What is Qtc and what value should I aim for?

Qtc is the total Q of the driver-in-box system. A Qtc of 0.707 (Butterworth) gives a maximally flat response with the best low-frequency extension before roll-off; 0.5 is over-damped and tight; values above 0.8 are punchier but boomier with a peak near Fc.

How is the box volume calculated from a target Qtc?

The compliance ratio alpha equals (Qtc ÷ Qts)² − 1, and the box volume is Vas ÷ alpha. A larger box (smaller alpha) gives a lower Qtc and deeper extension; a smaller box raises Qtc and Fc.

What is Fc and how does it relate to Fs?

Fc is the system resonance once the driver is in the sealed box. Adding the air spring of the enclosure always raises resonance above the free-air Fs by the factor √(alpha + 1), the same factor that scales Qts up to Qtc.

Do I need to add volume for the driver and bracing?

Yes. The calculated figure is the net internal air volume the driver sees. Add roughly 10-15 percent for the displacement of the driver basket, magnet and any internal bracing, then build to that gross internal volume.

Why choose sealed over ported?

Sealed boxes are smaller, simpler, have a gentler 12 dB/octave roll-off and superior transient response and group delay — ideal for accurate music. Ported boxes go louder and deeper for the same driver but are larger and ring more.

Sealed Subwoofer Box Volume Calculator

A design tool for car-audio and home-theatre builders sizing a sealed (closed) subwoofer enclosure. Feed it the driver’s Thiele-Small parameters and it returns the ideal box volume plus the system behaviour you can expect.

How it works

A sealed box turns the air inside into a spring that adds to the driver’s own suspension, raising both its resonance and its Q. The key relations are:

alpha = Vas / Vb              (compliance ratio)
Qtc   = Qts × √(alpha + 1)    (system Q)
Fc    = Fs  × √(alpha + 1)    (system resonance)

To design for a target Qtc, the tool inverts these: alpha = (Qtc / Qts)² − 1 and Vb = Vas / alpha. It then reports the resulting Fc, the −3 dB cutoff, and a predicted relative-response curve computed from the standard second-order high-pass transfer function.

Choosing a Qtc

Qtc	Character
0.5	Maximally damped, tightest transients, least extension
0.577	Bessel — best group delay
0.707	Butterworth — maximally flat, the usual sweet spot
0.8-1.0	Smaller box, more output near Fc, slightly boomy

A driver’s own Qts sets the floor: you can only raise Q by making the box smaller, never lower it below the free-air value with a sealed box.

Worked example

A driver with Vas = 50 L, Fs = 28 Hz, Qts = 0.40, targeting Qtc = 0.707:

alpha = (0.707 / 0.40)² − 1 ≈ 2.12
Vb = 50 / 2.12 ≈ 23.6 L
Fc = 28 × √3.12 ≈ 49.5 Hz

Tips and notes

The volume figure is net internal air. Add 10-15% gross volume for driver and bracing displacement.
Stuffing the box with polyfill makes it behave as slightly larger (lowering Qtc a touch) and tames internal reflections.
If your target Qtc is at or below the driver’s Qts, a sealed box cannot reach it — choose a driver with a lower Qts or accept a higher Q.

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