Paper size

There have been many standard sizes of paper at different times and in different countries, but today there are basically only two systems in place: 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 metric (the base format is a sheet of paper measuring 1 m²) and has been adopted by all countries in the world, except the United States and Canada. However, although Mexico and the Philippines have officially adopted the ISO standard, the U.S. "Letter" format is common in Mexico, as are the U.S. "Legal" and "Letter" formats in the Philippines. The most widely known size in the ISO format is A4.

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 1768 by the German scientist Georg Lichtenberg (in a letter to Johann Beckmann). In the beginning of the 20th 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:

Belgium (1924)
Netherlands (1925)
Norway (1926)
Switzerland (1929)
Sweden (1930)
Soviet Union (1934)
Hungary (1938)
Italy (1939)

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:

Spain (1947)
Austria (1948)
Romania (1949)
Japan (1951)
Denmark (1953)
Czechoslovakia (1953)
Israel (1954)
Portugal (1954)
Yugoslavia (1956)
India (1957)
Poland (1957)
United Kingdom (1959)
Venezuela (1962)
New Zealand (1963)
Iceland (1964)
Mexico (1965)

South Africa (1966)
France (1967)
Peru (1967)
Turkey (1967)
Chile (1968)
Greece (1970)
Zimbabwe (1970)
Singapore (1970)
Bangladesh (1972)
Thailand (1973)
Barbados (1973)
Australia (1974)
Ecuador (1974)
Colombia (1975)
Kuwait (1975)

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 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 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. 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.

There is also a much less common B series. The area of B series sheets is the geometric mean of successive A series sheets. So, B1 is between A0 and A1 in size, with an area of 0.71m² ( $\sqrt{2}^{-1}$ ). As a result, B0 has one side 1-metre long, and other sizes in the B series have one side that is a half, quarter or eighth of a metre. While less common in office use, it is used for a variety of special situations. Many posters use B-series paper or a close approximation, such as 50cm×70cm; B5 is a relatively common choice for books. The B series is also used for envelopes and passports.

The C series is used only for envelopes and is defined in ISO 269. 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 B4 slightly larger than C4. The practical usage of this is that a letter written on A4 paper fits inside a C4 envelope, and a C4 envelope fits inside a sturdier B4 envelope.

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

ISO/DIN paper sizes (in mm)
	A	B	C
0	841 × 1189	1000 × 1414	917 × 1297
1	594 × 841	707 × 1000	648 × 917
2	420 × 594	500 × 707	458 × 648
3	297 × 420	353 × 500	324 × 458
4	210 × 297	250 × 353	229 × 324
5	148 × 210	176 × 250	162 × 229
6	105 × 148	125 × 176	114 × 162
7	74 × 105	88 × 125	81 × 114
8	52 × 74	62 × 88	57 × 81
9	37 × 52	44 × 62	40 × 57
10	26 × 37	31 × 44	28 × 40

The tolerances specified in the standard are

±1.5 mm for dimensions up to 150 mm,
±2 mm for lengths in the range 150 to 600 mm, and
±3 mm for any dimension above 600 mm.

German extensions

The German standard DIN 476 was published in 1922 and is the original specification of the ISO A and B sizes. However, it still differs in two details from its international successor:

DIN 476 provides an extension to formats larger than A0, denoted by a prefix factor. In particular, it lists the two formats 2A0, which is twice the area of A0, and 4A0, which is four times A0:

4A0	1682 × 2378
2A0	1189 × 1682

DIN 476 also specifies slightly tighter tolerances, namely ±1 mm (< 150 mm), ±1.5 mm (150–600 mm), and ±2 mm (>600 mm), respectively.

Swedish extensions

The Swedish standard SIS 014711 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 2^1/16 from one size to the next. However, the SIS 014711 standard does not define any size between a D format and the next larger A format (called H in the previous example). None of these additional formats beyond C have turned out to be particularly useful in practice and they have not caught on internationally.

Japanese B-series variant

The JIS defines two main series of paper sizes. The JIS A-series is identical to the ISO A-series, but with slightly different tolerances. The area of B-series paper is 1.5 times that of the corresponding A-paper, 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 A-series paper. Both A- and B-series paper is widely available in Japan and most photocopiers are loaded with at least A4 and B4 paper.

