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 
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 
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 (ISO) paper sizes 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 folded in half lengthwise the paper retains its original aspect ratio: .
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The international ISO standard is based on the German DIN standard 476 (DIN 476) from 1922.
The formats that became A2, A3, B3, B4 and B5 were developed in France, and published in 1798 during the French Revolution, but were subsequently forgotten.^{[1]}
The aspect ratio used by this standard was mentioned in a letter by the German Georg Christoph Lichtenberg, written on 25 October 1786.^{[2]}
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, 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 which is 210 × 297 mm. A4 paper is 6 mm narrower and 18 mm longer than the "Letter" paper size, commonly used in North America.
The geometric rationale behind the square root of 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 An in metres and without rounding off is the geometric sequence: a_{n} = 2^{1 / 4 − n / 2}. The paper size An thus has the dimension a_{n} × a_{n + 1}.
The exact millimetre measurement of the long side of An is given by .
The B series are defined in a similar manner to the A series; the lengths still have the ratio , and folding one in half gives the next in the series. The difference however is that while A0 paper has total area of 1m^{2}, B0 is instead defined to have its shorter side of length 1m. It can be shown that the B series formats are geometric means 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.
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 Aseries paper. By comparison, the lengths of ISO B series paper are approximately 1.19 times those of Aseries paper.
The exact millimetre measurement of the long side of Bn is given by .
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).
A, B, and C paper fit together as part of a geometric progression, with ratio of successive side lengths of 2^{1/8}, though there is no size halfway between Bn and An1: A4, C4, B4, "D4," A3, ...; there is such a Dseries in the Swedish extensions to the system.
The exact millimetre measurement of the long side of Cn is given by .
The tolerances specified in the standard are:
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 
0+  914 × 1292  35.9 × 50.8  1118 × 1580  44 × 62.2   ×    ×  
1  594 × 841  23.4 × 33.1  707 × 1000  27.8 × 39.4  648 × 917  25.5 × 36.1 
1+  609 × 914  24 × 36   ×    ×    ×    ×  
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 
3+  329 × 483  12.9 × 19.0   ×    ×    ×    ×  
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 
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 nonmetric 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 and Canada, which use the Letter, Legal and Executive system.
Rectangular sheets of paper with the ratio are popular in paper folding, where they are sometimes called "A4 rectangles" or "silver rectangles".^{[3]} However, in other contexts, the term "silver rectangle" can also refer to a rectangle in the proportion , known as the silver ratio.
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a number allocated by ISO the International Organisation for Standardisation
ISO 216
