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[Francisco Raya]

The ISO 216 standard, which includes the commonly used A4 size, is the international standard for paper size. It is used across the world except in North America and parts of Central and South America, where North American paper sizes such as "Letter" and "Legal" are used.[1] The international standard for envelopes is the C series of ISO 269.

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 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.[3] 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 proposed by the mathematician Lazare Carnot, and published for judicial purposes in 1798 during the French Revolution.[4] These were never widely adopted, however:

Early in the 20th century, the ratio was used to specify the world format starting with 1 cm as the short edge of the smallest size. Walter Porstmann started with the largest sizes instead, assigning one an area of 1 m2 (A0) and the other a short edge of 1 m (B0). He thereby turned the forgotten French sizes (relatively few in number) into a logically-simple and comprehensive plan for a full range of paper sizes, while introducing systematic alphanumeric monikers for them. Generalized to nothing less than four series, this system was introduced as a DIN standard (DIN 476) in Germany in 1922, replacing a vast variety of other paper formats. Even today, the paper sizes are called "DIN A4" (.mw-parser-output .IPA-label-smallfont-size:85%.mw-parser-output .references .IPA-label-small,.mw-parser-output .infobox .IPA-label-small,.mw-parser-output .navbox .IPA-label-smallfont-size:100%IPA: [diːn.ʔaː.fiːɐ̯]) in everyday use in Germany and Austria.

By 1975, so many countries were using the German system that it was established as an ISO standard, as well as the official United Nations document format. By 1977, A4 was the standard letter format in 88 of 148 countries. Today the standard has been adopted by all countries in the world except the United States and Canada. In Mexico, Costa Rica, Colombia, Venezuela, Chile, and the Philippines, the US letter format is still in common use, despite their official adoption of the ISO standard.

While less common in office use, the B series is used for a variety of applications in which one A-series size would be too small but the next A-series size is too large, or because they are convenient for a particular purpose.

The B-series is widely used in the printing industry to describe both paper sizes and printing press sizes, including digital presses. B3 paper is used to print two US letter or A4 pages side by side using imposition; four pages would be printed on B2, eight on B1, etc.[need quotation to verify]

The C series is defined in ISO 269, which was withdrawn in 2009 without a replacement, but is still specified in several national standards. It is primarily used for envelopes. The area of C series sheets is the geometric mean of the areas of the A and B series sheets of the same number; for instance, the area of a C4 sheet is the geometric mean of the areas of an A4 sheet and a B4 sheet. This means that C4 is slightly larger than A4, and slightly smaller than B4. The practical usage of this is that a letter written on A4 paper fits inside a C4 envelope, and both A4 paper and C4 envelope fits inside a B4 envelope.

Some envelope formats with mixed sides from adjacent sizes (and thus an approximate aspect ratio of 2:1) are also defined in national adaptations of the ISO standard, e.g. DIN C6/C5 (also known as C65) is 114 mm 229 mm where the common side to C5 and C6 is 162 mm. This format allows an envelope holding an A-sized paper folded in three, e.g. for the C65, an A4.

The German standard DIN 476 was published on 18 August 1922 and is the original specification of the A, B and C sizes. In 1991, it was split into DIN 476-1 for the A and B formats and 476-2 for the C series. The former has been withdrawn in 2002 in favor of adopting the international standard as DIN EN ISO 216, but part 2 has been retained and was last updated in 2008.

The smallest formats in the original specifications for each series were A13, B13, C8, and D8. Sizes A11 through A13 were no longer listed in the 1930 edition, nor were B11 through B13. C9 and C10 were added in the 1976 revision for compatibility with photography sizes: C8 closely matches 69 photos, and C9 and C10 closely match 77 and 55 slides, respectively.

DIN 476 provides for formats larger than A0, denoted by a prefix factor. In particular, it lists the formats 2A0 and 4A0, which are twice and four times the size of A0 respectively.However, ISO 216:2007 notes 2A0 and 4A0 in the table of Main series of trimmed sizes (ISO A series) as well: "The rarely used sizes [2A0 and 4A0] which follow also belong to this series."

