Resonance Q Factor Calculator
Convert a synthesizer resonance control percentage into its equivalent Q factor value used in filter design. Use this when correlating a synth's resonance knob to the mathematical Q parameter in audio DSP and filter equations.
About this calculator
The Q factor (Quality factor) of a filter describes how sharply it resonates at its cutoff frequency. A higher Q produces a more pronounced, narrow peak; a lower Q produces a gentler, broader response. Many synthesizers expose resonance as a percentage (0–100%) for ease of use, but DSP filter implementations — such as the biquad filter — require Q as a numerical value. The conversion formula maps the percentage linearly onto a Q range: Q = 0.5 + (resonance / 100) × 19.5. At 0% resonance, Q = 0.5, which corresponds to a maximally flat (Butterworth-like) response with no resonant peak. At 100% resonance, Q = 20, which creates an extremely sharp, self-oscillating-like peak. This linear mapping is a common approximation; individual synthesizers may use different curves.
How to use
Suppose your synthesizer's resonance knob is set to 75%. Step 1 — divide by 100: 75 / 100 = 0.75. Step 2 — multiply by the range: 0.75 × 19.5 = 14.625. Step 3 — add the offset: Q = 0.5 + 14.625 = 15.125. A Q of 15.125 is a very high resonance value, producing a sharp, pronounced peak at the cutoff frequency. For comparison, at 50% resonance: Q = 0.5 + (0.5 × 19.5) = 0.5 + 9.75 = 10.25.
Frequently asked questions
What is the Q factor of a filter and why does it matter in synthesis?
The Q factor quantifies the sharpness of a resonant peak at a filter's cutoff frequency. A filter with Q = 0.707 (1/√2) is critically damped with no resonance peak — this is the classic Butterworth response. As Q increases, the peak at the cutoff frequency becomes taller and narrower, emphasizing those frequencies and creating the characteristic 'wah' or 'screaming' sound associated with high resonance. In subtractive synthesis, sweeping the cutoff while maintaining a high Q is the foundation of classic analog filter sounds.
Why does a resonance of 0% give a Q of 0.5 instead of 0?
A Q of 0 would be mathematically problematic and physically meaningless for a second-order filter. The minimum usable Q for a two-pole filter is typically around 0.5, which produces an overdamped response with no resonance peak. This formula sets 0% resonance to Q = 0.5 as a practical floor — the filter is still fully functional, just with the flattest, most gentle rolloff possible. Setting Q below 0.5 would cause the filter poles to become real rather than complex, fundamentally changing the filter's character.
How does Q factor relate to the bandwidth of a resonant filter?
For a bandpass filter, Q is defined as the center frequency divided by the −3 dB bandwidth: Q = f₀ / BW. A higher Q means a narrower bandwidth relative to the center frequency, creating a more selective, sharply tuned filter. For a low-pass filter, Q describes the height of the resonant peak rather than bandwidth directly, but the principle holds — higher Q equals a more pronounced, narrower resonance. Understanding this relationship helps sound designers predict how a filter will behave spectrally when they dial in a specific resonance percentage.