Cutoff Frequency Calculator

Background.

One resistor and one capacitor make the simplest filter electronics has, and a single number characterises it: the cutoff frequency f_c = 1/(2πRC). Below the cutoff a low-pass RC passes signals essentially untouched; above it, attenuation deepens at 6 dB per octave. Swap the two components' positions and the same corner frequency describes a high-pass instead.

The cutoff is not a wall. At f_c itself the output has fallen to 1/√2 of the input — the −3 dB point, where half the signal power is lost — and the transition is gentle on both sides. One octave above the corner a low-pass still passes about 45% of the amplitude; a decade above, 10%. Treating f_c as a brick-wall boundary is the most common misreading of a first-order filter, and the reason audio crossovers and anti-aliasing filters cascade several stages.

The product RC has units of seconds — it is the filter's time constant τ, the same τ that governs how the capacitor charges through the resistor. The frequency-domain corner and the time-domain step response are two views of one number: f_c = 1/(2πτ). A 1 kΩ resistor with a 1 µF capacitor has τ = 1 ms and therefore corners near 159 Hz, whether you look at it with a signal generator or an oscilloscope step.

This page computes the ideal first-order corner. Component tolerance (electrolytics commonly ±20%), source and load impedance loading the divider, and parasitic elements all move a built circuit's corner; the scope note beside the result keeps that boundary honest.

What is cutoff frequency calculator?

The cutoff (or corner, or −3 dB) frequency of a first-order RC filter is the frequency at which the output amplitude falls to 1/√2 ≈ 70.7% of the input — equivalently, where output power is halved. It is set entirely by the resistor-capacitor product: f_c = 1/(2πRC). At this frequency the capacitor's reactance equals the resistance, the phase shift is 45°, and the same value marks the corner whether the RC pair is arranged as a low-pass or a high-pass.

How to use this calculator.

1. 01Enter the resistance in ohms — the value in the signal path for a low-pass, the shunt value for a high-pass.
2. 02Enter the capacitance in farads: 1 µF is 1e-6, 100 nF is 1e-7, 22 pF is 2.2e-11 — unit slips of a thousand are the classic error here.
3. 03Read f_c and mark it mentally as the −3 dB point, not a cliff: signals an octave inside the passband are already down about 1 dB.
4. 04To hit a target corner instead, pick a convenient capacitor and rearrange to R = 1/(2πf_cC) — resistors come in finer value steps than capacitors.
5. 05Derate for reality: ±20% capacitor tolerance moves the corner ±20%, and a load impedance comparable to R drags the corner and passband gain with it.

The formula.

An RC low-pass is a voltage divider whose lower leg is the capacitor's reactance X_C = 1/(2πfC). At low frequency X_C is enormous and the divider passes nearly everything; at high frequency X_C collapses and the output follows it down. The crossover point where X_C = R defines the corner: solving 1/(2πf_cC) = R gives f_c = 1/(2πRC). At that frequency the divider's magnitude is |1/(1+j)| = 1/√2, hence −3 dB and a 45° phase lag. Above the corner each doubling of frequency halves the output — the 6 dB/octave (20 dB/decade) rolloff characteristic of any single pole. The same corner written as ω_c = 1/RC connects to the step response e^(−t/RC): fast filters settle fast, and a corner chosen for smoothing sets the settling time you must accept. The engine computes the reciprocal with Decimal arithmetic, rounding once to twelve significant digits.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, University Physics Volume 2, section 15.3, RLC Series Circuits with AC.
2. [2]Horowitz and Hill, The Art of Electronics, 3rd ed. (PRINT).
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.