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ablative of duodecimus


  1. In the context of "paper|printing": A size of paper, so called because it is originally made by folding and cutting a single sheet from a printing press into 12 leaves; (5 by 7¾ inches): 6.5 to 7.5 inches high, approximately 4.5 inches wide.
  2. A book having pages of this size





ablative of duodecimus 'twelfth'


  1. A size of paper, so called because it is originally made by folding and cutting a single sheet from a printing press into 12 leaves; (5 by 7¾ inches): 6.5 to 7.5 inches high, approximately 4.5 inches wide.
  2. A page of that size; hence, a whole book having pages of this size



ablative of the ordinal duodecimus 'twelfth'

Extensive Definition

There have been many standard sizes of paper at different times and in different countries, but today there are two widespread systems in use: the international standard (A4 and its siblings) and the North American sizes.

The international standard: ISO 216

The international paper size standard, ISO 216, is based on the German DIN 476 standard for paper sizes. Using the metric system, the base format is a sheet of paper measuring 1 in area (A0 paper size). Successive paper sizes in the series A1, A2, A3, etc., are defined by halving the preceding paper size parallel to its shorter side. The most frequently used paper size is A4 (210 × 297 mm). An advantage is that every A4 sheet made from 80 grams (per square meter, that is A0) paper weighs 5 grams, allowing to know the weight - and associated postage rate - by just counting the number of sheets used if the weight of the envelope is known.
This standard has been adopted by all countries in the world except the United States and Canada. In Mexico, Colombia, Chile and the Philippines, despite the ISO standard having been officially adopted, the U.S. "letter" format is still in common use.
anchor Lichtenberg ratio ISO paper sizes are all based on a single aspect ratio of the square root of two, or approximately 1:1.4142. The advantages of basing a paper size upon this ratio were already noted in 1786 by the German scientist Georg Lichtenberg (in a letter to Johann Beckmann): if a sheet with aspect ratio √2 is horizontally divided into two equal halves, then the halves will again have aspect ratio √2. In the beginning of the twentieth century, Dr Walter Porstmann turned Lichtenberg's idea into a proper system of different paper sizes. Porstmann's 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" in everyday use in Germany.
The DIN 476 standard spread quickly to other countries, and before the outbreak of World War II it had been adopted by the following countries:
During the war it was adopted by Uruguay (1942), Argentina (1943) and Brazil (1943); and directly afterwards the standard continued to spread to other countries: 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, and today only the U.S. and Canada have not adopted the system.
The largest standard size, A0, has an area of 1 . The length of the long side of the sheet in metres is the 4th root of 2—approximately 1.189 metres. The short side is the reciprocal of this number, approximately 0.841 metres. A1 is formed by cutting a piece of A0 into two equal area rectangles. Because of the choice of lengths, the aspect ratio is the same for A1 as for A0 (as it is for A2, A3, etc). This particular measurement system was chosen to allow folding of one standard size into another, which cannot be accomplished with traditional paper sizes.
Brochures are made by using material at the next size up i.e. material at A3 is folded to make A4 brochures. Similarly, material at A4 is folded to make A5 brochures.
It also allows scaling without loss of image from one size to another. Thus an A4 page can be enlarged to A3 and retain the exact proportions of the original document. Office photocopiers in countries that use ISO 216 paper often have one tray filled with A4 and another filled with A3. A simple method is usually provided (e.g. one button press) to enlarge A4 to A3 or reduce A3 to A4. This also allows two sheets of A4 (or any other size) to be scaled down and fit exactly 1 sheet without any cutoff or margins.
| page = 191 | url = | accessdate = 2008-03-06 }} | 17 × 11 || 432 × 279 |- ! Tabloid | 11 × 17 || 279 × 432 |}
There is an additional paper size, to which the name "government-letter" was given by the IEEE Printer Working Group: the 8 in × 10½ in (203.2 mm × 266.7 mm) paper that is used in the United States for children's writing. It was prescribed by Herbert Hoover when he was Secretary of Commerce to be used for U.S. government forms, apparently to enable discounts from the purchase of paper for schools. In later years, as photocopy machines proliferated, citizens wanted to make photocopies of the forms, but the machines did not generally have this size paper in their bins. Ronald Reagan therefore had the U.S. government switch to regular letter size (8½ in × 11 in). The 8 in × 10½ in size is still commonly used in spiral-bound notebooks and the like.
An alternative explanation in the past for the difference between "government size" (as government-letter size was referred to at the time) and letter size paper was that the slightly smaller sheet used less paper, and therefore saved the government money in both paper and filing space. However, when Reagan prescribed the change to letter size, it was commonly stated that U.S. paper manufacturers had standardized their production lines for letter size, and were meeting government orders by trimming ½" each from two sides of letter-size stock; thus the government was allegedly paying more for its smaller paper size before Reagan abolished it. The different paper size also reportedly restricted the government's ability to take advantage of modular office furniture designs, common in the 1980s, whose cabinets were designed for letter size paper.
U.S. paper sizes are currently standard in the United States and the Philippines. The latter uses U.S. "letter", but the Philippine "legal" size is 8½ in × 13 in (215.9 mm × 330.2 mm). ISO sizes are available, but not widely used, in both the U.S. and the Philippines.
In Canada, U.S. paper sizes are a de facto standard. The government, however, uses a combination of ISO paper sizes, and CAN 2-9.60M "Paper Sizes for Correspondence" specifies P1 through P6 paper sizes, which are the U.S. paper sizes rounded to the nearest 5 mm.
Mexico has adopted the ISO standard, but U.S. "letter" format is still the system in use throughout the country. It is virtually impossible to encounter ISO standard papers in day-to-day uses, with "Carta 216 mm × 279 mm" (letter), "Oficio 216 mm × 340 mm" (legal) and "Doble carta" (ledger/tabloid) being nearly universal. U.S. sizes are also widespread and in common use in Colombia
See switching costs, network effects and standardization for possible reasons for differing regional adoption rates of the ISO standard sizes.

