Electronics · Free Calculator
RC and RL Filter Cutoff Frequency Calculator
Find the cutoff (corner) frequency of a first order RC or RL filter, and see how much a signal is attenuated at any frequency.
Low passHigh passRC and RLGain and phase
Cutoff frequency fc159.2 Hz
Time constant1 ms
Low pass gain at 1 kHz0.1572 (−16.07 dB)
Low pass phase−81.0°
High pass gain at 1 kHz0.9876 (−0.11 dB)
High pass phase+9.0°
How this result was calculated
- fc = 1 ÷ (2π R C) = 159.2 Hz
- f ÷ fc = 6.283
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First Order Filter Formulas
RC: fc = 1 ÷ (2π R C)
RL: fc = R ÷ (2π L)
Low pass gain = 1 ÷ √(1 + (f/fc)²)
High pass gain = (f/fc) ÷ √(1 + (f/fc)²)
RL: fc = R ÷ (2π L)
Low pass gain = 1 ÷ √(1 + (f/fc)²)
High pass gain = (f/fc) ÷ √(1 + (f/fc)²)
Worked example
R = 10 kΩ and C = 100 nF give fc = 1 ÷ (2π × 10⁴ × 10⁻⁷) = 159 Hz. A 1 kHz signal through the low pass filter falls to 0.157 of its amplitude (−16.1 dB).
Key insight: at the cutoff frequency the output is 0.707 of the input (−3 dB) and every decade beyond it costs another 20 dB in a first order filter.
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Frequently Asked Questions
What is the cutoff frequency of an RC filter?
fc = 1/(2πRC), the frequency where the output falls to 70.7 % (−3 dB).
How do I make an RC low pass filter for a 4 to 20 mA signal?
Put R in series and C across the input. Choose fc about 5 to 10 times above the fastest change you need to see.
What is the difference between low pass and high pass?
Swap R and C. Low pass takes the output across C; high pass takes it across R.
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