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A Q factor calculator does one small job that comes up constantly: your measurement software reports a problem as a bandwidth in octaves, and your equaliser asks for Q. They describe the same bell, but almost no EQ will convert between them for you. The tool below does, in both directions, and draws the resulting filter so you can see what you are about to apply.
Q, bandwidth and octaves
Your measurement software reports a problem in octaves. Your equaliser asks for Q. They describe the same bell. Enter whichever one you have and read the other two, with the filter drawn underneath.
f₀ = 120 Hz, Q = 4.00, 0.36 octaves, Δf = 30.0 Hz, gain -6 dB
What Q factor actually means
Q is the ratio of a filter's centre frequency to its bandwidth. A peaking EQ band centred at 120 Hz with a Q of 4 has a bandwidth of 30 Hz, because 120 ÷ 4 = 30. That is the whole definition. Everything else follows from it:
- Higher Q means a narrower filter that affects less of the spectrum.
- Lower Q means a wider, gentler filter that shapes overall tone.
- Q is dimensionless, so the same Q is proportionally as wide at 60 Hz as at 6 kHz.
- The bandwidth is measured between the half-gain points, not the −3 dB points, for a peaking filter.
That last point matters. For a bell boosting 6 dB, the bandwidth is measured where the curve passes 3 dB — half the gain — not where it has fallen 3 dB below flat. Different manufacturers have historically used different conventions, which is one reason the same Q number can look slightly different between two equalisers.
Converting Q to bandwidth in octaves
Octaves are the unit measurement software speaks, because they describe width in a way that is musically meaningful. The conversion is the standard audio EQ relation:
N = (2 / ln2) × asinh(1 / 2Q) and Q = 1 / (2 × sinh((ln2 / 2) × N))
Those are not approximations — they are the definitions implemented inside the biquad filters in virtually every digital equaliser, including the DSP in the Xylem and Root 4 amplifiers.
| Q | Bandwidth (octaves) | At 60 Hz | At 120 Hz | At 1 kHz |
|---|---|---|---|---|
| 0.5 | 2.54 | 120.0 Hz | 240.0 Hz | 2000 Hz |
| 0.7 | 1.92 | 85.7 Hz | 171.4 Hz | 1429 Hz |
| 1 | 1.39 | 60.0 Hz | 120.0 Hz | 1000 Hz |
| 1.41 | 1.00 | 42.6 Hz | 85.1 Hz | 709 Hz |
| 2 | 0.71 | 30.0 Hz | 60.0 Hz | 500 Hz |
| 3 | 0.48 | 20.0 Hz | 40.0 Hz | 333 Hz |
| 4.32 | 0.33 | 13.9 Hz | 27.8 Hz | 231 Hz |
| 6 | 0.24 | 10.0 Hz | 20.0 Hz | 167 Hz |
| 10 | 0.14 | 6.0 Hz | 12.0 Hz | 100 Hz |
| 20 | 0.07 | 3.0 Hz | 6.0 Hz | 50 Hz |
Two rows there are worth memorising. Q 1.41 is almost exactly one octave wide, and Q 4.32 is almost exactly one-third of an octave — the resolution most RTA displays use, which makes it the natural starting Q when you are correcting something a third-octave analyser showed you.
Which Q to use, and when
- Q 0.5 to 0.7 — broad tonal shaping. Lifting a dull room or taming overall brightness. Nearly inaudible as an artefact.
- Q 1 to 1.5 — musical correction. Wide enough to sound natural, narrow enough to mean something.
- Q 2 to 4 — targeted. One room mode, one cabinet resonance, one boundary bump.
- Q 5 to 10 — surgical. Removing a single ringing mode. Only correct for the seat you measured.
- Q above 10 — effectively a notch. Feedback suppression, or a resonance you are certain about.
Why a narrow boost is not a narrow cut
This is the part worth internalising, because it is where most EQ goes wrong. A narrow cut removes energy from a resonance, and is nearly always safe. A narrow boost at the same Q and the same frequency drives that resonance harder, lengthens its decay, and consumes amplifier headroom you do not get back. Room correction is therefore mostly subtraction. If a measurement shows a 12 dB dip, the honest response is usually to move the speaker or the seat, not to add 12 dB of boost into a null — the null is a cancellation, and you cannot amplify your way out of one.
The same letter means something different in a crossover
Q appears twice in loudspeaker work and the two uses are easy to confuse. In a parametric equaliser, Q describes how wide a bell is. In a crossover or an enclosure alignment, Q describes damping — how a second-order filter behaves around its corner. A Butterworth crossover has a Q of 0.707, which is the maximally flat case; a Linkwitz-Riley alignment uses 0.5, which is why two Linkwitz-Riley halves sum flat while two Butterworth halves sum to a 3 dB bump. A driver's own Q, usually written Qts, describes how its resonance is damped and decides what kind of enclosure suits it. None of these are the EQ bandwidth above, even though they share the symbol. If you need the component values rather than the bandwidth, use the crossover calculator instead.
Q and room modes
Below the Schroeder frequency a room behaves modally, and those modes are themselves high-Q resonances. A mode with a long decay will show up on a frequency response as a narrow peak, which invites a narrow cut. That often helps, but EQ cannot shorten a decay the room is still generating — it only reduces how hard the mode is driven. Work out which modes you actually have first, then decide what is worth correcting.
What the calculator cannot tell you
The arithmetic is exact; the room is not. Above the Schroeder frequency the response varies so much from seat to seat that a high-Q correction fixes only the microphone position. Filters also interact: two overlapping bells do not sum to the curve either one draws alone. And a measurement taken at one volume will not describe a system whose DSP applies equal-loudness compensation at another. Measure in the room, apply, then measure again — which is what the calibration toolkit in XSCACE Studio is for.