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Equalizer Filter Q & Bandwidth

Calculate equalizer Q factor from center frequency and bandwidth, or convert between Q, octaves, and frequency limits.

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Formula

Q = f₀ / BW

f₀— Center frequency (Hz)
BW— -3 dB bandwidth (Hz)

How It Works

Q factor (Quality factor) in a parametric equalizer describes the sharpness of the peak or notch filter. Q = f₀ / BW, where f₀ is the center frequency and BW is the −3 dB bandwidth. A high Q produces a narrow, sharp boost or cut affecting a small range of frequencies; a low Q produces a broad, smooth adjustment. The relationship between Q and octave bandwidth is non-linear: BW_octaves = log₂(f_upper / f_lower), where f_upper and f_lower are the frequencies at which gain equals half the peak gain. For standard parametric EQ filters, the bandwidth in octaves is related to Q by: BW_oct ≈ log₂(1 + 1/(2Q²) + √(1/Q + 1/(4Q⁴))) — a formula that simplifies to BW ≈ 1/Q in octaves for narrow filters (Q > 2). Professional mixing typically uses Q values of 0.5–2 for broad tonal shaping and Q = 5–30 for narrow notch filtering to remove specific problem frequencies.

Worked Example

Parametric EQ: center frequency f₀ = 1000 Hz, bandwidth BW = 200 Hz. Q factor: Q = 1000 / 200 = 5.0 Bandwidth in octaves: Using the exact formula with Q = 5: BW_oct ≈ log₂(1 + 1/(2×25) + √(1/5 + 1/2500)) = log₂(1 + 0.02 + √(0.2004)) = log₂(1 + 0.02 + 0.4477) = log₂(1.4677) ≈ 0.554 octaves Approximate: BW_oct ≈ 1/Q = 1/5 = 0.2 oct (only accurate for higher Q) Frequency limits at −3 dB: f_lower = 1000 / 2^(0.554/2) = 1000 / 1.468 = 681 Hz f_upper = 1000 × 1.468 = 1468 Hz A Q of 5 produces a relatively narrow cut/boost centred on 1 kHz, affecting the range 681–1468 Hz.

Practical Tips

  • ✓For surgical notch filtering (removing hum, buzz, or specific resonances), use Q = 10–30 to precisely target the problem frequency without affecting surrounding frequencies. A 60 Hz hum notch at Q = 20 affects only ±3 Hz, leaving the bass guitar unaffected.
  • ✓Most digital parametric EQs (DAW plugins) offer a linked Q control where bandwidth scales with boost/cut amount — gentle boosts are broad, deep cuts are narrow. This is perceptually natural and reduces phase distortion at small boost amounts.
  • ✓The 'musical' Q range for broad tonal adjustments (bass, presence, air) is Q = 0.5–1.0 (1–2 octave bandwidth). This mimics the natural broad character of acoustic instruments and rooms rather than introducing coloration.

Common Mistakes

  • ✗Confusing Q with bandwidth in Hz — Q is dimensionless and constant for a given filter shape regardless of center frequency. The same Q = 2 filter centred at 100 Hz has a 50 Hz bandwidth; centred at 4000 Hz it has a 2000 Hz bandwidth.
  • ✗Assuming constant dB skirts — the −3 dB bandwidth is measured at the peak gain, not at 0 dB. A 12 dB boost with Q = 2 has a different perceptual bandwidth than a 3 dB boost with Q = 2, even though the −3 dB points are the same.
  • ✗Applying very narrow Q notches to fix room problems — a sharp notch (Q > 20) at a room mode frequency corrects only the on-axis measurement position. Moving slightly changes the mode's effect. Broader room treatment (acoustic panels) is more effective than narrow EQ for room-mode problems.

Frequently Asked Questions

Neve 1073: low shelf and high shelf with fixed broad Qs (≈0.7). SSL G-series: bell filters at approximately Q = 0.6–1.0 for broad tonal shaping. API 550: proportional-Q design where Q increases with boost/cut amount. Pultec EQP-1A: passive filter with very broad, overlapping bands (Q ≈ 0.5–0.7).
A graphic EQ has fixed center frequencies (typically 1/3-octave or 1-octave spacing) with adjustable gain only. A parametric EQ lets you adjust center frequency, gain, and Q independently, giving full control. Semi-parametric (quasi-parametric) EQs offer adjustable frequency but fixed Q.
For Q > 2 (narrow filters): BW_oct ≈ 1/Q. For Q = 1: BW_oct ≈ 1.39 octaves. For Q = 0.7: BW_oct ≈ 2 octaves. For Q = 0.5: BW_oct ≈ 3 octaves. These are approximations; use the full formula for precise calculations.

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