ANSI paper sizes

In 1995, the American National Standards Institute adopted ANSI/ASME Y14.1 which defined a regular series of paper sizes based upon the de facto standard 8½ in × 11 in "letter" size which it assigned "ANSI A". This series also includes "ledger"/"tabloid" as "ANSI B". This series is somewhat similar to the ISO standard in that cutting a sheet in half would produce two sheets of the next smaller size. Unlike the ISO standard, however, the arbitrary aspect ratio forces this series to have two alternating aspect ratios. The ANSI series is shown below.
With care, documents can be prepared so that the text and images fit on either ANSI or their equivalent ISO sheets at 1:1 reproduction scale.
Other, larger sizes continuing the alphabetic series illustrated above exist, but it should be noted that they are not part of the series per se, because they do not exhibit the same aspect ratios. For example, Engineering F size (28 in × 40 in, 711.2 mm × 1016.0 mm) also exists, but is rarely encountered, as are G, H, … N size drawings. G size is 22½ in (571.5 mm) high, but variable width up to 90 in (2286 mm) in increments of 8½ in, i.e., roll format. H and larger letter sizes are also roll formats. Such sheets were at one time used for full-scale layouts of aircraft parts, wiring harnesses and the like, but today are generally not needed, due to widespread use of computer-aided design (CAD) and computer-aided manufacturing (CAM).

Architectural sizes

In addition to the ANSI system as listed above, there is a corresponding series of paper sizes used for architectural purposes. This series also shares the property that bisecting each size produces two of the size below. It may be preferred by North American architects because the aspect ratios (4:3 and 3:2) are ratios of small integers, unlike their ANSI (or ISO) counterparts. Furthermore, the aspect ratio 4:3 matches the traditional aspect ratio for computer displays. The architectural series, usually abbreviated "Arch", is shown below:

Other sizes

Tablet sizes

The sizes listed above are for paper sold loosely in reams. There are many sizes of tablets of paper, that is, sheets of paper kept from flying around by being bound at one edge, usually by a strip of plastic or hardened PVA adhesive. Often there is a pad of cardboard (also known as chipboard or greyboard) at the bottom of the stack. Such a tablet serves as a portable writing surface, and the sheets often have lines printed on them, usually in blue, to make writing in a line easier. An older means of binding is to have the sheets stapled to the cardboard along the top of the tablet; there is a line of perforated holes across every page just below the top edge from which any page may be torn off. Lastly, a pad of sheets each weakly stuck with adhesive to the sheet below, trademarked as "Post-It" or "Stick-Em" and available in various sizes, serve as a sort of tablet.
"Letter pads" are of course 8½ by 11 inches, while the term "legal pad" is often used by laymen to refer to pads of various sizes including those of 8½ by 14 inches. There are "steno pads" (used by stenographers) of 6 by 9 inches.
Of course, in countries where the ISO sizes are standard, most notebooks and tablets are sized to ISO specifications (for example, most newsagents in Australia stock A4 and A3 tablets).