The Swedish standard SIS 01 47 11[9] generalized the ISO system of A, B, and C formats by adding D, E, F, and G formats to it. Its D format sits between a B format and the next larger A format (just like C sits between A and the next larger B). The remaining formats fit in between all these formats, such that the sequence of formats A4, E4, C4, G4, B4, F4, D4, *H4, A3 is a geometric progression, in which the dimensions grow by a factor 2 16 \displaystyle \sqrt[16]2 from one size to the next. However, this SIS standard does not define any size between a D format and the next larger A format (called *H in the previous example).

Of these additional formats, G5 (169 239 mm) and E5 (155 220 mm) are popular in Sweden and the Netherlands for printing dissertations,[10] but the other formats have not turned out to be particularly useful in practice. They have not been adopted internationally and the Swedish standard has been withdrawn.

The Japanese standard JIS P 0138 defines two main series of paper sizes. The JIS A-series is identical to the ISO A-series except that it has slightly different tolerances. The area of B-series paper is 1.5 times that of the corresponding A-paper (instead of the factor 2 = 1.414... \displaystyle \sqrt 2=1.414... for the ISO B-series), so the length ratio is approximately 1.22 times the length of the corresponding A-series paper. The aspect ratio of the paper is the same as for the A-series paper. Both A- and B-series paper are widely available in Japan, Taiwan and China, and most photocopiers are loaded with at least A4 and either one of A3, B4, and B5 paper.

The Bureau of Indian Standards recommends the "ISO-A series" size of drawing sheet for engineering drawing works. The Bureau of Indian Standards specifies all the recommendations for engineering drawing sheets in its bulletin IS 10711: 2001.[13]

The Bureau extended the ISO-A series with a Special Elongated Sizes (Second Choice). These sizes are achieved by increasing the shorter dimensions of a sheet of the ISO A series to lengths that are multiples of the shorter dimensions of the chosen basic sheet; in effect, all of the Indian elongated sizes emulate having several regular-size sheets joined on their long edge.

There is also a Exceptional Elongated Sizes (Third Choice). These sizes are obtained by increasing the shorter dimensions of a sheet of the ISO-A series to lengths that are multiples of the shorter dimensions of the chosen basic sheet. These sizes are used when a very large or extra elongated sheet is needed.

The first standard of paper size in the Soviet Union was OST 303 in 1926. Six years later, it was replaced by OST 5115 which generally followed DIN 476 principles, but used Cyrillic lowercase letters instead of Latin uppercase, had the second row shifted so that б0 (B0) roughly corresponded to B1 and, more importantly, had slightly different sizes:[14]

DIN 5008 (previously DIN 676) prescribes, among many other things, two variants, A and B, for the location of the address field on the first page of a business letter and how to fold the A4 sheet accordingly, so the only part visible of the main content is the subject line.

ISO 5457 specifies drawing paper sizes with a trimmed size equal to the A series sizes from A4 upward. The untrimmed sizes are 3 to 4 cm larger and rounded to the nearest centimetre. A0 through A3 are used in landscape orientation, while A4 is used in portrait orientation. Designations for preprinted drawing paper include the base sizes and a suffix, either T for trimmed or U for untrimmed sheets.

The withdrawn standard ISO 2784 did specify sizes of continuous, fan-fold forms based upon whole inches as was common for paper in continuous lengths in automatic data processing (ADP) equipment. Specifically, 12 inches (304.8 mm) were considered an untrimmed variant of the A4 height of 297 mm.

The PA formats did not end up in ISO 216, because the committee decided that the set of standardized paper formats should be kept to the minimum necessary.[citation needed] However, PA4 remains of practical use today. In landscape orientation, it has the same 4:3 aspect ratio as the displays of traditional TV sets, some computer displays (e.g. the iPad) and data projectors. PA4, with appropriate margins is, therefore, a good choice as the format of presentation slides.

As a compromise between the two most popular paper sizes globally, PA4 is used today by many international magazines, because it can be printed easily on equipment designed for either A4 or US Letter. That means (in practice) it has turned out to be not so much a paper size as a page format. Apple, for instance, requires this format for digital music album booklets.[18]

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