Some time ago, my 19 year-old son, Oscar, asked what a particular matrix was I had on my screen. It was the Freight Classes list, and he seemed to think it was sort of funny and arbitrary: table saws and framed artwork are Class 110, model boats and wood cabinets are Class 300, ping-pong balls and bags of gold dust are Class 500, etc. I tried to explain to him that the freight classes were standards of density and value. The higher the freight class number, the lower the density and/or the higher the value—the lower the freight class number, the higher the density and/or the lower the value. He thought it would be fun to add a couple of specific items to my list: Class 50-grass clippings (I needed to mention to him that in Class 50, the grass clippings would need to be extremely fresh or wet), and for Class 400, which is normally deer antlers, he thought it would be fun to add "lungs." He laughed and laughed at that. He's a weird kid.
Here's the list of Freight Classes, again, I found these online, and they're readily available out there, but they have been useful over time for checking against any errant LTL shipments. By the way, this list is only needed for LTL shipping, as FTL and Parcel don't really use it (to my knowledge).
If you have need to calculate the correct freight class for a particular LTL shipment, I've found this freight class calculator from TranzAct Technologies works well: