Paper size standards govern the size of sheets of paper used as writing paper, stationery, cards, and for some printed documents. Most countries adhere to the ISO 216 standard, which includes the widely recognized A series (including A4 paper), defined by a consistent aspect ratio of √2. The system, first proposed in the 18th century and formalized in 1975, allows scaling between sizes without distortion. Regional variations exist, such as the North American paper sizes (e.g., Letter, Legal, and Ledger) which are governed by the ANSI and are used in North America and parts of Central and South America. The standardization of paper sizes emerged from practical needs for efficiency. The ISO 216 system originated as DIN 476, later adopted internationally for its mathematical precision. The origins of North American sizes are lost in tradition and not well documented, although the Letter size (8.5 in × 11 in; 216 mm × 279 mm) became dominant in the US and Canada due to historical trade practices in the 20th century. Other historical systems, such as the British Foolscap and Imperial sizes, have largely been phased out in favour of ISO or ANSI standards. Regional preferences reflect cultural and industrial legacies. In addition to ISO and ANSI standards, Japan uses its JIS P 0138 system, which closely aligns with ISO 216 but includes unique B-series variants commonly used for books and posters. Specialized industries also employ non-standard sizes: newspapers use custom formats like Berliner and broadsheet, while envelopes and business cards follow distinct sizing conventions. The international standard for envelopes is the C series of ISO 269.
International standard paper sizes
The international paper size standard is ISO 216. It is based on the German DIN 476 standard for paper sizes. Each ISO paper size is one half of the area of the next larger size in the same series. ISO paper sizes are all based on a single aspect ratio of the square root of 2, or approximately 1:1.41421. There are different series, as well as several extensions. The following international paper sizes are included in Cascading Style Sheets (CSS): A3, A4, A5, B4, B5.
A series
There are 11 sizes in the A series, designated A0–A10, all of which have an aspect ratio of a b = 2 ≈ 1.41421 … {\displaystyle {\frac {a}{b}}={\sqrt {2}}\approx 1.41421\ldots } , where a is the long side and b is the short side. Since A series sizes share the same aspect ratio ( 2 ) , {\displaystyle ({\sqrt {2}}),} they can be scaled to other A series sizes without being distorted, and two sheets can be reduced to fit on exactly one sheet without any cutoff or margins. The A0 base size is defined as having an area of 1 m2; given an aspect ratio of 2 {\displaystyle {\sqrt {2}}} , the dimensions of A0 are:
2 4 m {\displaystyle {\sqrt[{4}]{2}}\,\mathrm {m} } by 1 2 4 m {\displaystyle {\frac {1}{\sqrt[{4}]{2}}}\,\mathrm {m} } . or, rounded to the nearest millimetre, 1,189 mm × 841 mm (46.8 in × 33.1 in). A series sizes are related in that the smaller dimension of a given size is the larger dimension of the next smaller size, and folding an A series sheet in half in its larger dimension—that is, folding it in half parallel to its short edge—results in two halves that are each the size of the next smaller A series size. As such, a folded brochure of a given A-series size can be made by folding sheets of the next larger size in half, e.g. A4 sheets can be folded to make an A5 brochure. The fact that halving a sheet with an aspect ratio of 2 {\displaystyle {\sqrt {2}}} results in two sheets that themselves both have an aspect ratio of 2 {\displaystyle {\sqrt {2}}} is proven as follows:
a b = 2 , {\displaystyle {\frac {a}{b}}={\sqrt {2}},}
where a is the long side and b is the short side. The aspect ratio for the new dimensions of the folded paper is:
b a 2 = 2 b a = 2 ⋅ 1 2 = 2 = a b . {\displaystyle {\frac {b}{\frac {a}{2}}}=2{\frac {b}{a}}=2\cdot {\frac {1}{\sqrt {2}}}={\sqrt {2}}={\frac {a}{b}}.}
The advantages of basing a paper size upon an aspect ratio of 2 {\displaystyle {\sqrt {2}}} were noted in 1786 by the German scientist and philosopher Georg Christoph Lichtenberg. He also observed that some raw sizes already adhered to that ratio so that when a sheet is folded, the length to width ratio does not change. Briefly after the introduction of the metric system, a handful of new paper formats equivalent to modern ones were developed in France, having been published for judicial purposes in 1798 during the French Revolution:
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