Electronics · Filters
RC filter cutoff calculator.
Enter R and C for the cutoff, add a test frequency for attenuation, or fill R and a target cutoff to find C.
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RC filter cutoff formulas
A first-order RC filter has a cutoff (−3 dB) frequency of fc = 1 ÷ (2π × R × C), in hertz when R is in ohms and C is in farads. At fc the output power is half the input (−3.01 dB) and the voltage gain is 0.707.
Gain at another frequency. With x = f ÷ fc, the voltage gain of a low-pass filter is 1 ÷ √(1 + x²) with phase −arctan(x). For a high-pass filter it is x ÷ √(1 + x²) with phase +arctan(1/x). These follow from the standard transfer functions H(s) = 1/(1 + sRC) and sRC/(1 + sRC).
Worked example. 1 kΩ and 100 nF give fc = 1 ÷ (2π × 1,000 × 10⁻⁷) = 1,591.5 Hz. At 10 kHz a low-pass filter passes about 0.157 of the voltage, or −16.1 dB.
A first-order filter rolls off at only 20 dB per decade. A real source and load impedance shift the effective R, so buffer the output if the load is small.
Frequently asked questions
What is the cutoff frequency of an RC filter?
fc = 1 ÷ (2πRC). For 1 kΩ and 100 nF it is about 1,591 Hz.
What does the −3 dB point mean?
It is where the output power falls to half, or the voltage to 70.7% of the input.
How do I choose C for a target cutoff?
C = 1 ÷ (2π R fc). Leave the capacitance blank and enter R and the target; the page also shows the nearest E12 value.
What is the difference between low-pass and high-pass?
A low-pass filter passes frequencies below fc and attenuates those above. A high-pass filter does the reverse. They use the same R and C and the same fc.
How steep is a first-order RC filter?
It falls 20 dB per decade (about 6 dB per octave) above the cutoff for low-pass.
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Scope and safety
Low-voltage hobby and study use only. Results are ideal-component arithmetic from the formulas shown, not an engineering design or professional advice. Real parts vary with tolerance, temperature and age, so check the datasheet for every part. Never work on mains-powered circuits from a calculator result, and discharge large capacitors safely before handling.