Paper size - Definition and Overview

There have been many standard sizes of paper at different times and in different countries.

International paper sizes

A comparison of different paper sizes

International standard paper sizes are now used in all countries except the United States, Canada, and some South American countries.

The international standard is ISO 216, which defines amongst others, A4. ISO paper sizes are all based on a single aspect ratio of the square root of two, 1:1.4142. Basing paper upon this ratio was conceived by Georg Lichtenberg in the eighteenth century, made law in Germany in the 1920s, but did not reach its culmination until the prevalence of photocopy machines from the 1960s made having all paper with the same aspect ratio far more convenient in scaling than any other system.

The largest standard size, A0, has an area of 1 m². A1 is formed by cutting a piece of A0 in half, which retains the aspect ratio. This particular measurement system was chosen in order 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 text, photograph or whatever. Office photocopiers in countries that use ISO 216 paper often have one tray filled with A4 and one filled with A3. A simple method is usually provided (e.g. one button press) to enlarge A4 to A3 or reduce A3 to A4. Thus an A4 brochure when open is A3 and can be placed on the copier and either printed directly onto the A3 paper or reduced to A4.

The ISO B series is a scaling of the A series; B1 is half way between A0 and A1 in area. The C series is half way between the A and B series of the same number; for instance, C0 is half way between A0 and B0. This way, C0 is slightly larger than A0, and B0 slightly larger than C0. This was intended to allow one to fit inside an envelope of the other. For instance, a letter written on A4 paper, the standard for this role, fits inside a C4 envelope. A C4 envelope can fit inside a B4 envelope.

The scalability also means that less paper (and hence money) is wasted by printing companies.

The measurements in millimetres are more appropriate for determining the aspect ratio of paper than the less-accurate measurement of book sizes in centimetres. However, there is a tolerance factor that lengths of paper less than 150 mm can have plus-or-minus 1.5 mm and still qualify for the size designation. Lengths from 150 to 600 mm can have plus-or-minus 2 mm, while those over 600 can have plus-or-minus 3 mm.

ISO 216 does not define any sizes larger than A0 and B0, but the German standard DIN 476 puts a factor in front of these. Thus paper designated 2A0 is twice the size of A0, while 4A0 is four times A0.

Although A4 is the standard size in the rest of the world, it doesn't fit in US three-ring binders (and there is a different standard for hole-punched binders to go with the international papers as well). However, the rarer E5 paper is less than a millimetre taller than US Letter size, though it is about five-eighths of an inch narrower. Photocopies from A4 to E5 are simply reduced to 95%, while from E5 to A4 increased to 105%. And notice that, as A4 is the standard size for international firms, their web sites (such as that of ISO itself) are designed to be printed on such paper of greater length. Printing them out without adjustment, on US Letter-size paper, prints the bottom of the page on a second sheet.

Traditional 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 3 times, so as to make eight sheets, and was thus 10 by 6¼ inches.

Some of the base sizes commonly used in the US were as follows (all in inches):

Atlas

34 × 26

Imperial

30 × 22

Elephant

28 × 23

Royal

25 × 20

Medium

23 × 18

Demy

22½ × 17½

Crown or Post

20 × 15

Foolscap

17 × 13½

The sizes used in the UK were similar but in a few cases differed in detail.

The common divisions and their abbreviations include:

Many of these sizes were only used for making books (see bookbinding), and would never have been offered for ordinary stationery purposes.

Current U.S. paper sizes

Current standard sizes of U.S. paper are a subset of the traditional sizes referred to above. Letter, legal, and ledger/tabloid are by far the most commonly used of these for everyday activities.

There is an additional paper size to which the name "government-letter" was given by the IEEE Printer Working Group: the 8-by-10½ inch paper that is used in America for children's writing and was prescribed by Herbert Hoover when he was Secretary of Commerce to be used for U.S. governmental forms. Apparently this would enable discounts from purchase of paper for schools. As photocopy machines later proliferated, citizens wanted to make photocopies of the forms, but as the machines did not generally have this size paper in their bins, they could not do so, thus Ronald Reagan had the U.S. government switch to letter size. 8" × 10½" is still commonly used in spiral-bound notebooks and the like.

US paper sizes are currently standard in the United States, Canada and Mexico.

See switch costs, network effects and standardization for possible reasons for differing regional adoption rates of the ISO standard sizes. A related phenomenon may the QWERTY keyboard layout, among other examples.

See also

• Punchhole - Filing holes

External links

• International Standard Paper Sizes (http://www.cl.cam.ac.uk/~mgk25/iso-paper.html) by Markus Kuhn
• Web page on traditional paper sizes used in books, with reference tables (http://www.trussel.com/books/booksize.htm)
• IEEE-ISTO 5101.1-2002 "The Printer Working Group Standard for Media Standardized Names" (PDF) (ftp://ftp.pwg.org/pub/pwg/standards/pwg5101.1.pdf)