International standard paper sizes

thumb|right|Visualization with paper sizes in formats A0 to A8, exhibited at the science museum CosmoCaixa Barcelona

ISO 216 is an international standard for paper sizes, used around the world except in North America, the Philippines and parts of Latin America. The standard defines the "A", "B" and "C" series of paper sizes, which includes the A4, the most commonly available paper size worldwide. Two supplementary standards, ISO 217 and ISO 269, define related paper sizes.

All ISO 216, ISO 217 and ISO 269 paper sizes (except some envelopes) have the same aspect ratio, Square root of 2#Paper size|, within rounding error. This ratio has the unique property that when cut or folded in half widthways, the halves also have the same aspect ratio. Each ISO paper size is one half of the area of the next larger size in the same series.

Dimensions of A, B and C series

{| class="wikitable"

|+ ISO paper sizes in millimetres and in inches

! rowspan="2" | Size

! colspan="3" | A series formats

! colspan="3" | B series formats

! colspan="3" | C series formats

! name !! mm !! inches

! −2

| 4A0 || 1682 × 2378 || 66.2 × 93.6 || || || || || ||

! −1

| 2A0 || 1189 × 1682 || 46.8 × 66.2

| 2B0 || 1414 × 2000 || 55.7 × 78.7

| 2C0 || 1297 × 1834 || 51.1 × 72.2

! 0

| A0 || 841 × 1189 || 33.1 × 46.8

| B0 || 1000 × 1414 || 39.4 × 55.7

| C0 || 917 × 1297 || 36.1 × 51.1

! 1

| A1 || 594 × 841 || 23.4 × 33.1

| B1 || 707 × 1000 || 27.8 × 39.4

| C1 || 648 × 917 || 25.5 × 36.1

! 2

| A2 || 420 × 594 || 16.5 × 23.4

| B2 || 500 × 707 || 19.7 × 27.8

| C2 || 458 × 648 || 18.0 × 25.5

! 3

| A3 || 297 × 420 || 11.7 × 16.5

| B3 || 353 × 500 || 13.9 × 19.7

| C3 || 324 × 458 || 12.8 × 18.0

! 4

| A4 || 210 × 297 || 8.3 × 11.7

| B4 || 250 × 353 || 9.8 × 13.9

| C4 || 229 × 324 || 9.0 × 12.8

! 5

| A5 || 148 × 210 || 5.8 × 8.3

| B5 || 176 × 250 || 6.9 × 9.8

| C5 || 162 × 229 || 6.4 × 9.0

! 6

| A6 || 105 × 148 || 4.1 × 5.8

| B6 || 125 × 176 || 4.9 × 6.9

| C6 || 114 × 162 || 4.5 × 6.4

! 7

| A7 || 74 × 105 || 2.9 × 4.1

| B7 || 88 × 125 || 3.5 × 4.9

| C7 || 81 × 114 || 3.2 × 4.5

! 8

| A8 || 52 × 74 || 2.0 × 2.9

| B8 || 62 × 88 || 2.4 × 3.5

| C8 || 57 × 81 || 2.2 × 3.2

! 9

| A9 || 37 × 52 || 1.5 × 2.0

| B9 || 44 × 62 || 1.7 × 2.4

| C9 || 40 × 57 || 1.6 × 2.2

! 10

| A10 || 26 × 37 || 1.0 × 1.5

| B10 || 31 × 44 || 1.2 × 1.7

| C10 || 28 × 40 || 1.1 × 1.6

|- valign="bottom"

|

| colspan="3" | 250px

| colspan="3" | 297px

| colspan="3" | 273px

thumb|Comparison of ISO 216 paper sizes between A4 and A3 and Swedish extension [[SIS 014711 sizes]]

History

The oldest known mention of the advantages of basing a paper size on an aspect ratio of <math display="inline">\sqrt{2}</math> is found in a letter written on 25 October 1786 by the German scientist Georg Christoph Lichtenberg to Johann Beckmann, both at the University of Göttingen. Early variants of the formats that would become ISO paper sizes A2, A3, B3, B4, and B5 then evolved in France, where they were listed in a 1798 French law on taxation of publications () that was based in part on page sizes.

thumb|Comparison of A4 (shaded grey) and C4 sizes with some similar paper and photographic paper sizes

Searching for a standard system of paper formats on a scientific basis at the Bridge association (), as a replacement for the vast variety of other paper formats that had been used before, in order to make paper stocking and document reproduction cheaper and more efficient, in 1911 Wilhelm Ostwald proposed, over a hundred years after the 1798 French law, One can derive the weight of other sizes by arithmetic division. A standard A4 sheet made from paper weighs , as it is (four halvings, ignoring rounding) of an A0 page. Thus the weight, and the associated postage rate, can be approximated easily by counting the number of sheets used.

