Calculating Volume of a Rectangular Box
This example is a rectangular shaped enclosure utilizing two 12" woofers. After taking measurements inside the vehicle, the following external dimensions of our planned enclosure resulted.
Exterior Dimensions
Accounting for 3/4-inch (0.75) thick material, the interior dimensions are then calculated. The thickness of the material is subtracted twice from each dimension, representing the two opposite sides for each dimension. When using a divider or partition, the material is subtracted three times for the width, representing the two sides and the partition. These calculations result in the interior dimensions.
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topInterior Dimensions
Volume can now be calculated. The formula for calculating volume of a rectangular box is:
Volume = Legnth x Width x Height
V
= |
Volume |
Length
= |
16.5 inches |
Width
= |
36.75 inches |
Height
= |
14.5 inches |
V
= |
16.5 x 36.75 x 14.5 |
V
= |
8792.438 cubic inches |
The volume of this rectangular enclosure measures 8792.438 cubic inches.
We now compensate for speaker basket and vent displacement. The basket displacement for an average 12" woofer measures 209 cubic inches. Vent (port) displacement calculation typically uses the formula for the volume of a cylinder.
Volume of a Cylinder
In this case, we are using a 4-inch port, and it’s outside diameter measures 4.5 inches. Due to thickness of port material, you will need to measure the outside diameter of the vent, and use this for calculation. The radius will be exactly half of the outside diameter. In the formula for vent volume, length represents the measure for the port that is inside the enclosure. For our example the vent volume goes like this:
Volume of a cylinder = 3.14 x Radius x Radius x Length
Volume = |
3.14 x Radius x Radius x Length |
Radius = |
4.5 x .5 = 2.25 inches |
Length = |
11.5 - .75
= 10.75 |
V = |
3.14 x 2.25 x 2.25 x 10.75 |
V = |
170.98 cubic inches |
Now we have obtained both speaker basket and vent displacement. When calculating we multiply the speaker and vent displacements by the number of each being used. Subtracting these from the enclosure volume, total usable volume yields
Usable airspace |
= |
Enclosure volume - speaker(s) volume - vent(s) volume |
= |
8792.438 - (2 x 209) - (2 x 170.98) | |
= |
8032.478 cubic inches | |
Finally, we convert this figure into cubic feet.
V |
= |
8032.478 / 1728 |
V = |
4.648 cubic feet | |
Since we are using two speakers in this enclosure, it is necessary to divide the total usable volume by two
Volume per speaker = 4.648 / 2
V = 2.324 cubic feet per speaker
Important Note: This example happened to work on the first attempt, and happened to achieve an enclosure that matched the recommended volume for that speaker. In most cases, one would need to vary the physical dimensions (length, width, or height) accordingly until the desired enclosure volume is achieved. This means that one might have to calculate the enclosure volume a few times before obtaining the appropriate enclosure dimensions for your specific application
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