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ISO 216
 
 
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ISO 216 specifies international standard
International Organization for Standardization

The International Organization for Standardization , widely known as ISO , is an international standard-setting body composed of representatives from various national standards organizations....
 (ISO) paper size
Paper size

There have been many standard sizes of paper at different times and in different countries, but today there are two widespread systems in use: the international standard and the North American sizes....
s used in most countries in the world today.






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 ISO 269 sizes
(mm × mm)
C Series
C0 917 × 1297
C1 648 × 917
C2 458 × 648
C3 324 × 458
C4 229 × 324
C5 162 × 229
C6 114 × 162
C7/6 81 × 162
C7 81 × 114
C8 57 × 81
C9 40 × 57
C10 28 × 40
DL 110 × 220


 ISO 216 sizes
(mm × mm)
B Series
B0 1000 × 1414
B1 707 × 1000
B2 500 × 707
B3 353 × 500
B4 250 × 353
B5 176 × 250
B6 125 × 176
B7 88 × 125
B8 62 × 88
B9 44 × 62
B10 31 × 44


 ISO 216 sizes
(mm × mm)
A Series
A0 841 × 1189
A1 594 × 841
A2 420 × 594
A3 297 × 420
A4 210 × 297
A5 148 × 210
A6 105 × 148
A7 74 × 105
A8 52 × 74
A9 37 × 52
A10 26 × 37


ISO 216 specifies international standard
International Organization for Standardization

The International Organization for Standardization , widely known as ISO , is an international standard-setting body composed of representatives from various national standards organizations....
 (ISO) paper size
Paper size

There have been many standard sizes of paper at different times and in different countries, but today there are two widespread systems in use: the international standard and the North American sizes....
s used in most countries in the world today. It is the standard which defines the commonly available A4 paper size. The underlying principle is that when rectangles with width/length ratio are cut or folded in half the rectangles thus formed retain the original width/length ratio.

History

The international ISO standard is based on the German DIN
Deutsches Institut für Normung

Deutsches Institut f?r Normung e.V. is the Germany national organization for standardization and is that country's International Organization for Standardization member body....
 standard 476 (DIN 476) from 1922.

Some of the formats contained therein were independently invented in France during its revolution, but were later forgotten.

The aspect ratio
Aspect ratio

The aspect ratio of a shape is the ratio of its longer dimension to its shorter dimension. It may be applied to two characteristic dimensions of a three-dimensional shape, such as the ratio of the longest and shortest axis, or for symmetrical objects that are described by just two measurements, such as the length and diameter of a rod....
 used by this standard was mentioned in a letter by the German Georg Christoph Lichtenberg
Georg Christoph Lichtenberg

Georg Christoph Lichtenberg was a Germany scientist, satirist and Anglophile. As a scientist, he was the first to hold a professorship explicitly dedicated to experimental physics in Germany....
, written on 25 October 1786.
  • ISO 216
    ISO 216

    ISO 216 specifies International Organization for Standardization paper sizes used in most countries in the world today. It is the standard which defines the commonly available A4 paper size....
    :1975, defines two series of paper sizes: A and B
  • ISO 269:1985, defines a C series for envelopes
  • ISO 217
    ISO 217

    The ISO 217:1995 standard defines the RA and SRA paper formats.These paper series are untrimmed raw paper. RA stands for ?raw format A? and SRA stands for ?supplementary raw format A?....
    :1995, defines two untrimmed series of raw paper sizes: RA and SRA


A series

A Size Illustration
Paper in the A series format has a aspect ratio, although this is rounded to the nearest millimetre. A0 is defined so that it has an area of 1 m²
Square metre

The square metre is the SI derived unit of area, with symbol m?. It is defined as the area of a square whose sides measure exactly one metre....
, prior to the above mentioned rounding. Successive paper sizes in the series (A1, A2, A3, etc.) are defined by halving the preceding paper size, cutting parallel to its shorter side (so that the long side of A(n+1) is the same length as the short side of An, again prior to rounding).

The most frequently used of this series is the size A4 (210 × 297 mm). A4 paper is 6 mm narrower and 18 mm longer than the "Letter
Letter (paper size)

Letter is the most common paper size for office use in the United States and Canada. It is 8? by 11 inches .Ronald Reagan made this the paper size for U.S....
" paper size, 8½ × 11 inches (216 × 279 mm), commonly used in North America
North America

North America is the northern continent of the Americas, situated in the Earth's northern hemisphere and almost totally in the western hemisphere....
.

The geometric rationale behind the square root of 2
Square root of 2

The square root of 2, also known as Pythagoras' constant,is the positive real number that, when multiplied by itself, gives the number 2 ....
 is to maintain the aspect ratio of each subsequent rectangle after cutting the sheet in half, perpendicular to the larger side. Given a rectangle with a longer side, x, and a shorter side, y, the following equation shows how the aspect ratio of a rectangle compares to that of a half rectangle: which reduces to or an aspect ratio of

The formula that gives the larger border of the paper size A in metres and without rounding off is the geometric sequence: . The paper size A thus has the dimension × .

The exact millimetre measurement of the long side of A is given by .

