Filter Cutoff Frequency Calculator
Find the -3dB cutoff frequency for low-pass and high-pass filters.
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Formulas
fc = 1 / (2πRC)RC filter cutoff
fc = R / (2πL)RL filter cutoff
Filter Cutoff Frequency
The cutoff frequency is where the output signal is attenuated by 3dB (about 70.7% of input). Below cutoff: signal passes (low-pass). Above cutoff: signal is attenuated. Used in audio, RF, and power supply design.
What the Cutoff Frequency Is
A simple RC filter passes some frequencies and attenuates others. The cutoff frequency marks the boundary — the point where the output power has fallen to half (−3 dB) of the passband. It is set by the resistor and capacitor values:
fc = 1 / (2πRC)fc is the cutoff frequency in hertz, R is resistance in ohms, C is capacitance in farads.
In a low-pass filter, frequencies below fc pass and higher ones are attenuated; a high-pass filter does the reverse, using the same formula.
Worked Example
R = 1.6 kΩ, C = 100 nF:
fc = 1 / (2π × 1600 × 100×10⁻⁹) ≈ 995 Hz
Signals above ~1 kHz are progressively rolled off at 6 dB per octave.
Filter Behaviour
A first-order RC filter rolls off at 6 dB per octave (20 dB per decade) beyond the cutoff. At the cutoff frequency itself the signal is attenuated by 3 dB and shifted 45° in phase. For sharper roll-off, multiple stages or active filter designs are used.
| Filter type | Passes | Attenuates |
|---|---|---|
| Low-pass | Below fc | Above fc |
| High-pass | Above fc | Below fc |
Frequently Asked Questions
Why is the cutoff defined at −3 dB?
That is the half-power point, where output power is exactly half the passband. It is a consistent, physically meaningful reference for comparing filters.
How do I make the roll-off steeper?
Cascade multiple RC stages or use an active filter (Sallen-Key, etc.). Each additional order adds another 6 dB/octave.
Does this formula work for RL filters too?
RL filters use fc = R/(2πL). The RC formula here is for resistor-capacitor filters specifically.