There are also a number of traditional paper sizes, which are now used mostly only by printers. The most common of these old series are the Shiroku-ban and the Kiku paper sizes.

JIS paper sizes (in mm)
	B-	Shiroku ban 4x6/	Kiku
-0	1030 x 1456
-1	728 x 1030
-2	515 x 728
-3	364 x 515
-4	257 x 364	264 x 379	227 x 306
-5	182 x 257	189 x 262	151 x 227
-6	128 x 182	189 x 262
-7	91 x 128	127 x 188
-8	64 x 91
-9	45 x 64
-10	32 x 45
-11	22 x 32
-12	16 x 22

A4 paper in the United States

Visitors are often surprised that – although A4 is the standard size in the rest of the world – it is not easily available in stationery shops in the United States. Several major U.S. paper suppliers produce and sell A4 paper, but their A4 offerings are mostly limited to one single brand of high-quality paper, which smaller shops have to order for customers first, and which they may be reluctant to do just for a single ream. Since A4 paper is 19 mm taller than the "Letter" size commonly used in the United States, many of the files, filing cabinets, folders and ring binders sold there are not suitable for it. It has therefore been suggested that it would be much easier in the United States to move from the "Letter" format to a transition format of 280 mm × 210 mm known as PA4 (see below), rather than to A4 directly.

Computer users in the United States are regularly confronted with A4 documents, for example from web sites and from correspondence with non-US companies, just as those that download documents created in the U.S. are confronted with the "Letter" size. Printing A4 formatted documents onto U.S. "Letter" paper without adjustment (for example size reduction to 94%) may print the bottom of the page on a second sheet. Similar problems happen when non-US users print documents formatted for U.S. paper sizes. A related problem is that software written in one part of the world often does not cater for the standard paper size used in the other part. A work-around is to distribute document files in PDF format and enable the "Fit to Page" option when printing from the PDF viewer program from the leader vendor of such software. This works both ways, to shrink A4 documents to fit on U.S. "Letter" paper and to shrink U.S. "Letter" documents onto A4 paper.

Approximate ISO paper sizes
(rounded to nearest ¼ inch)
	A	B	C
0	33 × 46¾	39¼ × 55¾	36 × 51
1	23½ × 33	27¾ × 39¼	25½ × 36
2	16½ × 23½	19¾ × 27¾	18 × 25½
3	11¾ × 16½	14 × 19¾	12¾ × 18
4	8¼ × 11¾	9¾ × 14	9 × 12¾
5	5¾ × 8¼	7 × 9¾	6½ × 9
6	4¼ × 5¾	5 × 7	4½ × 6½
7	3 × 4¼	3½ × 5	3¼ × 4½
8	2 × 3	2½ × 3½	2¼ × 3¼
9	1½ × 2	1¾ × 2½	1½ × 2¼
10	1 × 1½	1¼ × 1¾	1 × 1½

North American paper sizes

Loose sizes

Current standard sizes of U.S. paper are a subset of the traditional sizes referred to below. "Letter", "Legal", and "Ledger"/"Tabloid" are by far the most commonly used of these for everyday activities. The origin of the exact dimensions of "Letter" size paper (8.5" x 11", 216 mm × 279 mm) are lost in tradition and not well documented. The author of the American Forest and Paper Association website argues that the dimension originates from the days of manual paper making, and that the 11 inch length of the page is about a quarter of "the average maximum stretch of an experienced vatman's arms" ^*. However, this does not explain the width or aspect ratio.

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. 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 letter size. 8" × 10½" is still commonly used in spiral-bound notebooks and the like.

U.S. paper sizes are currently standard in the United States and (partly) the Philippines, which uses U.S. "Legal" and "Letter" in addition to the ISO range. 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 half-centimeter ^*. Mexico has adopted the ISO standard, but U.S. "Letter" format is very common, as the market is dominated by U.S. suppliers who offer "Letter" at a much lower price than A4. Elsewhere in the world, paper and other stationery in U.S. sizes is not easily available. See switch costs, network effects and standardization for possible reasons for differing regional adoption rates of the ISO standard sizes.

