Sealed Subwoofer Box Volume Calculator

Sealed (closed) speaker box volume: formula and example

Small's sealed-box equation works out the internal volume from the driver's Thiele/Small parameters: V_box = V_as / ((Qtc/Qts)² − 1). Take Vas = 60 L, Qts = 0.4, Qtc = 0.707. The ratio squared is (0.707/0.4)² ≈ 3.124, which puts V_box at 60 / 2.124 ≈ 28.2 L. The system tuning frequency climbs by that same factor: f_c = f_s · (Qtc / Qts).

Context and applications

DIY home-theater builders tend to pick Qtc ≈ 0.707 (Butterworth) because it gives the flattest response and bass that stays fast and tight, which suits music monitors. Car-audio subwoofers often run Qtc 1.0–1.2 instead, trading a "boomy" sound for a sensitivity bump near tuning. PA fillers usually sit around Qtc 0.5 (Bessel), where transients come through cleanly. Modelling tools such as WinISD, BassBox Pro, Hornresp run the same equation, adding corrections for leakage and stuffing on top.

FAQ

What does Qtc control? Qtc is the system Q once the box is sealed. A lower Qtc means a bigger box, a lower f3, and no overshoot. A higher Qtc gives you a smaller box, a higher f3, and a peak just before rolloff.

Why must Qtc be greater than Qts? A sealed box always raises Q, since the trapped air adds stiffness. So if Qtc ≤ Qts the formula spits out V_box ≤ 0, which can't exist. At that point you need a vented box or a different driver.

Does polyester stuffing change the volume? Yes. Stuffing bumps the effective acoustic volume up by 15–25%, so you can build a slightly smaller cabinet and still land on the same Qtc.