Traditional inch-based paper sizes

Traditionally, a number of different sizes were defined for large sheets of paper, and paper sizes were defined by the sheet name and the number of times it had been folded. Thus a full sheet of "royal" paper was 25 × 20 inches, and "royal octavo" was this size folded three times, so as to make eight sheets, and was thus 10 by 6¼ inches.
Imperial sizes were used in the United Kingdom and its territories. Some of the base sizes were as follows:
Traditional sizes for writing paper in the United Kingdom, :
The common divisions and their abbreviations include: Foolscap folio is often referred to simply as 'folio' or 'foolscap'. Similarly, 'quarto' is more correctly 'copy draught quarto'.
Many of these sizes were only used for making books (see bookbinding), and would never have been offered for ordinary stationery purposes.

Transitional paper sizes

PA series

A transitional size called PA4 (210 mm × 280 mm, 8¼ in × 11 in) was proposed for inclusion into the ISO 216 standard in 1975. It has the height of Canadian P4 paper (215 mm × 280 mm, about 8½ in × 11 in) and the width of international A4 paper (210 mm × 297 mm). The table to the right 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 felt that the set of standardized paper formats should be kept to the minimum necessary. 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, most computers and data projectors. PA4 is therefore a good choice as the format of computer presentation slides. At the same time, PA4 is the largest format that fits on both A4 and U.S./Canadian "Letter" paper without resizing.
PA4 is used today by many international magazines, because it can be printed easily on equipment designed for either A4 or U.S. "Letter".


Although the movement is towards the international standard metric paper sizes, on the way there from the traditional ones there has been at least one new size just a little larger than that used internationally. British architects and industrial designers once used a size called "Antiquarian" as listed above, but given in the New Metric Handbook (Tutt & Adler 1981) as 813 mm × 1372 mm. This is a little larger than the A0 size. So for a short time, a size called A0a (1000 mm × 1370 mm) was used in Britain.


F4 (210 mm × 330 mm) is common in Southeast Asia and Australia, and is sometimes called "foolscap". It has the same width as A4, but is longer.

Other metric sizes

See also


Further reading

  1. International standard ISO 216, Writing paper and certain classes of printed matter — Trimmed sizes — A and B series. International Organization for Standardization, Geneva, 1975.
  2. International standard ISO 217: Paper — Untrimmed sizes — Designation and tolerances for primary and supplementary ranges, and indication of machine direction. International Organization for Standardization, Geneva, 1995.
  3. Max Helbig, Winfried Hennig: DIN-Format A4 – Ein Erfolgssystem in Gefahr. Beuth-Kommentare, Beuth Verlag, Berlin, 1998. ISBN 3-410-11878-0
  4. Arthur D. Dunn: Notes on the standardization of paper sizes. Ottawa, Canada, 54 pages, 1972.
duodecimo in Catalan: Mida de paper
duodecimo in Czech: Formát papíru
duodecimo in Danish: Størrelser (papir)
duodecimo in German: Papierformat
duodecimo in Spanish: Formato de papel
duodecimo in Esperanto: Normaj dimensioj de folioj
duodecimo in French: Format de papier
duodecimo in Indonesian: Ukuran kertas
duodecimo in Hungarian: Papírméret
duodecimo in Malayalam: കടലാസ് വലിപ്പം
duodecimo in Malay (macrolanguage): Ukuran kertas
duodecimo in Dutch: Papierformaat
duodecimo in Japanese: 紙の寸法
duodecimo in Polish: Format arkusza
duodecimo in Portuguese: Tamanho de papel
duodecimo in Russian: Формат бумаги
duodecimo in Simple English: Paper size
duodecimo in Slovak: Formát papiera
duodecimo in Serbian: Формати папира
duodecimo in Swedish: Pappersformat
duodecimo in Tamil: தாள் அளவு
duodecimo in Vietnamese: Khổ giấy
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