Paper Sizes & Constants
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This text explains the ISO 216 and American paper sizes. For each paper size a "paper size constant property name" is given so that the page size can be specified by name when a page is constructed using page_type. In when using the page-type element you can also specify the page-orientation as landscape or portrait. The ISO paper size conceptIn the ISO paper size system, the height-to-width ratio of all pages is the square root of two (1.4142:1). This aspect ratio is especially convenient for a paper size. If you put two such pages next to each other, or equivalently cut one parallel to its shorter side into two equal pieces, then the resulting page will retain the same width/height ratio. The ISO paper sizes are based on the metric system. The square-root-of-two ratio does not permit both the height and width of the pages to be nicely rounded metric lengths. Therefore, the area of the pages has been defined to have round metric values. As paper is usually specified in grams per meter squared (g/m2), this simplifies calculation of the mass of a document if the format and number of pages are known. ISO 216 defines the A series of paper sizes based on these simple principles:
Format A1 is A0 cut into two equal pieces. In other words, the height of A1 is the width of A0 and the width of A1 is half the height of A0. All smaller A series formats are defined in the same way. If you cut format An parallel to its shorter side into two equal pieces of paper, these will have format A(n+1). For applications where the ISO A series does not provide an adequate format, the B series[1] has been introduced to cover a wider range of paper sizes and the C series of formats has been defined for envelopes. The width and height of a Bn format are the geometric mean[2] between those of the An and the next larger A(n-1) format. For instance, B1 is the geometric mean between A1 and A0, which means the same magnification factor that scales A1 to B1 also scales B1 to A0. Similarly, the formats of the C series are the geometric mean between the A and B series formats with the same number. For example, an A4 size letter fits into a C4 envelope, which in turn fits into a B4 envelope. If you fold this letter once to A5 format, then it will fit into a C5 envelope. B and C formats naturally are also a square-root-of-two format. The following table shows the width and height of all ISO A and B paper formats, as well as the ISO C envelope formats. The dimensions are in millimetres: A Series Formats
B Series Formats
C Series Formats
The allowed tolerances are 1.5 mm for dimensions up to 150 mm, �2 mm for dimensions above 150 mm up to 600 mm, and �3 mm for dimensions above 600 mm. Calculating the dimensionsAlthough the ISO paper sizes are specified in the standard with the width and height given in millimetres, the dimensions can also be calculated with the following formulas:
The actual millimetre dimensions in the standard have been calculated by progressively rounding down any division-by-two result, this guarantees that two A(n-1) pages together are never larger than an An page. Envelope formatsFor postal purposes, ISO 269 and DIN 678 define the following envelope formats:
The DL[3] format is the most widely used business letter format; ISO 269 explains this as Dimension Lengthwise. Untrimmed paper formats (ISO Press-sheet sizes)All A and B series formats described so far are trimmed paper end sizes, i.e. these are the dimensions of the paper delivered to the user or reader. Other ISO standards define the format series RA and SRA for untrimmed raw paper, where SRA stands for "supplementary raw format A". These formats are only slightly larger than the corresponding A series formats. Sheets in these formats will be cut to the end format after binding. The ISO RA0 format has an area of 1.05 m2 and the ISO SRA0 format has an area of 1.15 m2. These formats also follow the sqrt(2)-ratio and half-area rule, but the dimensions of the start format have been rounded to the full centimetre. The common untrimmed paper formats that printers order from the paper manufacturers are[4]:
Overhead projectorsWhen you prepare overhead projector slides for a conference, you might wonder, how large will be the picture area of the projector that you will have available. ISO 7943-1 specifies two standard sizes of overhead projector picture areas:Type A is 250 x 250 mm (corners rounded with a radius less than 60 mm) and Type B is 285 x 285 mm (corners rounded with a radius less than 40 mm or cut off diagonally no more than 40 mm). Therefore, if you use A4 transparencies, you should leave at least a 30 mm top and bottom margin. NOTE There is no 'Paper Size Constant Name' for the Overhead projectors sizes even though they have a ISO standard. Most companies have their own preferred size for these types of documents. Identification cardsISO 7810 specifies three formats for identification cards:
ID-1 is the common format for banking cards (0.76 mm thick) and is also widely used for business cards and driver's licences. Some people prefer A8 (74 x 52 mm) for business cards. The standard passport format is B7 (= ID-3). North American paper sizesThe United States and Canada are today the only industrialized nations in which the ISO standard paper sizes are not yet widely used. In U.S. office applications, the paper formats "Letter", "Legal", "Executive" and "Ledger/Tabloid" are widely used. There exists also an American National Standard ANSI/ASME Y14.1 for technical drawing paper sizes A (216 x 279 mm), B (279 x 432 mm), C (432 x 559 mm), D (559 x 864 mm), E (864 x 1118 mm), and there are many other unsystematic formats for various applications in use. The "Letter", "Legal", "Executive" and "Ledger/Tabloid", and other formats (although not these names) are defined in the American National Standard ANSI X3.151-1987. While all ISO paper formats have consistently the same aspect ratio of sqrt(2)=1.414, the U.S. format series has two different alternating aspect ratios 17/11=1.545 and 22/17=1.294. Therefore you cannot reduce or magnify from one U.S. format to the next higher or lower without leaving an empty margin. The Canadian standard CAN 2-9.60M "Paper Sizes for Correspondence" defines the six formats P1, P2, P3, P4, P5 and P6. These are just the U.S. sizes rounded to the nearest half centimetre (P4 -> U.S. Letter, P3 -> U.S. Ledger). Even though these Canadian paper sizes look somewhat like a pseudo-metric standard, they still suffer from the two major inconveniences of the U.S. formats. Firstly they have no common height/width ratio and secondly they differ significantly from the rest of the world standards. The following table shows the width and height of Both the North American and Canadian page sizes:
ReferencesThis text summarizes and explains the content of the following international standards: ISO 216:1975, Writing paper and certain classes of printed matter Trimmed sizes and B series. ISO 269:1985, Correspondence envelopes Designation and sizes. ISO 623:1974, Paper and board Folders and files Sizes. ISO 838:1974, Paper Holes for general filing purposes Specifications. ISO 7943-1:1987, Overhead Projectors Projection Stages Dimensions The following standards contain related information but are not covered here completely: ISO 217:1995, Paper Untrimmed sizes Designation and tolerances for primary and supplementary ranges, and indication of machine direction. ISO 328:1974, Picture postcards and lettercards Size. ISO 353:1975, Processed writing paper and certain classes of printed matter Method of expression of dimensions. ISO 416:1974, Picture postcards Area reserved for the address. ISO 478:1974, Paper Untrimmed stock sizes for the ISO-A Series ISO primary range. ISO 479:1975, Paper Untrimmed sizes Designation and tolerances. ISO 593:1974, Paper Untrimmed stock sizes for the ISO-A Series ISO supplementary range. ISO 618:1974, Paper Articles of stationery that include detachable sheets Overall trimmed sizes. Links to other paper size referenceshttp://home.inter.net/eds/paper/papersize.html http://home.inter.net/eds/paper/env.html http://www.prepressure.com/library/papersizes.htm Footnotes[1] The Japanese JIS P 0138-61 standard defines the same A series as ISO 216, but a slightly different B series of paper sizes, sometimes called the JIS B or JB series. JIS B0 has an area of 1.5 m2, such that the area of JIS B pages is the arithmetic mean of the area of the A series pages with the same and the next higher number, and not as in the ISO B series the geometric mean. For example, JB3 is 364 x 515, JB4 is 257 x 364, and JB5 is 182 x 257 mm. Using the JIS B series should be avoided because it introduces additional magnification factors and is not an international standard. [2] The geometric mean of two numbers x and y is the square root of their product, (xy)1/2, whereas their arithmetic mean is half their sum, (x+y)/2. For example, the geometric mean of the numbers 2 and 8 is 4 (because 4/2=8/4), whereas their arithmetic mean is 5 (because 5-2=8-5). The arithmetic mean is half-way between two numbers by addition, whereas the geometric mean is half-way between two numbers by multiplication. [3] The DL size falls somewhat out of the system, manufacturers have complained that it is slightly too small for the reliable automatic enveloping, therefore DIN 678 introduced the C6/C5 format as an alternative for DL. [4] The RA and SRA dimensions are also used as roll widths in rotating printing presses. [5] ANSI is the American National Standards Institute. [6] Arch = architecture. |