Name	Inches	mm	Ratio
Quarto	10 × 8	254 × 203	1.25
Foolscap	13 × 8	330 × 203	1.625
Executive, (or Monarch)	10½ × 7¼	267 × 184	1.4483
Government-Letter	10½ × 8	267 × 203	1.3125
Letter	11 × 8½	279 × 216	1.2941
A	11 × 8½	279 × 216	1.2941
Legal	14 × 8½	356 × 216	1.6471
Ledger, Tabloid	17 × 11	432 × 279	1.5455
Post	19¼ × 15½	489 × 394	1.2419
Crown	20 × 15	508 × 381	1.3333
Large Post	21 × 16½	533 × 419	1.2727
Demy	22½ × 17½	572 × 445	1.2857
Medium	23 × 18	584 × 457	1.2778
Royal	25 × 20	635 × 508	1.25
Elephant	28 × 23	711 × 584	1.2174
Double Demy	35 × 23½	889 × 597	1.4894
Quad Demy	45 × 35	1143 × 889	1.2857
Statement	8½ × 5½	216 × 140	1.5455
B	17 × 11	432 × 279	1.5455
C	22 × 17	559 × 432	1.2941
D	34 × 22	864 × 559	1.5455
E	44 × 34	1118 × 864	1.2941
index card	5 × 3	127 x 76	1.667
index card	6 × 4	152 x 102	1.5
index card	8 × 5	203 x 127	1.6
international business card	3.370 × 2.125	85.60 × 53.98	1.586
U.S. business card	3.5 × 2	89 × 51	1.75

Tablet sizes

The sizes listed above are for paper sold loosely in reams. There are a large number of 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 (or greyboard) at the bottom of the stack. Such a tablet serves as a portable writing surface, and the sheets 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, trade-marked as "Post-It" or "Stick-Em" and available in various sizes, serve as a sort of tablet.

The significance of taking separate note of these sizes is that their contents are just as likely to be photocopied and enlarged, of course onto loose paper, as are the more standardized international sizes of paper.

"Letter pads" are of course 8½ by 11 inches, but the term "Legal pad" is often used for pads of this size besides those of 8½ by 14 inches. There are "Steno pads" (used by stenographers) of 6 by 9 inches, and pads for pre-school children of twice and four times this size, but which have lines going the long way across the paper: 9 by 12 inches and 12 by 18 inches. For the latter use, there are also pads 10¾ by 13½ inches.

For varied commercial purposes, all sorts of sizes have been recently observed: 4 by 5½ inches; 5 by 8 inches; 5-3/8 by 8-1/4 inches; 6 by 9½ inches; 7¼ by 9½ inches; and 7¾ by 9-7/8 inches.

The only "metric" paper in the shops where this observation was taken are a few Chinese-made "composition books" for children which are 190 mm by 247 mm, a slight modification from the 7¾ by 9¾ inch ones. But the holes in the sheets of any of these tablets fit American-standard binders.

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 3 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:

Name	inches	mm	Ratio
Emperor	72 × 48	1829 × 1219	1.5
Antiquarian	53 × 31	1346 × 787	1.7097
Grand Eagle	42 × 28¾	1067 × 730	1.4609
Colombier	34½ × 23½	876 × 597	1.4681
Atlas*	34 × 26	864 × 660	1.3077
Imperial*	30 × 22	762 × 559	1.3636
Pinched Post	28½ × 14¾	724 × 375	1.9322
Elephant*	28 × 23	711 × 584	1.2174
Princess	28 × 21½	711 × 546	1.3023
Cartridge	26 × 21	660 × 533	1.2381
Royal*	25 × 20	635 × 508	1.25
Sheet and Half Post	23½ × 19½	597 × 495	1.2051
Medium*	23 × 18	584 × 457	1.2778
Demy*	22½ × 17½	572 × 445	1.2857
Large Post	21 × 16½	533 × 419	1.2727
Large Post	20 × 15½	508 × 394	1.2903
Copy Draught	20 × 16	508 × 406	1.25
Crown*	20 × 15	508 × 381	1.3333
Post*	19¼ × 15½	489 × 394	1.2419
Foolscap*	17 × 13½	432 × 343	1.2593
Small Foolscap	16½ × 13¼	419 × 337	1.2453
Brief	16 × 13½	406 × 343	1.1852
Pott	15 × 12½	381 × 318	1.2

* The sizes marked with an asterisk are used in the US.

