RC & RL Filter Calculator — cutoff frequency and response

Cutoff frequency and −3 dB response for low-pass, high-pass and band-pass filters, with a plotted Bode curve.

Example: A RC low-pass filter with these values has a cutoff of 1.592 kHz, rolling off at 20 dB per decade.

Formula

RC: f_c = 1 / (2πRC)    RL: f_c = R / (2πL)    LC: f_c = 1 / (2π√(LC))

Worked example

A RC low-pass filter with these values has a cutoff of 1.592 kHz, rolling off at 20 dB per decade.

  1. f_c = 1 / (2πRC)

    f_c = 1 / (2π × 1 kΩ × 100 nF)

    f_c = 1.592 kHz

  2. at f_c, gain = 1/√2

    20 × log₁₀(0.707)

    −3.01 dB

    The cutoff is defined as the half-power point, not where the filter stops working.

Frequently asked questions

How do I calculate RC filter cutoff frequency?

f_c = 1 / (2πRC). A 1 kΩ resistor with a 100 nF capacitor gives about 1.59 kHz. Swapping which component sits in series determines whether it is low-pass or high-pass; the cutoff formula is the same either way.

What does the −3 dB cutoff actually mean?

It is where output power drops to half the input, which is a voltage ratio of 1/√2 ≈ 0.707. It is not where the filter stops passing signal — a first-order filter still passes 10% of a signal a decade past cutoff.

Why is my filter not blocking noise as well as I expected?

First-order filters roll off at only 20 dB per decade, which is gentle. To reject something close to your passband you need a steeper filter: cascade stages, use an LC or active topology, or move the cutoff further from the signal you want to keep.

Does the load affect the cutoff frequency?

Yes, and it is a common surprise. Whatever the filter drives appears in parallel with its output element and shifts the cutoff. Keep the load impedance well above the filter's own, or buffer the output with an op-amp.

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