Octave-Band Frequency Edges Calculator｜Lower/Upper Edges, Bandwidth & Q From a Center Frequency
Enter a center frequency and a band fraction to see the lower edge, upper edge, bandwidth, Q factor, and the offset to the nearest ISO 266 standard center, all on one screen. Six band fractions from 1/1 to 1/24 are supported.
💡 About this tool
If you do room acoustics measurements or set up EQ, you keep running into the same question: "For a 1/3-octave band centered at 1000 Hz, where exactly do the edges fall?" Punching 2^(1/6) into a calculator is tedious, and pulling the Q factor and the nearest standard band at the same time is extra work even when you know the formula by heart.
This tool takes the center frequency fc and the band fraction 1/N and immediately shows the lower edge f_lower = fc / 2^(1/2N), the upper edge f_upper = fc · 2^(1/2N), the bandwidth BW = f_upper − f_lower, and the quality factor Q = fc / BW. It then scans the ISO 266 preferred centers (both the 1/1-octave grid and the 1/3-octave grid), finds the closest band, and reports the offset in cents. Seeing how far your target sits from a standard band in semitone-scaled units makes it straightforward to lay out graphic-EQ bands or set measurement bands on an analyzer.
Inputs run from 1 Hz to 200000 Hz, so beyond the audible range (20 Hz to 20 kHz) you can also work with sub-audio vibration analysis or ultrasonic bands.
🧐 Frequently Asked Questions
Q. What are the edges of a 1/3-octave band centered at 1000 Hz? The lower edge is about 890.90 Hz and the upper edge is about 1122.5 Hz. Each edge sits one-sixth of an octave (a factor of 2^(1/6)) from the center.
Q. The Q came out as 4.32. What does that mean? Q = center frequency / bandwidth is a dimensionless measure of how sharp the band is. A 1/3 octave is roughly Q ≈ 4.3; the finer the fraction (the larger N), the narrower the band and the higher the Q.
Q. What are the ISO 266 standard center frequencies? They are the preferred centers defined by ISO 266, ANSI S1.11, and IEC 61260: a logarithmic series anchored at 1000 Hz (16, 20, 25, 31.5, … 16000, 20000 Hz). The tool shows the nearest standard band on both the 1/1 and 1/3 grids and gives the offset in cents.
Q. Does base-2 vs base-10 change the result? The edge math here uses the base-2 definition (2^(1/2N)). The ISO preferred centers themselves are defined on a base-10 grid (10^(1/10) ≈ 2^(1/3.32)), but the practical difference is tiny and the band numbering matches either way.
📚 Why third-octave is the working standard
Third-octave analysis became the de-facto standard in acoustics because human hearing perceives frequency logarithmically. The audible 20 Hz–20 kHz range splits into roughly 10 bands at full octave and about 31 bands at one-third octave, and the latter hits the sweet spot between spectral detail and a manageable band count. That is exactly why so many graphic EQs ship as "31-band" models.
The word "octave" comes from the musical eighth (a 2:1 frequency ratio), but in acoustics it is decoupled from note names and simply means "the interval over which frequency doubles." Because the bands stack geometrically rather than linearly, equal screen widths on a spectrum analyzer represent equal ratios of frequency, which is why log-frequency plots dominate the field.