Band Pass Filter Calculator
Design a band-pass filter from its lower and upper cutoff frequencies.
About Band Pass Filter Calculator
The centre frequency of a band-pass filter is the geometric mean of its cutoffs, not the arithmetic mean, because filter response is logarithmic in frequency. Q is the centre frequency divided by bandwidth. Telephone audio uses roughly a 300 to 3,400 Hz band-pass, giving a Q of about 0.32 — a very wide filter by comparison with radio tuning.
Formula
Band Pass Filter
Centre frequency = √(f_L f_H); bandwidth = f_H − f_L; Q = f₀ ÷ bandwidth
- centre frequency
- Geometric rather than arithmetic mean of the two cutoffs
Worked example
With the default values below, Band Pass Filter Calculator returns Centre Frequency of 1,009.951. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Lower cutoff frequencyminimum 0.01 Hz
- 300 Hz
- Upper cutoff frequencyminimum 0.02 Hz
- 3,400 Hz
- Signal frequencyminimum 0.01 Hz
- 1,000 Hz
Results
- Centre Frequency
- 1,009.951 Hz
- Bandwidth
- 3,100.000 Hz
- Quality Factor
- 0.3258
- Is the Signal in the Passband
- Yes — the signal falls inside the passband
- Fractional Bandwidth
- 306.95%
Step by step
- 1Values used
- 2Band Pass Filter
- 3Centre Frequency= 1,009.951 Hz
- 4Bandwidth= 3,100.000 Hz
- 5Quality Factor= 0.3258
- 6Is the Signal in the Passband= Yes — the signal falls inside the passband
- 7Fractional Bandwidth= 306.95
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax or fees or charges into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How is Band Pass Filter calculated?
Centre frequency = √(f_L f_H); bandwidth = f_H − f_L; Q = f₀ ÷ bandwidth The centre frequency of a band-pass filter is the geometric mean of its cutoffs, not the arithmetic mean, because filter response is logarithmic in frequency. Q is the centre frequency divided by bandwidth.
Why does Band Pass Filter matter?
Telephone audio uses roughly a 300 to 3,400 Hz band-pass, giving a Q of about 0.32 — a very wide filter by comparison with radio tuning.
What values do I need to enter?
This calculator takes 3 inputs: Lower cutoff frequency, Upper cutoff frequency, Signal frequency. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.