How to use the sealed speaker box volume calculator
- Choose Box size for a Qtc or Qtc of a given box, and the volume unit.
- Enter the driver Vas and Qts from its data sheet. Add Fs if you also want the resonance and the minus 3 dB point.
- For the first mode, enter the Qtc you want. For the second, enter the net box volume.
- Read the box volume in liters and cubic feet, the Qtc, and the box resonance. Add the driver and brace volume in Advanced options to get the size to build.
Formula
Qtc = Qts x sqrt(1 + Vas / Vb)
Vb = Vas / ((Qtc / Qts)^2 - 1)
Fc = Fs x Qtc / Qts
F3 = Fc x sqrt(((1/Qtc^2 - 2) + sqrt((1/Qtc^2 - 2)^2 + 4)) / 2)
A sealed box acts like a spring that raises the resonance and the Q of the driver. A smaller box raises them more. F3 is the frequency where the output is 3 dB below the passband.
A driver with Vas 100 L and Qts 0.40
For a target Qtc of 0.707, the net box volume is 100 / ((0.707 / 0.4)^2 - 1) = 47.08 liters, or 1.6626 cubic feet. With Fs of 28 Hz, the box resonance is 49.49 Hz and the minus 3 dB point is 49.497 Hz, almost the same because 0.707 is the flattest response.
A driver with Vas of 4.2 cubic feet, Qts of 0.38 and Fs of 28 Hz in a 1.5 cubic foot box (42.475 liters) has a Qtc of 0.7408, a resonance of 54.58 Hz and a minus 3 dB point of 52.21 Hz.
Choosing a Qtc
A Qtc near 0.707 gives the flattest response with the least ringing. Lower values such as 0.5 give a tighter, slower roll-off in a larger box. Values above 0.9 add a bump near the resonance, which some people like for a fuller sound, in a smaller box. The best choice depends on the room, the amplifier and taste, so the page lets you try any value above the Qts.
The room itself shapes the bass, which you can explore with the room modes calculator. For splitting a signal between two drivers see the speaker crossover calculator, and for sound speed and wavelengths the speed of sound calculator.
Net and gross volume
The volume the formula gives is the air space the driver sees. The driver itself, any port, bracing and a layer of damping material take space inside the cabinet, so the inside of the box must be larger by that amount. Enter that volume under Advanced options to get the internal size to build.
Assumptions and limits
- The driver follows the small signal model, and the Vas, Qts and Fs values are correct for your unit.
- The box is airtight, rigid and free of port leaks, and any damping material is not counted as a change in volume.
- The target Qtc must be larger than the Qts, because a sealed box can only raise the Q of a driver.
- Room gain, the amplifier and cabinet losses are not modeled.
Frequently asked questions
How do I calculate a sealed box size?
Divide Vas by the square of Qtc over Qts, minus 1. With Vas 100 liters, Qts 0.4 and a Qtc of 0.707 the box is about 47 liters.
What does Qtc mean?
It is the total quality factor of the driver and box together. It describes how the response rolls off near the resonance, with about 0.707 being the flattest.
Where do I find Vas and Qts?
They are listed on the data sheet of the driver, or measured with a test setup. Use the values for your exact model, since similar-looking drivers can differ a great deal.
Why is my box larger than the answer?
The page gives the net air volume. The driver magnet and cone, bracing and any port occupy space, so the inside of the cabinet must be larger by their volume.