There are many square shaped stamps and a couple of brands as well.
To help you visualise them we have produced a pdf for you with them all on a page side by side to compare brand at a time.

See the square stamp sizes side by side.

Use this pdf below to see all the self-inking stamps side by side. Print it out to see them in actual size to find the perfect one for you.
Click here to view a pdf guide to view rubber stamp sizes alongside each other.
Click on the stamp in the pdf to get to the stamp in the website nice and quick to order.

The 40mm size stamps can also be used for a Company Common Seal Stamp or a Society Common Seal stamp.

The small 12x12mm stamps are excellent for loyalty cards. Do check the surface of your card for a porous surface for the standard water based ink. Gloss or coated surfaces will need to us supply special ink for these circumstances and that adds cost.