ISO 216

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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 international ISO standard is based on the German DIN standard 476 (DIN 476) from 1922. Some of the formats contained therein were independently invented in France during its revolution, but were later forgotten.^[1] The aspect ratio used by this norm was mentioned in a letter by the German Georg Christoph Lichtenberg, written on 25 October 1786.^[2]

[edit] A series

A size chart illustrating the ISO A series.

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 An+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" paper size, 8½ × 11 inches (216 × 279 mm), commonly used in North America.

The geometrical rationale behind the square root of 2 is to maintain the aspect ratio of both of the rectangles after cutting the larger rectangle in half. 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 .

[edit] B series

A size chart illustrating the ISO B series.

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. 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 Bn is given by .

[edit] C series

A size chart illustrating the ISO 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 Cn is given by .

[edit] Tolerances

The tolerances specified in the standard are:

[edit] A, B, C comparison

ISO/DIN paper sizes in millimetres and in inches

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

[edit] 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. This simplifies copying (e.g. two A4 sheets in reduced size onto one A4 sheet; an A4 sheet in magnified size on to a A3 sheet; or a A5 sheet in magnified size on to a A4 sheet). The principal countries not generally using the ISO paper sizes are the United States and Canada, which use the Letter, Legal and Executive system. (Canada uses a P-series of sizes, which are the US paper sizes rounded to metric dimensions.)

Rectangular sheets of paper with the ratio are popular in paper folding, where they are sometimes called "A4 rectangles" or "silver rectangles".^[3] (Confusingly, "silver rectangle" can also refer to a rectangle in the proportion ), known as the silver ratio.)

[edit] References

[edit] See also

[edit] External links