What is the size of my seatpost clamp nut? I have this bicycle given by me by a friend, I kept adjusting the height of the bicycle saddle for different members of my family and now the sides of the nut are rounded.
The nut is used to adjust the height of the bicycle saddle using a range.
I believe that the bolt is a carriage bolt? Now I am trying to find what size the nut is and the thread which I don’t understand.
Anyone know where I can buy the same nut online? Please tell me if the pictures aren’t clear, I’m still waiting to use the bike.
This looks like 16 threads per inch, which would indicate a 3/8 inch bolt if you are using SAE sizing.  It would take a 9/16 inch wrench.  If you use a box wrench (or even an open end) you are much less likely to round off the nut than if you use an adjustable wrench.  It could be 10mm, which would have a thread pitch of 1.5 mm and looks like it would take a 17mm wrench.
The threads on your bolt look fine, so take it to the store and test fit the new nut to see if it matches.
Note that your nut has a captive washer on it.  If you buy a standard hex nut you should use a washer behind it.  There may not be enough flat space for a standard washer.  Nuts like this are fairly common, but not as common as the vanilla hex nut variety.