Octave Band Center Frequency Calculator

Octave and fractional-octave bands are defined by ANSI S1.11 and IEC 61260 relative to the 1,000 Hz reference. For base-10 systems, the center frequency of band index x is fc = 1000 * 10^(x / (10 * n)) for fractional-octave designation, but the common base-2 convention uses fc = 1000 * 2^(x / n), where n is the number of bands per octave (1 for octave, 3 for one-third octave).

A full octave band spans a 2:1 frequency ratio: the upper edge is the square root of two above the center and the lower edge is the square root of two below it, so upper / lower = 2. The edges are fc * 2^(1/(2n)) and fc / 2^(1/(2n)) for a 1/n-octave band, so a one-third-octave band has edges about 2^(1/6) above and below the center.

The bandwidth is the upper edge frequency minus the lower edge frequency. For an octave band it is about 70.7 percent of the center frequency, and for a one-third-octave band about 23.2 percent. The calculator returns the band edges and bandwidth from the center frequency and the bands-per-octave setting you choose.

One-third-octave analysis gives finer frequency resolution than full octaves while still smoothing the response into perceptually meaningful bands. It is the standard resolution for many acoustic measurements such as room response, noise spectra and sound-level meter displays, because it balances detail against the manageable number of bands (about 31 across the audible range).

The nominal (rounded) octave band centers used in acoustics are 31.5, 63, 125, 250, 500, 1000, 2000, 4000, 8000 and 16000 Hz. These are convenient labels; the exact calculated centers differ slightly (for example 31.25 or 31.623 Hz depending on the base-2 or base-10 convention). This calculator returns the exact computed values.