Paper size

A series

A size chart illustrating the ISO A series.

The base A0 size of paper is defined as having an area of 1 m² and a dimension ratio of 1 to √2, making the A0 paper size exactly  m ×  m. Rounded to the nearest millimetre, that is 841 by 1,189 millimetres (33.1 in × 46.8 in).

Successive paper sizes in the series A1, A2, A3, and so forth, are defined by halving the preceding paper size across the larger dimension. This also effectively halves the area of each sheet. The most frequently used paper size is A4 measuring 210 by 297 millimetres (8.27 in × 11.7 in).

The significant advantage of this system is its scaling: if a sheet with an aspect ratio of √2 is divided into two equal halves parallel to its shortest sides, then the halves will again have an aspect ratio of √2. Folded brochures of any size can be made by using sheets of the next larger size, e.g. A4 sheets are folded to make A5 brochures. The system allows scaling without compromising the aspect ratio from one size to another—as provided by office photocopiers, e.g. enlarging A4 to A3 or reducing A3 to A4. Similarly, two sheets of A4 can be scaled down and fit exactly on 1 sheet without any cutoff or margins.

The behavior of the aspect ratio is easily proven: on a sheet of paper, let a be the long side and b be the short side; thus, a/b = √2. When the sheet of paper is folded in half widthwise, let c be the length of the new short side: c = a/2. If we take the ratio of the newly folded paper we have:

Therefore, the aspect ratio is preserved for the new dimensions of the folded paper.

Weights are easy to calculate as well: a standard A4 sheet made from 80 g/m² paper weighs 5 g (as it is ​¹⁄₁₆ of an A0 page, measuring 1 m²), allowing one to easily compute the weight—and associated postage rate—by counting the number of sheets used.

The advantages of basing a paper size upon an aspect ratio of √2 were first noted in 1786 by the German scientist and philosopher Georg Christoph Lichtenberg.^[3] The formats that became A2, A3, B3, B4 and B5 were developed in France on proposition of the mathematician Lazare Carnot and published for judiciary purpose in 1798 during the French Revolution.^[4] Early in 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" (IPA: [diːn.ʔaː.fiːɐ̯]) in everyday use in Germany and Austria.

The DIN 476 standard spread quickly to other countries. Before the outbreak of World War II, it had been adopted by the following countries:

During World War II, the standard was adopted by Uruguay (1942), Argentina (1943) and Brazil (1943), and afterwards 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. 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.

B series

A size chart illustrating the ISO B series.

In addition to the A series, there is a 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 0.707 m² (​¹⁄_√2 m²). As a result, B0 is 1 metre wide, and other sizes in the B series are a half, a quarter or further fractions of a metre wide. 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 50 cm × 70 cm; B5 is a relatively common choice for books. The B series is also used for envelopes and passports. 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

A size chart illustrating the ISO C series.

The C series is usually used 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 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 and C4 paper 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 is 114 mm × 229 mm where the common side to C5 and C6 is 162 mm.

Overview: ISO paper sizes

ISO paper sizes in portrait view (with rounded inch values)

Format	A series[5]		B series[6]		C series[7]
Size	mm × mm	in × in	mm × mm	in × in	mm × mm	in × in
0	841 × 1189	33.1 × 46.8	1000 × 1414	39.4 × 55.7	917 × 1297	36.1 × 51.1
1	594 × 841	23.4 × 33.1	707 × 1000	27.8 × 39.4	648 × 917	25.5 × 36.1
2	420 × 594	16.5 × 23.4	500 × 707	19.7 × 27.8	458 × 648	18.0 × 25.5
3	297 × 420	11.7 × 16.5	353 × 500	13.9 × 19.7	324 × 458	12.8 × 18.0
4	210 × 297	8.27 × 11.7	250 × 353	9.84 × 13.9	229 × 324	9.02 × 12.8
5	148 × 210	5.83 × 8.27	176 × 250	6.93 × 9.84	162 × 229	6.38 × 9.02
6	105 × 148	4.13 × 5.83	125 × 176	4.92 × 6.93	114 × 162	4.49 × 6.38
7	74 × 105	2.91 × 4.13	88 × 125	3.46 × 4.92	81 × 114	3.19 × 4.49
8	52 × 74	2.05 × 2.91	62 × 88	2.44 × 3.46	57 × 81	2.24 × 3.19
9	37 × 52	1.46 × 2.05	44 × 62	1.73 × 2.44	40 × 57	1.57 × 2.24
10	26 × 37	1.02 × 1.46	31 × 44	1.22 × 1.73	28 × 40	1.10 × 1.57
i

