RC Filter Cutoff Calculator
Cutoff frequency of a first-order RC or RL low-pass or high-pass filter, the gain and phase at any frequency, and the R or C (L) to hit a target cutoff.
Where a simple filter rolls off and how much it attenuates a given frequency — with the −3 dB point, the 20 dB per decade slope and the phase shift stated — or the part to fit for a cutoff you want.
Example: 10 kΩ and 10 nF cut off at 1,592 Hz. As a low-pass that leaves 10 kHz at −16.1 dB (×0.157, −81°); as a high-pass, 100 Hz sits at −24 dB. For a 1 kHz cutoff with 10 kΩ, C = 15.9 nF.
−3 dB at the corner,
−20 dB every decade after.
Where the cutoff comes from, how gain and phase behave around it, and why the load matters.
The cutoff frequency
A resistor and a capacitor (or inductor) form a frequency-dependent divider. The corner is where the reactance equals the resistance: for a capacitor 1 ÷ 2πfC = R, so f_c = 1 ÷ 2πRC; for an inductor 2πfL = R, so f_c = R ÷ 2πL. At that frequency the output is 1/√2 of the input, −3.01 dB, and the phase shift is 45°. Which of the two parts feeds the output decides whether the network passes low or high frequencies.
Gain and phase at any frequency
A first-order low-pass has |H| = 1 ÷ √(1 + (f/f_c)²): flat well below the corner, then falling at 20 dB per decade (6 dB per octave); the high-pass is the mirror image, and the two responses satisfy |H_lp|² + |H_hp|² = 1 at every frequency. The phase runs from 0 to −90° for the low-pass and +90° to 0 for the high-pass. The page evaluates both at a frequency you name and tabulates a decade either side of the corner.
Solving, loading and limits
Given a target cutoff and one component, the other follows by rearranging the corner formula; pick a preferred value afterwards and re-check. The formulas assume nothing is connected to the output and the source has zero impedance; a load resistor in parallel with the capacitor, or a source resistance in series, moves the corner, so buffer the output or fold those impedances into R. Second-order and active filters, ripple and component tolerance are outside this page. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- First-order RC/RL frequency response, |H| = 1/√(1 + (f/f_c)²) — standard circuit theory (e.g. Nilsson & Riedel, Electric Circuits, chapter 14)
Last reviewed 19 September 2026. How results are checked: How we verify.