# Print and Paper sizes

Many paper size standards conventions have existed at different times and in different countries. Today, the A and B series of ISO 216, which includes the commonly used A4 size, are the international standard used by almost every country. However, in many countries in the Americas as well as in the Philippines, the North American series of paper sizes such as 'Letter' and 'Legal' is more prevalent.

Paper sizes affect writing paper, stationery, cards, and some printed documents. The international standard for envelopes is the C series of ISO 269.

## Contents

• 1 International paper sizes
• 2 North American paper sizes
• International paper sizes

The international paper size standard is ISO 216. It is based on the German DIN 476 standard for paper sizes. ISO paper sizes are all based on a single aspect ratio of the square root of 2, or approximately 1:1.4142. There are different series, as well as several extensions.

The following international paper sizes are included in Cascading Style Sheets (CSS): A3, A4, A5, B4, B5.

### 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 ${\displaystyle {\sqrt[{4}]{2}}}$ m × ${\displaystyle {\frac {1}{\sqrt[{4}]{2}}}}$ 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:

${\displaystyle {\frac {a}{b}}={\frac {b}{\frac {a}{2}}}={\frac {2b}{a}}}$

by rearranging the terms, we get:

${\displaystyle {\frac {a^{2}}{b^{2}}}=2}$
${\displaystyle {\frac {a}{b}}={\sqrt {2}}}$

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 116 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. 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. 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:

 Belgium (1924) Netherlands (1925) Norway (1926) Finland (1927) Switzerland (1929) Sweden (1930) Soviet Union (1934) Hungary (1938) Italy (1939)

During World War II, the standard was adopted by Uruguay (1942), Argentina (1943) and Brazil (1943), and afterwards spread to other countries:

 Spain (1947) Austria (1948) Iran (1948) Romania (1949) Japan (1951) Denmark (1953) Czechoslovakia (now Czech Republic and Slovakia) (1953) Israel (1954) Portugal (1954) Yugoslavia (now Croatia, Serbia, Slovenia, Bosnia and Herzegovina, Montenegro, and North Macedonia) (1956) India (1957) Poland (1957) United Kingdom (1959) Ireland (1959) Venezuela (1962) New Zealand (1963) Iceland (1964) Mexico (1965) South Africa (1966) France (1967) Peru (1967) Turkey (1967) Chile (1968) Greece (1970) Rhodesia (now 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. 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

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 ${\displaystyle {\sqrt[{4}]{2}}}$ m × ${\displaystyle {\frac {1}{\sqrt[{4}]{2}}}}$ 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:

${\displaystyle {\frac {a}{b}}={\frac {b}{\frac {a}{2}}}={\frac {2b}{a}}}$

by rearranging the terms, we get:

${\displaystyle {\frac {a^{2}}{b^{2}}}=2}$
${\displaystyle {\frac {a}{b}}={\sqrt {2}}}$

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 116 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. 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. 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:

 Belgium (1924) Netherlands (1925) Norway (1926) Finland (1927) Switzerland (1929) Sweden (1930) Soviet Union (1934) Hungary (1938) Italy (1939)

During World War II, the standard was adopted by Uruguay (1942), Argentina (1943) and Brazil (1943), and afterwards spread to other countries:

 Spain (1947) Austria (1948) Iran (1948) Romania (1949) Japan (1951) Denmark (1953) Czechoslovakia (now Czech Republic and Slovakia) (1953) Israel (1954) Portugal (1954) Yugoslavia (now Croatia, Serbia, Slovenia, Bosnia and Herzegovina, Montenegro, and North Macedonia) (1956) India (1957) Poland (1957) United Kingdom (1959) Ireland (1959) Venezuela (1962) New Zealand (1963) Iceland (1964) Mexico (1965) South Africa (1966) France (1967) Peru (1967) Turkey (1967) Chile (1968) Greece (1970) Rhodesia (now 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. 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.