The α variables are the distinct first terms in the three geometric progressions of the same common-ratio equal to the square root of two. Each of the three geometric progressions (corresponding to the three series A, B, C) is formed by all possible paper dimensions (length and width) of the series arranged in a decreasing order. This interesting arrangement of dimensions is also very useful - not only it forms a geometric progression with easy to remember formulae, it also has that each consecutive pair of values (like a sliding window of size 2) will automatically correspond to the dimensions of a standard paper format in the series.

The tolerances specified in the standard are

• ±1.5 mm (0.06 in) for dimensions up to 150 mm (5.9 in),
• ±2 mm (0.08 in) for lengths in the range 150 to 600 mm (5.9 to 23.6 in) and
• ±3 mm (0.12 in) for any dimension above 600 mm (23.6 in).

German extensions

The German standard DIN 476 was published on 18 August 1922 and is the original specification of the A, B and C sizes. In 1991, it was split into DIN 476-1 for the A and B formats on the one hand and 476-2 for the C series on the other hand. The former has been withdrawn in 2002 in favor of adopting the international standard as DIN EN ISO 216, but part 2 has been retained and was last updated in 2008.

The first and the second editions of DIN 476 from 1922 and 1925 also included a D series.

The smallest formats specified originally were A13, B13, C8 and D8.

DIN 476 provides for formats larger than A0, denoted by a prefix factor. In particular, it lists the formats 2A0 and 4A0, which are twice and four times the size of A0 respectively. However, ISO 216:2007 notes 2A0 and 4A0 in the table of Main series of trimmed sizes (ISO A series) as well: "The rarely used sizes [2A0 and 4A0] which follow also belong to this series."

DIN 476 also used to specify slightly tighter tolerances than ISO 216:

• ±1 mm (0.04 in) for dimensions up to 150 mm (5.9 in),
• ±1.5 mm (0.06 in) for lengths in the range 150 mm to 600 mm (5.9 to 23.6 in) and
• ±2 mm (0.08 in) for any dimension above 600 mm (23.6 in).

Swedish extensions

Comparison of ISO 216 and Swedish standard SIS 014711 paper sizes between A4 and A3 sizes.

The Swedish standard SIS 014711^[8] 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 ¹⁶√2 from one size to the next. However, this SIS standard does not define any size between a D format and the next larger A format (called H in the previous example).

Of these additional formats, G5 (169 × 239 mm) and E5 (155 × 220 mm) are popular in Sweden and the Netherlands for printing dissertations,^[9] but the other formats have not turned out to be particularly useful in practice and they have not been adopted internationally.

The Swedish and German D series basically contain the same sizes, but are offset by one, i.e. DIN D4 equals SIS D5 and so on.

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 (instead of the factor √2 = 1.414... for the ISO B-series), 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, Taiwan and China, and most photocopiers are loaded with at least A4 and either one of A3, B4 and B5 paper.

