Paper sizes

My boyfriend and I went to a printing shop last month and saw a poster with different paper sizes, from A0 to A8. What do these numbers mean and how are they defined?

Definition of A-series paper sizes

The A-series paper follows the ISO 216 standard of writing paper and certain classes of printed matter. There are three main requirements:
  1. The length divided by the width (aspect ratio) is 1.4142 (√2).
  2. The A0 size has an area of 1 square meter.
  3. Each subsequent size is defined as the previous size cuts in half parallel to its shorter side. For instance, A1 has half of the area of A0 and it can be created by folding an A0 paper parallel to its shorter side.
The dimension of an A0 paper is 841 mm x 1,189 mm to the nearest millimetre. An A1 paper has a  dimension of 594 mm x 841 mm. The image below compares different paper sizes in the A series.
Image from Wikipedia


The magic root 2

An advantage of the A-series paper is that it can be up/down scaled to other A-series sizes without any distortion, meaning the paper manufacturers do not have to cut off the margins. Thanks to the magic number root 2, it has never been so easy to change among paper sizes. The aspect ratio of 
√2 was discovered in 1786 by the German scientist and philosopher Georg Christoph Lichtenberg. When we look at the example of A0 to A1 paper again, you will find the short side of A0 becomes the long side of A1 and the width of A1 is half of the length of A0. A0 is twice the size of A1, four times A2, eight times A3, and sixteen times A4. Interesting, right? 

US paper sizes: Letter and legal paper sizes

North America and parts of Mexico are the only areas of the first world that do not use the A-series paper sizes. Instead, the American National Standards Institute (ANSI) developed a regular series based on the Letter (8.5" x 11") format as size A, with B to E as larger sizes. The Letter size is slightly smaller than an A4 paper and the Legal size is longer than an A4 paper. Unlike the ISO standard, the ANSI standard has 2 aspect ratios 1: 1.2941 and 1: 1.5455.

Image from Papersizes.org


References

https://www.papersizes.org/a-paper-sizes.htm

https://www.papersizes.org/a4-foolscap-letter.htm

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