Paper size
Paper size standards govern the size of sheets of paper used as writing paper, stationery, cards, and for some printed documents.
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.
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.[2]
A series
There are 11 sizes in the A series, designated A0–A10, all of which have an aspect ratio of _____ where a is the long side and b is the short side.
Since A series sizes share the same aspect ratio (√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, the dimensions of A0 are:
_____
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 results in two sheets that themselves both have an aspect ratio of √2 is proven as follows:
_____
where a is the long side and b is the short side. The aspect ratio for the new dimensions of the folded paper is:
_____
The advantages of basing a paper size upon an aspect ratio of √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:
- grand registre (A2)
- moyen papier (A3)
- grand papier (B3)
- petit papier (B4)
- demi feuille(B5)
- effets de commerce (half-B5)
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 into a proper system of different 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" (IPA: [diːn.ʔaː.fiːɐ̯]) in everyday use in Germany and Austria.
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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.
The weight of an A-series sheet of a given paper weight can be calculated by knowing the ratio of its size to the A0 sheet. For example, an A4 sheet is 1⁄16 the size of an A0 sheet, so if it is made from 80-g/m2 paper, it weighs 1⁄16 of 80 g, which is 5 g.
B series
The B series paper sizes are less common than the A series. They have the same aspect ratio of A series:
_____
However, they have a different area. The area of B series sheets is in fact the geometric mean of successive A series sheets. B1 is between A0 and A1 in size, with an area of 0.707 m2 (1⁄√2 m2). As a result, B0 is 1 metre wide, and other sizes of the series are a half, a quarter, or further fractions of a metre wide: in general, every B size has exactly one side of length _____. That side is the short side for B0, B2, B4, etc., and the long side for B1, B3, B5, etc.
While less common in office use, the B series is used for a variety of special applications.
- B4, B5, and B6 are used for envelopes that fit C-series envelopes.
- B5 is a relatively common choice for books.
- B7 is equal to the passport size ID-3 from ISO/IEC 7810.
- Many posters use B-series paper or a close approximation, such as 50 cm × 70 cm ~ B2.
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.
C series
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.
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Transitional paper sizes
PA4 or L4
A transitional size called PA4 (210 mm × 280 mm or 8.27 in × 11.02 in), sometimes dubbed L4, was proposed for inclusion into the ISO 216 standard in 1975. It has the height of Canadian P4 paper (215 mm × 280 mm, about 8+1⁄2 in × 11 in) and the width of international A4 paper (210 mm × 297 mm or 8.27 in × 11.69 in), i.e. it uses the smaller value among the two for each side. The table shows how this format can be generalized into an entire format series.
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 it is not as much a paper size as a page format. Apple, for instance, requires this format for digital music album booklets.[18]
The size 210 mm × 280 mm was documented in the Canadian standard CAN2-200.2-M79 "Common Image Area for Paper Sizes P4 and A4".[19]
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