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

Following Japanese paper sizes are included in Cascading Style Sheets (CSS): JIS-B4, JIS-B5.^[2]

Chinese extensions

The Chinese standard GB/T 148-1997^[11], which replaced GB 148-1989, documents the standard ISO series, A and B, but adds a custom D series. This Chinese format originates from the Republic of China (1912–49). The D series is not identical to the Swedish D series. It does not strictly follow the same principles as ISO paper sizes: The aspect ratio is only very roughly √2. The short side of a size is always 4 mm longer than the long side of the next smaller size. The long side of a size is always exactly – i.e. without further rounding – twice as long as the short side of the next smaller size.

Russian variants

The general adaptation of ISO 216 in the Soviet Union was GOST 9327-60. In its 1960 version, it lists formats down to A13, B12 and C8 and also specifies ½, ¼ and ⅛ prefixes for halving the shorter side (repeatedly), e.g. ½A4 = 105 mm × 297 mm.

A1, A2, A3, A4 and non-ISO sizes as GOST 3450-60 formats

A standard for technical drawings from 1960, GOST 3450-60^[12], introduces alternative numeric format designations to deal with very high or very wide sheets. These 2-digit codes are based upon A4 = "11": The first digit is the factor the longer side (297 mm) is multiplied by and the second digit is the one for the shorter side (210 mm), so "24" is 2×297 mm × 4×210 mm = 594 mm × 840 mm.

A2, A3, A4 and some of their derived non-ISO sizes as GOST 2301-68 formats

GOST 3450-60 was replaced 8 years later by ESKD GOST 2301-68^[13], but the numeric designations remained in popular use much longer. The new designations were not purely numeric, but consisted of the ISO label followed by an 'x', or possibly the multiplication sign '×', and the factor, e.g. DIN 2A0 = GOST A0×2, but DIN 4A0 ≠ GOST A0×4, also listed are: A0×3, A1×3, A1×4, A2×3–A2×5, A3×3–A3×7, A4×3–A4×9. The formats …×1 and …×2 usually would be aliases for existing formats.

Loose sizes

The United States, Canada, and the Philippines^[1] primarily use a different system of paper sizes compared to the rest of the world. The current standard sizes are unique to those countries, although due to the size of the North American market and proliferation of both software and printing hardware from the region, other parts of the world have become increasingly familiar with these sizes (though not necessarily the paper itself). Some traditional North American inch-based sizes differ from the Imperial British sizes described below.

Standardized American paper sizes

A size chart illustrating the ANSI sizes, superimposed on an "ANSI E" sheet.

In 1996, the American National Standards Institute adopted ANSI/ASME Y14.1 which defined a regular series of paper sizes based upon the de facto standard 8 ¹⁄₂ in × 11 in (216 mm × 279 mm) Letter size which it assigned "ANSI A", intended for technical drawings, hence sometimes labeled "Engineering". 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 and therefore also includes Ledger/Tabloid as "ANSI B". Unlike the ISO standard, however, the arbitrary base sides forces this series to have two alternating aspect ratios. For example, ANSI A is less elongated than A4, while ANSI B is more elongated than A3.

The Canadian standard CAN2-9.60-M76 and its successor CAN/CGSB-9.60-94 "Paper Sizes for Correspondence" specified paper sizes P1 through P6, which are the ANSI paper sizes rounded to the nearest 5 mm.^[20] All custom Canadian paper size standards were withdrawn in 2012 and the respective ISO standards took their places.

Canadian custom paper size standards

Title	Original	Release	Replacement	Release	Withdrawal
Paper Sizes for Correspondence	CAN2-9.60-M76	1976-04	CAN/CGSB-9.60-94	1994-07	2012-04
Paper Sizes for Printing	CAN2-9.61-M76	1976-04	CAN/CGSB-9.61-94	1994-07	2012-04
Paper Sizes for Single Part Continuous Business Forms	CAN2-9.62-81	1981-12	CAN/CGSB-9.62-94	1994-07	2012-04
Drawing Sheet Sizes	CAN2-9.64-M79	1979-04	CAN/CGSB-9.64-94	1994-07	2012-04
Common Image Area for Paper Sizes P4 and A4	CAN2-200.2-M79	1979-04			2012-03

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.

