Why do we use A4 as a paper size? We use A4 because it is a ratio of A0, which is 1 square meter of paper. The A system of paper was invented in Germany and adopted by almost all of the countries in the world in 1975. The only countries that don’t use it as the official document size for most government functions are the USA and Canada.
Paper has existed since it was invented in China in roughly 100 AD. The invention is attributed to a court official called Cai Lun, but fragments of paper that predate him have been discovered, so it must have been invented earlier. Before the invention of paper, most countries use papyrus, vellum, parchment, or other types of surface. China was the first country to make a paper from the fibers of plants. They soaked and pounded rags and plants until they could take the mat of fibers and dry them, producing rudimentary paper. Paper was a world changing invention and slowly spread around the world. There were gradual improvements in how it was made but there were no official sizes. Paper was cut as big or as small as the person buying it needed. Books were written by hand so there was no need to have a standard paper size that could fit into a machine, as we do today. Old books, like old bibles, tend to be a variety of sizes. When the printing press was invented, it did standardize paper in some ways, but not others. A printer was likely to print all of one print run of books on paper that was roughly the same size, but different printers might use different sized paper.
As printing became more common and mass-produced paper became possible, the price of books dropped and more people learned to read. Once this happened, books were generally printed on similar sized paper, but it was still not exactly the same. The first person to come up with the idea for standardized paper was a German physicist called Georg Lichtenberg in 1786. He never introduced the system, but he came up with the idea for it. He proposed that paper should be sized on an aspect ratio of the square root of 2. The easiest way to think about this is that each size of paper can be cut into two pieces of the next size down. For example, A3 can be perfectly cut into two pieces of A4. Lichtenberg wrote this idea in an essay, but it was never published during his lifetime. He wrote many essays and kept numerous notebooks that he called scrapbooks. These were all published after his death by his sons.
The idea for standardizing paper was taken up again by a German engineer and mathematician called Walter Porstmann and a Nobel prize winning chemist called Wilhelm Ostwald in 1922. Portsmann worked for the Standards Committee of German Industry, which became the German Institute of Standardization. One of the things Porstmann was involved with was the standardization of paper sizes. The system he came up with was called the DIN system. DIN stands for Deutsches Institut für Normung, which means “German Institute of Standardization”. The DIN system was simple and it was metric. It caught on and over the next fifty years it gradually spread around the world, becoming the accepted size of paper. In 1975, the International Organization for Standardization decide that the German system would be the International system and they renamed it ISO. (Incidentally, ISO doesn’t stand for International Organization for Standardization. It is taken from the Greek word isos, which means equal.)
So, how does the ISO paper system work? Well, there are 3 different systems that use a different starting size, but then they all progress the same way. They all go back to the original idea thought up by Lichtenberg. The A series came first. A0 is the first one and it is a rectangle with an area of 1m2. It has a width of 841 mm and a height of 1189 mm. The next size is A1, which is half the width of AO. 2 A1 papers will fit side by side inside the A0 area. The width of A1 is 594 mm, but the length is 841 mm. The length of each subsequent size is the width of the previous size. This continues all the way down to A10, which is the smallest. If you tried and were very patient, you could fit 2048 A10 pages in the area of one A0 page. The same works for the B sizes and the C sizes, although they start with a different area. The size of B0 is 1.414 m2 and the size of C0 is 1.189 m2. The same properties apply, though, because the width of the previous size is always the length of the next size and you can always fit two of the next size in the area of the previous size. This makes it very easy to scale and very simple to use. And this is what I learned today.
Photo by Mikhail Nilov: https://www.pexels.com/photo/close-up-of-woman-standing-by-desk-with-printer-8297818/
Sources
https://en.wikipedia.org/wiki/Paper_size
https://en.wikipedia.org/wiki/ISO_216
https://en.wikipedia.org/wiki/International_Organization_for_Standardization