Why is A4 Paper… A4?

It’s getting to that time of the semester again, the part where your brain is somewhere between tired and trying its best, and every test paper starts to look the same. And sometimes, when I’m staring at an exam I’m meant to be focusing on, my mind wanders into questions that have nothing1 to do with the module I’m sitting. The other day, one such thought hit me: why is this sheet of paper, this exact A4 sheet in front of me, the size it is? Why 297 × 210 mm? Why not a nice round 300 × 200? Why not squares? A4 is everywhere from worksheets, lecture notes, problem sheets, printer trays, so if we use it constantly, surely there must be a reason for its exact shape. And even then, what does the ‘A’ even stand for in A4? Are there B4s and C4s? (Spoiler: Yes)