Crank a bargain Bluetooth speaker to full blast and the bass vanishes while the treble turns shrill — no volume knob explains that, because every speaker treats frequencies unequally. In plain words, frequency response reports what fraction of each tone survives the trip through a system: divide the output amplitude by the input amplitude at every frequency, and the curve of those ratios is the response. A flat line near 1.0 means honest sound; a curve that dives past 5,000 hertz means cymbals and consonants arrive muffled. Audio engineers, hearing-aid fitters, and car-stereo installers all read these curves before trusting their ears, because showroom impressions lie and curves do not.

This calculator evaluates the gain at a single point on a simple low-pass response — the curve followed by basic tone controls and speaker crossovers. Type the test frequency in hertz into the Variable A box, say 1000, and the system's cutoff frequency into the Variable B box, say 500. Read the gain ratio from the Result box: about 0.447, meaning a 1,000-hertz tone emerges at less than half its original strength when the cutoff sits at 500 hertz. Sweep Variable A upward to watch high frequencies fade, or drop it below the cutoff to see the gain settle near 1.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Frequency Response Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.