ANSI and CAN paper sizes

US size	in × in	mm × mm	Ratio	Canadian size (mm × mm)		Similar size (mm × mm)
N/A				CAN P6	107 × 140	ISO A6	105 × 148
N/A				CAN P5	140 × 215	ISO A5	148 × 210
ANSI A	​8 1⁄2 × 11	216 × 279	1.2941	CAN P4	215 × 280	ISO A4	210 × 297
ANSI B	11 × 17	279 × 432	1.5455	CAN P3	280 × 430	ISO A3	297 × 420
ANSI C	17 × 22	432 × 559	1.2941	CAN P2	430 × 560	ISO A2	420 × 594
ANSI D	22 × 34	559 × 864	1.5455	CAN P1	560 × 860	ISO A1	594 × 841
ANSI E	34 × 44	864 × 1118	1.2941	N/A		ISO A0	841 × 1187

Other, informal, larger sizes continuing the alphabetic series illustrated above exist, but they are not part of the series per se, because they do not exhibit the same aspect ratios. For example, Engineering F size is 28 in × 40 in or 711 mm × 1,016 mm with ca. 1.4286:1; it is commonly required for NAVFAC drawings, but is generally less commonly used. Engineering G size is 22 ¹⁄₂ in (572 mm) high, but it is a roll format with a variable width up to 90 in (2,286 mm) in increments of 8 ¹⁄₂ in (216 mm). Engineering H through N sizes are also roll formats.

Such huge sheets were at one time used for full-scale layouts of aircraft parts, automotive parts, wiring harnesses and the like, but are slowly being phased out, due to widespread use of computer-aided design (CAD) and computer-aided manufacturing (CAM). Some visual arts fields also continue to use these paper formats for large-scale printouts, such as for displaying digitally painted character renderings at life-size as references for makeup artists and costume designers, or to provide an immersive landscape reference.

Architectural sizes

A size chart illustrating the Architectural sizes.

In addition to the system as listed above, there is a corresponding series of paper sizes used for architectural purposes defined in the same standard, ANSI/ASME Y14.1, which is usually abbreviated "Arch". This series also shares the property that bisecting each size produces two of the size below, with alternating aspect ratios. 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 size Arch E1 has a different aspect ratio because it derives from adding 6 inches to each side of Arch D or subtracting the same amount from Arch E. An intermediate size between Arch C and D with a long side of 30 inches (760 mm) does not exist.

US architectural standard paper sizes^[21]

Names		in × in	mm × mm	Ratio
Arch A	Arch 1	9 × 12	229 × 305	3:4
Arch B	Arch 2	12 × 18	305 × 457	2:3
Arch C	Arch 3	18 × 24	457 × 610	3:4
Arch D	Arch 4	24 × 36	610 × 914	2:3
Arch E1	Arch 5	30 × 42	762 × 1067	5:7
Arch E	Arch 6	36 × 48	914 × 1219	3:4
Arch E2		26 × 38	660 × 965	13:19
Arch E3		27 × 39	686 × 991	9:13

Notebook sizes

The sizes listed above are for paper sold loose in reams. There are many sizes of tablets of paper, that is, sheets of paper 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 non-repro 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 8 ¹⁄₂ by 11 inches (215.9 by 279.4 mm), while the term "legal pad" is often used by laymen to refer to pads of various sizes including those of 8 ¹⁄₂ by 14 inches (215.9 by 355.6 mm). There are "steno pads" (used by stenographers) of 6 by 9 inches (152.4 by 228.6 mm).

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).

Office sizes

The international business card has the same size as the smallest rectangle containing a credit card. However, credit card size, as defined in ISO/IEC 7810, also specifies rounded corners and thickness.

Photography sizes

Postage sizes

This implies that all postcards have a width:height aspect ratio in the range 1.18 to 1.71. The only ISO 216 size in the post card range is A6.

