-pass or high-pass filter.
Enter the resistance and the capacitance or inductance.
Enter the signal frequency to get the gain, the phase and a Bode plot.
Formulas used
- f_c = \frac{1}{2\pi R C}
- f_c = \frac{R}{2\pi L}
- |H| = \frac{1}{\sqrt{1 + (f/f_c)^2}}
- \phi = -\arctan(f/f_c)
Worked example
With the default numbers in the calculator above:
- Cut-off frequency (where the gain is -3 dB): 1591.5 Hz
- Time constant: 0.0001 s
- Gain at your frequency (output voltage divided by input voltage): 0.46865
- Gain in decibels: -6.583 dB
- Phase shift of the output: -62.053 degrees
Change the numbers in the calculator to see the full working, every step, for your own case.
A second worked example
A different case, with these numbers: Filter type High-pass (the output is across the resistor, or across the inductor for RL).
- Cut-off frequency (where the gain is -3 dB): 1591.5 Hz
- Time constant: 0.0001 s
- Gain at your frequency (output voltage divided by input voltage): 0.88338
- Gain in decibels: -1.077 dB
- Phase shift of the output: 27.947 degrees
Common questions
What is the cut-off frequency?
The frequency where the output power falls to half, which is where the gain is 0.707 of the input or -3 dB.
What is the roll-off of a first-order filter?
20 dB per decade, which is 6 dB per octave, beyond the cut-off frequency.
What is the phase shift at the cut-off frequency?
45 degrees: a lag for a low-pass filter and a lead for a high-pass filter.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any electronics or circuits text (first-order filters, Bode plots).
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