I need to order some welding cable for our shop, but am not sure the correct size to get. I have seen some reference charts, but would like an explanation on how to use them.

Welding cable is the electrical conductor for the welding current. It consists of a series of fine copper strands wrapped inside a non-conductive, durable jacket (typically some type of synthetic or natural rubber of various colors). The fine copper strands give welding cable more flexibility than other types of electrical conductors and the insulating jacket is designed to hold up to repeated movement over rough surfaces. As the current level increases (measured in amperage or amps), the diameter of the welding cable and resulting cross sectional area of the copper stranding needs to increase. The concept is similar to the flow of water through a hose. A larger diameter hose is needed in order to carry a greater volume of water. You use a smaller hose to water your garden, while the fire department uses a much larger hose to fight fires. 

Welding cable “ampacity”, also known as current capacity or amperage rating, refers to the maximum amount of electrical current that a cable can safely conduct.  Besides the cross sectional area, other factors that impact the ampacity of welding cable are its length, ohm rating (i.e., resistance rating), temperature ratings of the insulation material and the ambient temperature. Shorter cables can carry more current than longer cables of the same diameter. Welding cable is often rated with a conductor temperature of 75°C (167° F), 90°C (194⁰F) or 105°C (221°F). While the copper wire itself can handle the high temperatures generated by higher amperages before sustaining damage, the insulation protecting them would melt. Welding cables are also often rated for an ambient temperature of 30°C (86°F). Higher ambient temperatures can reduce their ability to dissipate heat into the surrounding environment, and thus reduce their ampacity. In addition, several cables packed tightly together can also have a reduction in their ability to dissipate heat. Multiple cables should be slightly spread apart.

Note that while copper is an excellent conductor of electricity, it still has a degree of resistance to the flow of electrons through it. Therefore, some amount of resistance heating will occur in the cable. It is normal for a properly sized welding cable to feel warm to the touch after prolonged welding. However, if the diameter of cable is too small for the level of current flowing through it, then the cable will overheat. This can result in a potential fire hazard, as well as damage to the cable itself (and ultimately to cable breakage and failure). A breakdown of the insulation jacket can also be an electrical shock hazard.  Conversely, cable that is oversized for a given amperage level does not conduct current any more effectively than properly sized cable. However, larger diameter cable typically costs more per foot or per meter than smaller diameter cable, because of the increased amount of copper strands. Therefore, oversized cables may not be cost effective.

Electrical cable is typically categorized by an AWG (American Wire Gauge) size, where the smaller diameter cable has a larger number. Figure 1 lists the AWG sizes. Gauge (or gage) sizes larger than one are zero, also expressed as 1/0 (pronounced “one aught”), two zeros, expressed as 2/0 (pronounced "two aught"), 3/0 and 4/0. Cable sizes between #4 and #4/0 are typically used for welding cable.