Speaker enclosure design is one of the few places in DIY audio where a small amount of maths makes a dramatic difference to the end result. Build a box that is too large and bass becomes boomy and ill-defined; too small and the driver is over-damped, losing low-frequency output. This calculator uses the Thiele-Small parameter model — the accepted engineering standard for loudspeaker enclosure design since the early 1970s — to tell you exactly how large to build your cabinet and, for ported (vented) designs, exactly how long to cut the port tube.
How it works
Every loudspeaker driver can be described by a handful of electromechanical constants called Thiele-Small (T/S) parameters, published on the driver datasheet. This calculator uses three of them:
- fs — the driver’s free-air resonant frequency in Hz. Below this point, output drops sharply.
- Qts — the total Q factor, a dimensionless ratio that describes how much mechanical and electrical damping the driver has. Values around 0.3–0.5 suit ported boxes; values above 0.4 suit sealed boxes.
- Vas — the equivalent compliance volume in litres. This is the volume of air that has the same spring stiffness as the driver’s suspension.
Sealed box formula (Thiele-Small, JAES 1972)
For a sealed enclosure with a target system Q of Qtc, the required internal box volume is:
Vb = Vas ÷ ((Qtc ÷ Qts)² − 1)
The system’s resonant frequency then becomes:
fc = Qtc × (fs ÷ Qts)
And the −3 dB rolloff frequency follows from the second-order high-pass response:
f3 = fc × √( (1/Qtc² − 2 + √((1/Qtc²−2)² + 4)) ÷ 2 )
The default Qtc = 0.707 is the Butterworth (B2) alignment — the mathematically flattest possible amplitude response with no bass hump and the best all-round transient behaviour.
Ported box formula (QB3 alignment)
For vented enclosures the calculator applies the QB3 (quasi-Butterworth third-order) alignment, which gives maximally flat group delay. The optimal box tuning frequency relative to the chosen volume is:
fb = fs × (Vas ÷ Vb)^0.32
Port length is calculated with the Thelen round-port formula:
Lp = (23562.5 × d² × Np) ÷ (fb² × Vb) − 0.732 × d
where d is the port diameter in centimetres, Np is the number of ports (one), and Vb is in litres. If you leave the box volume blank, the calculator chooses the QB3-optimal volume automatically using the rule-of-thumb Vb ≈ 20 × Qts³ × Vas.
Worked example
A popular 10-inch woofer has fs = 30 Hz, Qts = 0.38, Vas = 62 L.
Sealed at Qtc = 0.707:
- Vb = 62 ÷ ((0.707 ÷ 0.38)² − 1) = 25 L
- fc = 0.707 × (30 ÷ 0.38) = 55.8 Hz
- f3 ≈ 55.8 Hz
Ported (QB3, 75 mm port diameter):
- Optimal Vb = 20 × 0.38³ × 62 = 68 L
- fb = 30 × (62 ÷ 68)^0.32 = 29 Hz
- Port length ≈ 175 mm at 75 mm diameter
- f3 ≈ 28 Hz — noticeably lower than the sealed design
| Enclosure | Vb | fb / fc | f3 | Character |
|---|---|---|---|---|
| Sealed Qtc 0.707 | 25 L | 55.8 Hz | 55.8 Hz | Tight, accurate |
| Sealed Qtc 1.0 | 10.5 L | 79 Hz | 62 Hz | Warm, smaller box |
| Ported QB3 | 68 L | 29 Hz | 28 Hz | Extended bass |
The ported alignment extends the usable bass output by roughly 20 Hz over the sealed box, at the cost of a steeper rolloff below fb and the need for careful port construction to avoid chuffing at high SPL.
Practical tips
Internal volume is what matters — measure the inside of the box and subtract the driver displacement (usually 0.5–2 L for a 10-inch driver), the port tube volume and any internal bracing. Adding acoustic damping material (polyester wool or long-fibre wool) makes a sealed box behave as if it were about 20–40% larger than its geometric volume, which can be a useful way to hit a target alignment in a slightly-too-small cabinet.