### 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 ${\displaystyle \left(\alpha _{A}\cdot 2^{-{\frac {i+1}{2}}}\right)\times \left(\alpha _{A}\cdot 2^{-{\frac {i}{2}}}\right),}$ ${\displaystyle \alpha _{A}=1000\,{\text{mm}}\cdot {\sqrt[{4}]{2}}}$ ${\displaystyle \left(\alpha _{B}\cdot 2^{-{\frac {i+1}{2}}}\right)\times \left(\alpha _{B}\cdot 2^{-{\frac {i}{2}}}\right),}$ ${\displaystyle \alpha _{B}=1000\,{\text{mm}}\cdot {\sqrt {2}}}$ ${\displaystyle \left(\alpha _{C}\cdot 2^{-{\frac {i+1}{2}}}\right)\times \left(\alpha _{C}\cdot 2^{-{\frac {i}{2}}}\right),}$ ${\displaystyle \alpha _{C}=1000\,{\text{mm}}\cdot {\sqrt[{8}]{8}}}$

### 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.

### North American paper sizes

North American paper sizes Loose sizes North American paper sizes Size in × in mm × mm Aspect ratio Letter 8 12 × 11 216 × 279 1.2941... Legal 8 12 × 14 216 × 356 1.6470... Tabloid 11 × 17 279 × 432 1.54 Ledger 17 × 11 432 × 279 0.6470... Junior Legal 5 × 8 127 × 203 1.6 Half Letter, Memo 5 12 × 8 12 140 × 216 1.54 Government Letter 8 × 10 12 203 × 267 1.3125 Government Legal 8 12 × 13 216 × 330 1.5294...

The United States, Canada, and the Philippines primarily use a different system of paper sizes from 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.

#### Common loose sizes

Letter, Legal and Ledger/Tabloid are by far the most commonly used of these for everyday activities, and the only ones included in Cascading Style Sheets (CSS).

The origins of the exact dimensions of Letter size paper (8 12 in × 11 in or 216 mm × 279 mm) are lost in tradition and not well documented. The American Forest and Paper Association 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.

Outside of North America, Letter size may also be known as "American Quarto". If one accepts some trimming, the size is indeed one quarter of the old Imperial paper size known as Demy, 17 12 in × 22 12 in (444 mm × 572 mm). A double demy is 572 by 902 millimetres (22.5 in × 35.5 in).

US paper sizes are currently standard in the United States and are the most commonly used formats at least in the Philippines, most of Mesoamerica and Chile. The latter use US Letter, but their Legal size is one inch shorter than its US equivalent.

Mexico and Colombia, for instance, have adopted the ISO standard, but US 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 (Letter), Oficio (Government-Legal) and Doble carta (Ledger/Tabloid) being nearly universal.

In Canada, US paper sizes are a de facto standard. The government, however, also uses ISO paper sizes[citation needed].

#### Variant loose sizes

There is an additional paper size, 8 in × 10 12 in (203 mm × 267 mm), to which the name Government-Letter was given by the IEEE Printer Working Group (PWG). It was prescribed by Herbert Hoover when he was Secretary of Commerce to be used for US government forms, apparently to enable discounts from the purchase of paper for schools, but more likely due to the standard use of trimming books (after binding) and paper from the standard letter size paper to produce consistency and allow "bleed" printing. 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 US government switch to regular Letter size, which is both half an inch longer and wider. The former government size is still commonly used in spiral-bound notebooks, for children's writing and the like, a result of trimming from the current Letter dimensions.

By extension of the American standards, the halved Letter size, 5 12 in × 8 in (140 mm × 203 mm), meets the needs of many applications. It is variably known as Statement, Stationery, Memo, Half Letter, Half A (from ANSI sizes) or simply Half Size. Like the similar-sized ISO A5, it is used for everything from personal letter writing to official aeronautical maps. Organizers, notepads, and diaries also often use this size of paper; thus 3-ring binders are also available in this size. Booklets of this size are created using word processing tools with landscape printing in two columns on letter paper which are then cut or folded into the final size.

Curiously, a foot-long sheet with the common width of Letter and (Government) Legal, i.e. 12 in × 8 12 in (305 mm × 216 mm), would have an aspect ratio very close to the square root of two as used by international paper sizes and would actually almost exactly match ISO RA4 (305 mm × 215 mm).

#### Standardized American paper sizes

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 12 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. All custom Canadian paper size standards were withdrawn in 2012 and the respective ISO standards took their places.