Why are some electrical cords and wires fatter than others?

The current carrying capacity of a particular wire is dictated by its "ampacity" - how many amps it can handle. Ampacity is a function of the cross section area or diameter of the wire and its material type. Larger diameter wires have larger cross section areas and can safely carry more electrical current without overheating. The maximum ampacity for different types of wires is reported in the electrical codes used throughout the industry. These tables are based on the size of the wire and the particular insulation type for the particular wire.

Wire Size Graphic

Insulation Type is important since some insulation materials dissipate heat better than others.