The National Motor Freight Traffic Association (NMFTA) publishes a list of freight class designations, codes, and subclasses for commonly shipped items (https://classit.nmfta.org/). A subscription is required to view this list. You can read more about freight classes at Koho for free on our freight classes pages.
Your freight cost is determined by a number of variables, such as how far your shipment needs to go, the freight class number, whether or not accessorials are needed, as well as fluctuating fuel costs and truck capacity.
If you don't include an NMFC code on your BOL, it is very likely that your carrier will charge you a reclassification fee and charge you the cost of shipping the freight they they determine your shipment is.