The common divisions and their abbreviations include:

Name(s)	Abbr.	Folds	Leaves	Pages
Folio	fo/f	1	2	4
Quarto	4to	2	4	8
Sexto or Sixmo	6to/6mo	3	6	12
Octavo	8vo	3	8	16
Duodecimo or Twelvemo	12mo	4	12	24
Sextodecimo or Sixteenmo	16mo	4	16	32

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

PA4-based series
Name	mm²	Ratio
PA0	840 × 1120	3:4
PA1	560 × 840	2:3
PA2	420 × 560	3:4
PA3	280 × 420	2:3
PA4	210 × 280	3:4
PA5	140 × 210	2:3
PA6	105 × 140	3:4
PA7	70 × 105	2:3
PA8	52 × 70	≈3:4
PA9	35 × 52	≈2:3
PA10	26 × 35	≈3:4

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".

Antiquarian

Although the movement is toward 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 "New Metric Handbook," (Tutt & Adler 1981) as 813 by 1372 mm. This is a bit larger than the A0 size. So for a short time, a size called A0a was used in Britain, being 1000 mm by 1370 mm, to get that extra 100 mm on the longer side, write Tutt & Adler.

Expressing paper thickness and density

Grammage

Throughout the world, except in regions using US paper sizes, the product of thickness and density of paper is expressed in grams per square metre (g/m²). This quantity is commonly called grammage in both English and French (ISO 536).

Typical office paper has a grammage of 80 g/m², therefore a typical A4 sheet (1/16 m²) weighs 5 g.

The unofficial unit symbol "gsm" instead of the official "g/m²" is also occasionally encountered in English speaking countries.

"Uncut" ream basis weight

In countries using U.S. paper sizes, paper density is often specified in pounds. The stated mass is that of a ream of 500 sheets. However, the ream of that mass is normally not the one sold to the customer. Instead, the specified number of pounds is the mass of a "basis ream" in which the sheets have some larger size. Often, this is a size used during the manufacturing process before the paper was cut to the dimensions in which it is sold. So, to compute the weight per area, one must know

the weight of the basis ream, which is labeled in pounds;
the number of sheets in that ream, which is usually 500;
the dimensions of an "uncut" sheet in that ream.

These "uncut" basis sizes vary between paper types, are not normally labelled on the product, are not formally standardized, and therefore have to be guessed or inferred somehow from trading practice. Common examples are:

17 in × 22 in	19 in × 24 in	20 in × 26 in
22 in × 28 in	22.5 in × 28.5 in	22 in × 34 in
24 in × 36 in	25 in × 38 in	25.5 in × 30.5 in

For conversion to grammage, in addition the ratio between avoirdupois pound and gram (1 lb ≈ 454 g) and between square inch and square metre (1 m² ≈ 1550 in²) are needed: 1 lb/in² ≈ 7037 g/m².

For example, a "20 pound ream of Letter paper" has a weight of only 5 pounds if the basis dimensions used are twice the cut dimensions. Since the cut dimensions are 8½ in × 11 in, the "uncut" basis dimensions are probably 17 in × 22 in. Therefore, paper weight per area of this type of paper is likely to be:

\frac {20\ \frac{\mathrm{lb}}{\mathrm{ream}} \times 1\ \mathrm{sheet}} {17\ \mathrm{in} \times 22\ \mathrm{in} \times 500\ \frac{\mathrm{sheet}}{\mathrm{ream}}} \approx 1.1 \times 10^{-4}\ \frac{\mathrm{lb}}{\mathrm{in^2}} \approx 75\ \frac{\mathrm{g}}{\mathrm{m^2}}

References

International standard ISO 216, Writing paper and certain classes of printed matter — Trimmed sizes — A and B series. International Organization for Standardization, Geneva, 1975.
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.
M. Kuhn: International standard paper sizes. Web page, Computer Laboratory, University of Cambridge, 1996–2006.
Max Helbig, Winfried Hennig: DIN-Format A4 – Ein Erfolgssystem in Gefahr. Beuth-Kommentare, Beuth Verlag, Berlin, 1998. ISBN 3-410-11878-0
Arthur D. Dunn: Notes on the standardization of paper sizes. Ottawa, Canada, 54 pages, 1972.
American Forest and Paper Association - FAQ: Why is the standard paper size in the U.S. 8 ½" x 11"?

External links

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