Biquad Filter Coefficient Calculator
Generate normalized low-pass, high-pass or peaking biquad coefficients and inspect ideal response and pole magnitudes.
YOUR CALCULATION
Result
—
Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Apply the RBJ Audio EQ Cookbook formulas, normalize denominator a0 to one and evaluate the complex response.
H(z)=(b0+b1z⁻¹+b2z⁻²)/(1+a1z⁻¹+a2z⁻²)
Worked example
A low-pass section with Q=1/√2 at design cutoff 1000 Hz has magnitude 1/√2 at that frequency, about −3.0103 dB. Returned recurrence subtracts the a1/a2 feedback terms.
Assumptions and input details
Design frequency must be between 0.00001fs and 0.49999fs, Q between 0.05 and 100, peaking gain −40 to 40 dB. Query spans DC to Nyquist. Pole magnitudes near one are rejected within the stated numerical margin. Q follows the cookbook, including its peaking convention. Coefficients are floating point and do not guarantee fixed-point implementation behavior; no audio is uploaded or installed.
References: W3C: RBJ Audio EQ Cookbook formulas
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
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?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
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.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Evaluate the magnitude and wrapped phase of an entered real FIR filter at a query frequency and plot its DC-to-Nyquist response.
Calculate a real numeric record’s one-sided DFT amplitude spectrum, complex bins, phase, DC mean and dominant non-DC bin.
Calculate first-order low-pass or high-pass amplitude, phase and corner frequency.
Reserved advertising space.