How this calculator works
A loudspeaker driver has a mechanical resonance in free air, Fs, and a damping figure, Qts. Putting it in a box adds a spring of air, which raises the resonance and changes the damping. For a sealed box the closed air volume is the spring, and the ratio of the driver Qts to the system Qtc sets the box size: a lower Qtc needs a bigger box, and 0.707 gives the flattest response without a bass peak. For a vented box the port adds a second resonator and the response becomes a fourth-order alignment; the simple Hoge equations estimate the volume and tuning from Vas and Qts alone. Both are approximations, and a full simulation with the driver's other parameters gives a better answer.
Formula
sealed box volume = Vas / ((Qtc / Qts)^2 - 1), with Qtc above Qts. vented box volume = 20 x Vas x Qts^3.3. vented tuning frequency Fb = 0.42 x Fs x Qts^-0.96. All volumes in the same unit as Vas, here litres.
Worked example
A driver with Vas 50 litres and Qts 0.4 in a sealed box tuned for Qtc 0.707: (0.707 / 0.4)^2 = 3.124, so the volume is 50 / (3.124 - 1) = 23.54 litres. In a vented box the estimate is 20 x 50 x 0.4^3.3 = 20 x 50 x 0.0487 = 48.7 litres, tuned to 0.42 x 40 x 0.4^-0.96 = 40.5 Hz.
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Frequently asked questions
What are Vas, Qts and Fs?
They are Thiele-Small parameters measured from the driver. Vas is the volume of air with the same compliance as the driver suspension, Qts describes the overall damping at resonance, and Fs is the free-air resonant frequency. Driver datasheets usually list them, and they are enough to choose a box type and starting volume.
Is a sealed or vented box better?
A sealed box is smaller and simpler, rolls off gradually and handles below-tuning signals without unloading the cone. A vented box is usually bigger and plays louder and lower in its passband, but the cone moves freely below tuning and needs a high-pass filter. The music, the room and the driver all matter more than a general rule.
Why limit the vented alignment to Qts 0.7?
The empirical equations assume a driver with moderate damping. Above about 0.5 the suggested box grows quickly and the response is less flat, and above 0.7 the result is unreliable. Such drivers usually suit a sealed box better, or a different alignment worked out by simulation.
Do I need to add the driver and port volume?
Yes. The calculated volume is the air volume the driver needs. The driver, the port tube and any bracing take up space inside the box, so the external box must be larger by their volume. Add about 10 to 15 percent for a typical build and check the final volume after assembly.