How can I tell the size of a barrel power connector?
Just look up a fractional inch to mm conversion chart.  Then break out the drill bits.

5/64 inch = 1.9844 mm

3/32 inch = 2.3813 mm

7/64 inch = 2.7781 mm

a 5/64 bit will fit the 2.1mm barrel but not a 3/32

a 3/32 bit will fit the 2.5mm barrel but not a 7/64