Understanding Thiele/Small Parameters for Subwoofer Boxes

Fs is the driver's free-air resonant frequency in Hz, the frequency at which the moving mass and the suspension's springiness naturally want to oscillate when the driver is not mounted in any enclosure. Vas is the equivalent compliance volume, expressed in cubic feet or liters: it is the volume of air that would have the same springiness as the driver's own suspension, which is a way of expressing how stiff or how loose the suspension is in terms everyone can compare across different drivers. Qts is the total Q at resonance, a single number combining Qms, the mechanical Q from the suspension's friction and stiffness, and Qes, the electrical Q from the voice coil and magnet's damping effect. Xmax is the linear one-way excursion in millimeters, the distance the cone can travel from rest in one direction while still moving linearly and accurately. Sd is the effective cone area, and it is smaller than the driver's nominal size suggests because it excludes the surround and only counts the area that actually moves air.

For a sealed box, the target enclosure volume and the resulting system resonance both come directly from Vas, Fs, and the chosen Qts alignment, called Qtc. The equations are Vb = Vas / ((Qtc/Qts)^2 - 1) for the box volume, and Fc = Fs x (Qtc/Qts) for the resulting system resonance in that box. Qtc of 0.707 is the maximally flat alignment, meaning the frequency response rolls off without a peak or an early dip, and it is the most commonly targeted value for a general-purpose sealed subwoofer box. A higher Qtc trades a small response peak near resonance for a smaller box, while a lower Qtc trades a larger box for a gentler, earlier roll-off.

For a vented box using the QB3 alignment, the equations are Vb = 20 x Vas x Qts^3.3 for box volume, Fb = 0.42 x Fs x Qts^-0.96 for the tuning frequency, and F3 = 0.26 x Fs x Qts^-1.4 for the resulting low-frequency roll-off point. These equations are published and standard, but they only describe a useful, well-behaved vented alignment over roughly a Qts range of 0.2 to 0.5. Outside that range the resulting box either becomes impractically large and the tuning too low to be useful, or the alignment stops behaving like a clean vented response at all.

Thiele/Small parameters are published on the manufacturer's product page or spec sheet for a specific driver model, not estimated from the driver's nominal size or price point. Two subwoofers marketed as the same size can have meaningfully different Fs, Vas, and Qts figures depending on their motor design and suspension, which is exactly why a box built for one driver is not automatically correct for another, even one that looks similar on the outside.

In practice, a spec sheet gives Fs, Vas, and Qts, and those three numbers alone are enough to compute either a sealed box volume and resulting resonance, or, if Qts falls in the right range, a vented box volume, tuning frequency, and roll-off point. Xmax and Sd matter for a different question, which is how loud the driver can play cleanly before running out of linear travel, and they do not change the box volume calculation but do matter when pairing a driver with an amplifier and deciding how hard to drive it.