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Subwoofer Enclosure Volume

Calculate optimal subwoofer box (sealed and ported) volume and port tuning frequency from Thiele-Small parameters (Vas, Qts, Fs).

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Formula

Vb = Vas / ((Qtc/Qts)² − 1) [sealed]

Vas— Equivalent compliance volume (L)
Qtc— Target box Q (0.707 Butterworth)

How It Works

Subwoofer enclosure design relies on Thiele-Small (T/S) parameters: Fs (free-air resonant frequency), Qts (total Q factor combining electrical and mechanical damping), and Vas (equivalent compliance volume in litres — the air volume that matches the driver's mechanical compliance). For a sealed box, the optimal internal volume for a Butterworth (maximally flat) response with system Q of Qtc = 0.707 is: Vb = Vas / ((Qtc/Qts)² − 1). This gives a response 3 dB down at approximately F3 = Fs × (Qtc/Qts). For vented (ported) boxes, empirical formulas based on Qts give a larger box volume with a lower tuning frequency and greater bass extension but a steeper rolloff below the tuning frequency. Drivers with Qts < 0.35 are suited for vented enclosures; Qts 0.35–0.7 suit sealed boxes; Qts > 0.7 may work in open-back (free-air) or infinite baffle applications.

Worked Example

Driver T/S parameters: Vas = 50 L, Qts = 0.35, Fs = 35 Hz. Sealed box (Butterworth, Qtc = 0.707): Vb = 50 / ((0.707/0.35)² − 1) = 50 / (4.082 − 1) = 50 / 3.082 = 16.2 L F3 = 35 × (0.707/0.35) = 35 × 2.02 = 70.7 Hz Vented box (approximate empirical formulas): Vb = 20 × Qts^3.3 × Vas = 20 × (0.35)^3.3 × 50 = 20 × 0.032 × 50 ≈ 32 L Port tuning frequency: Fb = 0.76 × Qts^0.26 × Fs = 0.76 × (0.35)^0.26 × 35 = 0.76 × 0.722 × 35 ≈ 19.2 Hz The vented box extends bass deeper (~20 Hz tuning) but requires twice the enclosure volume. Sealed at 16 L is more compact with a higher but well-controlled F3.

Practical Tips

  • ✓Add 15–20% to the calculated Vb to allow for air volume displaced by internal bracing, damping material, and driver displacement. Measure the finished box volume with water or calculate from interior dimensions minus structures.
  • ✓Line the sealed box with 25–50 mm of acoustic foam or polyester fibrefill. This acoustically 'stretches' the box — a stuffed sealed box behaves as if it were 10–25% larger, allowing a smaller physical enclosure.
  • ✓Port length and diameter interact with box volume to determine tuning frequency. The formula Fb ≈ (c/(2π)) × √(A/(Vb × L_eff)) (Helmholtz resonance) sets port tuning, where A = port area, L_eff = effective port length including end corrections (~0.85 × radius per open end).

Common Mistakes

  • ✗Using net internal volume without subtracting driver displacement and bracing — a driver with Vd = 2 L in a 16 L box leaves only 14 L net. Always subtract driver, port tube, and bracing volumes from the target Vb.
  • ✗Treating the formulas as precise — these are simplified alignment formulas. Real-world enclosures need simulation software (WinISD, REW, Hornresp) to account for port losses, driver nonlinearity, room gain, and baffle step effects.
  • ✗Building a ported box for a driver with Qts > 0.5 — high-Qts drivers in vented enclosures tend to produce a bloated, one-note bass with a pronounced hump around the port tuning frequency. Sealed boxes are more forgiving of driver Qts variations.

Frequently Asked Questions

A sealed box is simpler to build and has a gentler rolloff below F3 (−12 dB/octave). A ported box uses a Helmholtz resonator port to extend bass output below the driver's natural resonance, but rolls off much more steeply below the port tuning frequency (−24 dB/octave). Ported boxes are generally larger and more complex to design.
Qts < 0.35: vented (ported) alignment preferred — these drivers have high damping and benefit from the port's contribution to bass extension. Qts 0.35–0.7: sealed box is optimal — moderate damping suits the sealed alignment. Qts > 0.7: the driver is underdamped and may need a very large or open enclosure; conventional sealed or vented designs may not work well.
Yes. The same Thiele-Small equations apply to any moving-coil driver. The formulas are valid for woofers covering 40–500 Hz as long as you use the driver's correct T/S parameters. For full-range and midrange drivers in small sealed boxes, the same Vb formula applies.

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