We are often asked for help figuring out what size wire you currently have so we have the following tips:

Always start by looking on the side of the wire for printing that should tell you the wire size. 
Sometimes there is a stamp in the connector which indicates the size as well. 

Different styles of stranding in the cable as well as various insulation thicknesses mean there is not a "one size fits all" exact measurement but here are measurements based on a range of typical battery cable styles as a reference. (when in doubt between wire sizes ALWAYS choose the larger wire size)

Wire Gauge Size COPPER CONDUCTOR Diameter (no insulation) Overall Outside Diameter with Insulation
80.143-0.165 inch (3.63-4.19 mm) 0.218-0.270 inch (5.54-6.86 mm)
60.181-0.200 inch (4.60-5.08 mm) 0.305-0.340 inch (7.75-8.64 mm)
40.219-0.252 inch (5.56-6.40 mm) 0.343-0.405 inch (8.71-10.29 mm)
20.289-0.326 inch (7.34-8.28 mm) 0.418-0.475 inch (10.62-12.07 mm)
10.341-0.361 inch (8.66-9.17 mm) 0.479-0.520 inch (12.17-13.21 mm)
1/0 (0)0.348-0.405 inch (8.84-10.29 mm) 0.500-0.565 inch (12.70-14.35 mm)
2/0 (00)0.429-0.460 inch (10.90-11.68mm) 0.568-0.655 inch (14.43-16.64 mm)
3/0 (000)0.485-0.510 inch (12.32-12.95mm) 0.641-0.670 inch (16.28-17.02 mm)
4/0 (0000)0.555-0.580 inch (14.10-14.73mm) 0.695-0.741 inch (17.65-18.82 mm)

The table above was built using commonly found battery cable styles from an assortment of manufacturers and is a great resource to help you narrow down what cable size you're looking at.