A 1/2” wrench or socket may or may not fit a 13 mm fastener depending on dimensional tolerance. A 13mm wrench or socket can be used on a 1/2” fastener. It is always good to have a vise grip and a crescent wrench. I keep two sizes of both in my box. Also I have one of the universal sockets that will fit any size square or hex head fastener up to 3/4”, metric or SAE. But I have used it only once that I can remember. It worked. One of my most used hand tools is a water pump pliers.