ISO 216 and its related standards were first published between 1975 and 1995:

ISO 216:2007, defining the A and B series of paper sizes
ISO 269:1985, defining the C series for envelopes
ISO 217:2013, defining the RA and SRA series of raw ("untrimmed") paper sizes

Properties

A series

Paper in the A series format has an aspect ratio of (≈ 1.414, when rounded). A0 is defined so that it has an area of 1 m<sup>2</sup> (about 11 ft<sup>2</sup>) before rounding to the nearest . Successive paper sizes in the series (A1, A2, A3, etc.) are defined by halving the area of the (unrounded) preceding paper size and rounding down, so that the long side of is the same length as the short side of An. Hence, each next size is nearly exactly half the area of the prior size. So two A2 pages (in landscape orientation) fit together over an A1 page (in portrait orientation), an A3 page is half an A2 page, A4 is half an A3 and so on.

The most used of this series is the A4 paper size, which is and thus almost exactly in area. For comparison, the letter paper size commonly used in North America () is about () wider and () shorter than A4. Then, the size of A5 paper is half of A4, i.e. × ( × ).

The geometric rationale for using the square root of 2 is to maintain the aspect ratio of each subsequent rectangle after cutting or folding an A-series sheet in half, perpendicular to the larger side. Given a rectangle with a longer side, x, and a shorter side, y, ensuring that its aspect ratio, , will be the same as that of a rectangle half its size, , which means that , which reduces to ; in other words, an aspect ratio of .

Any paper can be defined as , where (measuring in metres)

<math display="block">\text{A}_n = \begin{cases}

S = \left(\sqrt{\frac{1}{2\,\right)^{n + 1/2}\\

L = \left(\sqrt{\frac{1}{2\,\right)^{n - 1/2}

\end{cases}</math>

Therefore

<math display="block">\text{A}_0 = \begin{cases}

S = \left(\sqrt{\frac{1}{2\,\right)^{0 + 1/2} \approx 0.841\,\text{m}\\

L = \left(\sqrt{\frac{1}{2\,\right)^{0 - 1/2} \approx 1.189\,\text{m}

\end{cases}</math>

<math display="block">\text{A}_1 = \begin{cases}

S = \left(\sqrt{\frac{1}{2\,\right)^{1 + 1/2} \approx 0.595\,\text{m}\\

L = \left(\sqrt{\frac{1}{2\,\right)^{1 - 1/2} \approx 0.841\,\text{m}

\end{cases}</math>

<math display="block">\text{A}_2 = \begin{cases}

S = \left(\sqrt{\frac{1}{2\,\right)^{2 + 1/2} \approx 0.420\,\text{m}\\

L = \left(\sqrt{\frac{1}{2\,\right)^{2 - 1/2} \approx 0.595\,\text{m}

\end{cases}</math>

etc.

B series

The B series is defined in the standard as follows: "A subsidiary series of sizes is obtained by placing the geometrical means between adjacent sizes of the A series in sequence." The use of the geometric mean makes each step in size: B0, A0, B1, A1, B2 ... smaller than the previous one by the same factor. As with the A series, the lengths of the B series have the ratio , and folding one in half (and rounding down to the nearest millimetre) gives the next in the series. The shorter side of B0 is exactly 1 metre.

There is also an incompatible Japanese B series which the JIS defines to have 1.5 times the area of the corresponding JIS A series (which is identical to the ISO A series). Thus, the lengths of JIS B series paper are ≈ 1.22 times those of A-series paper. By comparison, the lengths of ISO B series paper are ≈ 1.19 times those of A-series paper (and ≈ 1.41 times the area).