B series

B Size Illustration
The B series formats are geometric mean
Geometric mean

The geometric mean, in mathematics, is a type of mean or average, which indicates the central tendency or typical value of a set of numbers. It is similar to the arithmetic mean, which is what most people think of with the word "average," except that instead of adding the set of numbers and then dividing the sum by the count of numbers in the...
s between the A series format with a particular number and the A series format with one lower number. For example, B1 is the geometric mean between A1 and A0. The sides of B0 are 1 m to m.

There is also an incompatible Japanese B series defined by the JIS. The lengths of JIS B series paper are approximately 1.22 times those of A-series paper.

The exact millimetre measurement of the long side of B is given by .

C series

The C series formats are geometric means between the B series format with a particular number and the A series format with the same number, (e.g., C2 is the geometric mean between B2 and A2). The C series formats are used mainly for envelopes. An A4 page will fit into a C4 envelope. C series envelopes follow the same ratio principle as the A series pages. For example, if an A4 page is folded in half so that it is A5 in size, it will fit into a C5 envelope (which will be the same size as a C4 envelope folded in half).

The exact millimetre measurement of the long side of C is given by .

Tolerances

The tolerances specified in the standard are:
  • ±1.5 mm for dimensions up to 150 mm,
  • ±2.0 mm for lengths in the range 150 to 600 mm, and
  • ±3.0 mm for any dimension above 600 mm.


A, B, C comparison

 ISO/DIN paper sizes in millimetres and in inch
Inch

An inch is the name of a Units of measurement of length in a number of different systems, including Imperial units, and United States customary units....
es
A Series Formats B Series Formats C Series Formats
size mm inches mm inches mm inches
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 8.3 × 11.7 250 × 353 9.8 × 13.9 229 × 324 9.0 × 12.8
5 148 × 210 5.8 × 8.3 176 × 250 6.9 × 9.8 162 × 229 6.4 × 9.0
6 105 × 148 4.1 × 5.8 125 × 176 4.9 × 6.9 114 × 162 4.5 × 6.4
7 74 × 105 2.9 × 4.1 88 × 125 3.5 × 4.9 81 × 114 3.2 × 4.5
8 52 × 74 2.0 × 2.9 62 × 88 2.4 × 3.5 57 × 81 2.2 × 3.2
9 37 × 52 1.5 × 2.0 44 × 62 1.7 × 2.4 40 × 57 1.6 × 2.2
10 26 × 37 1.0 × 1.5 31 × 44 1.2 × 1.7 28 × 40 1.1 × 1.6
 


Application

Before the adoption of ISO 216, many different paper formats were used internationally. These formats did not fit into a coherent system and were defined in terms of non-metric units.

The ISO 216 formats are organized around the ratio ; two sheets next to each other together have the same ratio, sideways. In scaled photocopying, for example, two A4 sheets in reduced size fit exactly onto one A4 sheet, an A4 sheet in magnified size onto an A3 sheet, and an A5 sheet scaled up onto a A4 sheet, in each case there is neither waste nor want. The principal countries not generally using the ISO paper sizes are the United States
United States

The United States of America is a Federal government constitutional republic comprising U.S. state and a federal district. The country is situated mostly in central North America, where its Contiguous United States and Washington, D.C., the Capital districts and territories, lie between the Pacific Ocean and Atlantic Oceans, Borders of the U...
 and Canada
Canada

Canada is a country occupying most of northern North America, extending from the Atlantic Ocean in the east to the Pacific Ocean in the west and northward into the Arctic Ocean....
, which use the Letter, Legal and Executive system
Paper size

There have been many standard sizes of paper at different times and in different countries, but today there are two widespread systems in use: the international standard and the North American sizes....
. (Canada uses a P-series of sizes, which are the US paper sizes rounded to metric dimensions.)

Rectangular
Rectangle

In geometry, a rectangle is a Closed set planar quadrilateral with four right angles. A rectangle with vertices ABCD would be denoted as .A rectangle with adjacent sides of lengths a and b has area ab and diagonals of equal length ....
 sheets of paper with the ratio are popular in paper folding
Paper folding

Paper folding is the art of folding paper; it is known in many societies that use paper. In much of the Western world, the term origami is used synonymously with paper folding, though the term properly only refers to the art of paper folding in Japan....
, where they are sometimes called "A4 rectangles" or "silver rectangles". (Confusingly, "silver rectangle" can also refer to a rectangle in the proportion ), known as the silver ratio
Silver ratio

The silver ratio is a Mathematics constant. Its name is an allusion to the golden ratio; analogously to the way the golden ratio is the limiting ratio of consecutive Fibonacci numbers, the silver ratio is the limiting ratio of consecutive Pell numbers....
.)

See also

  • ISO 128
    ISO 128

    ISO 128 is an International Organization for Standardization , about the general principles of presentation in technical drawings. This standard specifies the graphical representation of objects on technical drawings with the aim of facilitating the international exchange of information on drawings and ensuring their uniformity in a comprehen...
  • Letter (paper size)
    Letter (paper size)

    Letter is the most common paper size for office use in the United States and Canada. It is 8? by 11 inches .Ronald Reagan made this the paper size for U.S....
  • Paper size
    Paper size

    There have been many standard sizes of paper at different times and in different countries, but today there are two widespread systems in use: the international standard and the North American sizes....


External links

  • : ISO 216 details and rationale