if it is single solid core, measure the size AWG and use charts to determine the ampacity and AWG or if it is strand, measure size of one strand and cound the number of all strands in a cable, compare the size with any cable chart in AWG, company by company cable size ampacity differs but not too much. Finally you can find approximately but not exactly the cable ampacity.
With practice and experience you can tell the size by looking at the outside diameter and the the internal cross section (for example to see if it is copper, aluminium, multi core, steel wire armour, strand count, compacted/un-compacted, etc). Fine selection can then be done with calipers.
This method has many advantages (andI believe is the most common method used in the industry), especially in that samples do not need to be removed for weighing, and yard stock (be it sheathed or unsheathed cable) generally will only consist of a selection of known conductor sizes.
Oh! Pal! You are my type! I too prefer to tell the cable size just by looking at it. And, more often than not, I was correctly judging. That is what you would call experience, huh!
First thing you should do is see if there is still a label on the drum, secondly the ID on the cable sheath. Do this before cutting up cables, stripping insulation and getting precision scales out.