AWG is an acronym as American Wire Gauge, a standardised method for measuring the cross-sectional size of the wire. It is used to calculate the amount of current that the wire can carry. 

How do you calculate AWG?

If a cable were one that was a solid circular wire then AWG is relatively easy to determine. Find a size (pi + radius squared) to calculate the cross-sectional area. Then, go to the AWG diagram (example shown below) to determine AWG.

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 If a cable is made up of several strands, the same procedure is used to determine the cross-sectional size of each strand. 

How does AWG influence the electrical property?

You've probably noticed how the lower the size of the AWG the larger the cable. More powerful cables will have lower DC resistance.

What is the reason why certain cables with the same AWG are different in the thickness?

Two factors dominate here. The first is that the AWG is a single-source analysis of the conductors inside. Thus, a manufacturer of cables can easily raise the size of the jacket, making the cable appear to be thicker. 

Another reason why two identical AWG cables might appear different in terms of thickness is the way the internal strands are constructed. 

Wire gauges are certainly an excellent indicator of the quality of a cable to meet your requirements. But it is not a judgment about quality, nor is it an indicator to be used only.