Measure the dimensions of the speaker enclosure from inside the enclosure. For example, if the enclosure is a rectangle, you must measure the length, width and height of the inner space. If necessary, you can measure the dimensions from outside the speaker enclosure, then subtract the thickness of the enclosure material.
Calculate the volume of the enclosure. The volumes of many common shapes are well known. For example, if the speaker is rectangular in shape (a common design for speaker enclosures), you can calculate the volume by multiplying the length, width and height together. If you have an enclosure with a height of 12 inches, a width of 6 inches and a length of 6 inches, the volume of the enclosure is therefore 432 cubed inches.
If the enclosure has an unusual shape, you can fill the container with a known volume with packing material and then measure the volume of the material when it's poured into a standard shape. For example, if material from a 100 cubic-inch box can fill the enclosure 5 times, than the volume of the enclosure is 5 times 100 = 500 cubic-inches.