Grain

Most industry standards express the direction of the grain last when giving dimensions (that is, 17 × 11 inches is short grain paper and 11 × 17 inches is long grain paper), although alternatively the grain alignment can be explicitly indicated with an underline (11 × 17 is short grain) or the letter "M" for "machine" (11M × 17 is short grain). Grain is important because paper will crack if folded across the grain: for example, if a sheet 17 × 11 inches is to be folded to divide the sheet into two 8.5 × 11 halves, then the grain will be along the 11-inch side.^[25] Paper intended to be fed into a machine that will bend the paper around rollers, such as a printing press, photocopier or typewriter, should be fed grain side first so that the axis of the rollers is along the grain.

Traditional British paper sizes

These sizes are no longer commonly used since the UK switched to ISO sizes.^[26] Many of these sizes were only used for making books (see bookbinding), and would never have been offered for ordinary stationery purposes.^[27]

Foolscap folio is often referred to simply as "folio" or "foolscap". Similarly, "quarto" is more correctly "copy draught quarto" and "Kings" is an alias for "Foolscap quarto".

Demitab

The demitab or demi-tab (from the French "demi" or half tabloid) is 5 ¹⁄₂ in × 8 ¹⁄₂ in (140 mm × 216 mm), equal to one quarter of a sheet of 11 in × 17 in (279 mm × 432 mm) tabloid size paper. In actual circulation, the size 8 in × 10 ¹⁄₂ in (203 mm × 267 mm) is common for a demitab.^[28] Tabloid newspapers, which are "generally half the size of a broadsheet", also vary in size. To add to the lack of uniformity, broadsheets also vary in size.

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 below, 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. 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. 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 than a page format.

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"^[32].

F4

A non-standard F4 paper size is common in Southeast Asia. It is a transitional size with the shorter side from ISO A4 (210 mm) and the longer side from British Foolscap (13 in, 330 mm) and is sometimes known as (metric) foolscap or folio as well.

In Indonesia and Philippines, F4 paper is 215 × 330 mm (8.5 × 13 in). In Indonesia it is sometimes called Folio, while in Philippines it is sometimes also called Long Bond.

A sheet of F4 can be cut from a sheet of SRA4 with very little wastage. The size is also smaller than its Swedish equivalent SIS F4 at 239 mm × 338 mm.

A0a

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", 31 in × 53 in (787 mm × 1,346 mm), as listed above, but given in the New Metric Handbook (Tutt & Adler 1981) as 813 mm × 1,372 mm (32 in × 54 in) for board size. This is a little larger than ISO A0, 841 mm × 1189 mm. So for a short time, a size called A0a of 1,000 mm × 1,370 mm (39.4 in × 53.9 in) was used in Britain, which is actually just a slightly shorter version of ISO B0 at 1414 mm.

Pliego

The most common paper sizes used for commercial and industrial printing in Colombia are based upon a size referred to as pliego that is ISO B1 (707 mm × 1000 mm) cut to full decimetres. Smaller sizes are derived by halving as usual and just get a vulgar fraction prefix: ​¹⁄₂ pliego and ​¹⁄₄ pliego.

Envelope and insert sizes

DL is a common envelope size from DIN 678-1 often with 90 mm × 45 mm address window in the lower left, which also fits ​¹⁄₃A4 well. Sometimes, it is erroneously labeled "DLE" instead, the E apparently standing for "envelope".

Raw sizes

Drawing paper

ISO 5457 specifies drawing paper sizes with a trimmed size equal to the A series sizes from A4 upward. The untrimmed sizes are 3 to 4 cm larger and rounded to the nearest centimeter. A0 through A3 are used in landscape orientation, while A4 is used in portrait orientation. Designations for preprinted drawing paper include the base sizes and a suffix, either T for trimmed or U for untrimmed sheets.