RC/RL First-Order Filter Calculator

A single resistor with a single capacitor or inductor makes the simplest possible frequency-selective circuit: a first-order filter with one cutoff (corner) frequency. For the RC forms, f_c = 1/(2πRC); for the RL forms, f_c = R/(2πL). At that corner the output is 3.01 dB below the passband — the half-power point — and the phase shift is exactly 45°.

Above or below the corner the behavior is beautifully simple: magnitude rolls off at 20 dB per decade (6 dB per octave), and the phase runs from 0° to −90° for the low-pass (or +90° to 0° for the high-pass), passing through its 45° midpoint at the corner. The normalized response is the same whether the components are an RC anti-aliasing filter, an RL choke feeding a load, or the unintended pole formed by a source resistance and cable capacitance.

This calculator computes the cutoff for any of the four topologies, evaluates magnitude (in dB and as a linear ratio) and phase at any frequency of interest, and draws the full Bode plot — magnitude on the left axis, phase dashed on the right — over four decades around the corner. Use it to place a pole where you need it, or to check how much a known pole disturbs the band you care about: at one-tenth of f_c a low-pass still passes 99.5% amplitude but has already accumulated 5.7° of phase lag, which is often the surprise in feedback loops.

For resonant (second-order) behavior with Q and peaking, use the second-order filter calculator.