RC Low Pass Filter Calculator
Enter the resistor and capacitor values to get the −3 dB cutoff frequency and the RC time constant. The same formula applies to first-order low pass and high pass filters.
Result
- Cutoff frequency in hertz
- 159.155 Hz
- Angular cutoff frequency
- 1 krad/s
- Time to charge to 99.3% (5τ)
- 5 ms
Formula
- f_c = 1 ÷ (2π × R × C)
- τ = R × C
- At f_c the output is 70.7% of the input, which is −3 dB
How the RC Low Pass Filter Calculator works
A resistor and capacitor form the simplest filter. Taking the output across the capacitor passes low frequencies and attenuates high ones. Taking it across the resistor does the opposite. Both share the same cutoff frequency.
Above the cutoff a first-order low pass filter rolls off at 20 dB per decade. The time constant is the time the capacitor takes to charge to 63.2 percent of a step input.
Worked example
With R = 10 kΩ and C = 100 nF, τ = 10,000 × 0.0000001 = 0.001 s, or 1 ms. The cutoff frequency is 1 ÷ (2π × 0.001) = 159.15 Hz.
Frequently asked questions
What does −3 dB mean?
It is the point where output power is half the input power and output voltage is 70.7 percent of the input. It is the standard definition of a filter's cutoff frequency.
How do I choose R and C for a given cutoff?
Pick a convenient capacitor, then compute R = 1 ÷ (2π × f_c × C). For 1 kHz with 10 nF, R is about 15.9 kΩ.
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