ISO 216

ISO 216 specifies international standard (ISO) paper sizes used in most countries in the world today, although not in Canada or the United States. The standard defines the "A" and "B" series of paper sizes, including A4, the most commonly available size. Two supplementary standards, ISO 217 and ISO 269, define related paper sizes; the ISO 269 "C" series is commonly listed alongside the A and B sizes.

All ISO 216, ISO 217 and ISO 269 paper sizes (except some envelopes) have the same aspect ratio, 1:√2, at least to within the rounding to whole numbers of millimetres. This ratio has the unique property that when cut or folded in half widthwise, the halves also have the same aspect ratio. Each ISO paper size is one half of the area of the next larger size.

In 1786, the German scientist Georg Christoph Lichtenberg described the advantages of basing a paper size on an aspect ratio of ${\displaystyle {\sqrt {2}}}$ in a letter to Johann Beckmann. The formats that became ISO paper sizes A2, A3, B3, B4, and B5 were developed in France. They were listed in a 1798 law on taxation of publications that was based in part on page sizes.

The main advantage of this system is its scaling. Rectangular paper with an aspect ratio of ${\displaystyle {\sqrt {2}}}$ has the unique property that, when cut or folded in half midway between its shorter sides, each half has the same ${\displaystyle {\sqrt {2}}}$ aspect ratio and half the area of the whole sheet before it was divided. Equivalently, if one lays two same-sized sheets paper with an aspect ratio of ${\displaystyle {\sqrt {2}}}$ side-by-side along their longer side, they form a larger rectangle with the aspect ratio of ${\displaystyle {\sqrt {2}}}$ and double the area of each individual sheet.

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