Band Pass Q and Half Power Bandwidth Calculator
Convert an ideal second-order band-pass center frequency and Q into half-power edges, hertz bandwidth and octave width.
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Result
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Calculation steps
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How to calculate
Calculate bandwidth as center frequency divided by Q. Recover the two positive edge frequencies whose product is center frequency squared and whose difference is bandwidth.
BW=f0/Q; fL×fH=f0²; fH−fL=BW; octaves=log2(fH/fL)
Worked example
At center 1000 Hz and Q=1, bandwidth is 1000 Hz, lower edge about 618.034 Hz and upper edge about 1618.034 Hz.
Assumptions and input details
Half-power (approximately −3.0103 dB) bandwidth of an ideal analog second-order band-pass response with center gain normalized to one. The center is geometric, not the arithmetic mean of the edges. Digital equalizer peaking, constant-Q conventions and octave bandwidth definitions can differ; no digital-filter coefficients or sampled-frequency warping are calculated.
Unit definitions
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SI prefixes are explicit: for example, milli means one thousandth, micro one millionth and kilo one thousand. Changing a unit changes the interpretation of the entered number.
Using this calculator
Can I enter my own problem?
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Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
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