AudioCalcs
Frequency Response Calculator — Bandwidth & Octave Range
Convert between frequency response specifications and calculate bandwidth.
How We Calculate This
Octaves
Octaves = log2(f_high / f_low)
Decades
Decades = log10(f_high / f_low)
Geometric Centre Frequency
f_centre = sqrt(f_low × f_high)
The geometric centre is used rather than the arithmetic average because frequency perception is logarithmic — each octave sounds like an equal step regardless of the absolute frequency.
Frequently Asked Questions
The standard human hearing range is 20 Hz to 20,000 Hz. Most quality headphones cover this range. Some headphones extend below 10 Hz or above 40 kHz, but these extremes are generally inaudible. More important than range is how flat the response is within the audible range.
A specification like "20 Hz - 20 kHz ±3 dB" means the response stays within a 6 dB window (2 × tolerance) across that range. A tighter tolerance like ±1 dB indicates flatter response. Manufacturers rarely specify tolerance, making frequency range alone less meaningful. Enter your tolerance in Advanced Options and the calculator shows the resulting response window.
The range from 20 Hz to 20 kHz spans approximately 10 octaves (log2(20000/20) = log2(1000) ≈ 9.97). Each octave represents a doubling of frequency. Bass covers about 20-250 Hz (~3.6 octaves), midrange 250-4000 Hz (4 octaves), and treble 4000-20000 Hz (~2.3 octaves).
The geometric centre is the square root of the product of the low and high frequencies. For 20 Hz to 20 kHz, the centre is about 632 Hz. This is more perceptually meaningful than the arithmetic mean because human hearing is logarithmic.
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Last updated: February 2026
All calculations are estimates based on standard formulas. Always verify results for critical applications.