How raised bed volume is calculated
A raised bed is a box, so its soil volume is length x width x depth. A standard 4 by 8 foot bed filled 12 inches deep holds 4 x 8 x 1 = 32 cubic feet. Dividing by 27 gives 1.185 cubic yards. Three of those beds need 96 cubic feet, or about 3.56 yards, which is the point where a bulk delivery usually beats buying bags.
If you measure in inches, the calculator converts to feet first: 48 x 96 x 12 inches is 55,296 cubic inches, and dividing by 1,728 cubic inches per cubic foot gives the same 32 cubic feet. Use the inside dimensions of the frame, since 2 inch thick lumber trims several cubic feet from a large bed.