How this calculator works
Bandwidth is the difference between the upper and lower cutoff frequencies. For a resonant second-order band-pass filter, centre frequency is their geometric mean and Q is centre divided by bandwidth. These relations recover both cutoff edges from centre and bandwidth using a quadratic equation. A geometric centre differs from an arithmetic midpoint for wide bands; choose the convention required by the application.
Formula
BW = fH - fL; f0 = sqrt(fL fH); Q = f0/BW. fH = (sqrt(BW² + 4f0²) + BW)/2; fL = f0²/fH.
Worked example
Cutoffs of 100 Hz and 400 Hz give bandwidth 300 Hz, geometric centre 200 Hz and Q = 2/3. A 1000 Hz centre with Q = 10 gives bandwidth 100 Hz.
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Frequently asked questions
Is centre the average of the cutoffs?
This tool uses the geometric mean. The arithmetic mean is a different convention and is only close for narrow bands.
Which cutoff level is assumed?
Use the same reference level at both edges, commonly the half-power points of a second-order resonant response.
Can bandwidth be negative?
No. The upper edge must exceed the lower edge, and both must be positive for this geometric-centre model.