Octave Bandwidth and Q Calculator
What lower and upper frequencies correspond to a geometric center and octave span?
Method, formula and assumptions
Edges are center x 2^(+/-octaveWidth/2). Linear bandwidth is upper minus lower; geometric Q here is center / linear bandwidth.
Input definitions and supported units
- Geometric center frequency (Hz): Measured or assumed numerical value, from 0.01 to 100000; must be positive.
- Total width (octaves): Measured or assumed numerical value, from 0.001 to 10; must be positive.
Worked example with answer
A one-octave band centered at 1,000 Hz spans 707.1068 to 1,414.2136 Hz. Its width is 707.1068 Hz and center/bandwidth ratio is 1.4142.
How to use the results
The center is geometric, not the arithmetic midpoint. Use this to communicate band edges, not to assume a plug-in's Q-to-bandwidth control is identical.
Results retain full precision internally and display up to four decimal places. Very small nonzero results use scientific notation rather than appearing as zero. Check the labels before comparing values across units.
Limitations and references
Manufacturers use different filter conventions, particularly for boosted/cut peaking filters. No filter topology, gain-dependent bandwidth or -3 dB response is implied.
The method is a self-contained arithmetic, geometric or explicitly stated mathematical model. There are no imported tariffs, empirical presets or equipment specifications; measured values and allowances must come from your own process.
Related planning tools
Creator & reviewers
Creator persona
- Casey RowanUnits, conversions & measurement
Reviewer personas
- Devon ShawFormula & assumptions review
- Sage MitchellClarity & usability review