Any paper (according to the ISO standard) can be defined as , where (measuring in metres)

<math display="block">\text{B}_n = \begin{cases}

S = \left(\sqrt{\frac{1}{2\,\right)^n\\

L = \left(\sqrt{\frac{1}{2\,\right)^{n - 1}

\end{cases}</math>

Therefore

<math display="block">\text{B}_0 = \begin{cases}

S = \left(\sqrt{\frac{1}{2\,\right)^0 = 1\,\text{m}\\

L = \left(\sqrt{\frac{1}{2\,\right)^{0 - 1} \approx 1.414\,\text{m}

\end{cases}</math>

<math display="block">\text{B}_1 = \begin{cases}

S = \left(\sqrt{\frac{1}{2\,\right)^1 \approx 0.707\,\text{m}\\

L = \left(\sqrt{\frac{1}{2\right)^{1 - 1} = 1\,\text{m}

\end{cases}</math>

<math display="block">\text{B}_2 = \begin{cases}

S = \left(\sqrt{\frac{1}{2\,\right)^2 = 0.5\,\text{m}\\

L = \left(\sqrt{\frac{1}{2\,\right)^{2 - 1} \approx 0.707\,\text{m}

\end{cases}</math>

etc.

C series

The C series formats are geometric means between the B series and A series formats with the same number (e.g. C2 is the geometric mean between B2 and A2). The width to height ratio of C series formats is as in the A and B series. A, B, and C series of paper fit together as part of a geometric progression, with ratio of successive side lengths of , though there is no size half-way between Bn and : A4, C4, B4, "D4", A3, ...; there is such a D-series in the Swedish extensions to the system. The lengths of ISO C series paper are therefore ≈ 1.09 times those of A-series paper.

The C series formats are used mainly for envelopes. An unfolded A4 page will fit into a C4 envelope. Due to same width to height ratio, 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).

Any paper can be defined as , where (measuring in metres)

<math display="block">\text{C}_n = \begin{cases}

S = \left(\sqrt{\frac{1}{2\,\right)^{n + 1/4}\\

L = \left(\sqrt{\frac{1}{2\,\right)^{n - 3/4}

\end{cases}</math>

Therefore

<math display="block">\text{C}_0 = \begin{cases}

S = \left(\sqrt{\frac{1}{2\,\right)^{0 + 1/4} \approx 0.917\,\text{m}\\

L = \left(\sqrt{\frac{1}{2\,\right)^{0 - 3/4} \approx 1.297\,\text{m}

\end{cases}</math>

<math display="block">\text{C}_1 = \begin{cases}

S = \left(\sqrt{\frac{1}{2\,\right)^{1 + 1/4} \approx 0.648\,\text{m}\\

L = \left(\sqrt{\frac{1}{2\,\right)^{1 - 3/4} \approx 0.917\,\text{m}

\end{cases}</math>

<math display="block">\text{C}_2 = \begin{cases}

S = \left(\sqrt{\frac{1}{2\,\right)^{2 + 1/4} \approx 0.458\,\text{m}\\

L = \left(\sqrt{\frac{1}{2\,\right)^{2 - 3/4} \approx 0.648\,\text{m}

\end{cases}</math>

etc.

Tolerances

The tolerances specified in the standard are:

±1.5 mm for dimensions up to 150 mm,
±2.0 mm for dimensions in the range 150 to 600 mm, and
±3.0 mm for dimensions above 600 mm.

These are related to comparison between series A, B and C.

Application

The ISO 216 formats are organized around the ratio 1:; two sheets next to each other together have the same ratio, sideways.

In scaled photocopying, for example, two A4 sheets reduced to A5 size fit exactly onto one A4 sheet, and an A4 sheet in magnified size onto an A3 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 North American paper sizes. Although many Latin American countries have also officially adopted the ISO 216 paper format, Mexico, Panama, Peru, Colombia, the Philippines, and Chile also use mostly U.S. paper sizes.

Rectangular sheets of paper with the ratio 1: are popular in paper folding, such as origami, where they are sometimes called "A4 rectangles" or "silver rectangles". In other contexts, the term "silver rectangle" can also refer to a rectangle in the proportion 1:(1 + ), known as the silver ratio.

Matching technical pen widths

thumb|upright|Rotring Rapidographs in ISO nib sizes

An adjunct to the ISO paper sizes, particularly the A series, are the technical drawing line widths specified in ISO 128. For example, line type A ("Continuous – thick", used for "visible outlines") has a standard thickness of 0.7 mm on an A0-sized sheet, 0.5 mm on an A1 sheet, and 0.35 mm on A2, A3, or A4.

The matching technical pen widths are 0.13, 0.18, 0.25, 0.35, 0.5, 0.7, 1.0, 1.40, and 2.0 mm, as specified in ISO 9175-1. Colour codes are assigned to each size to facilitate easy recognition by the drafter. Like the paper sizes, these pen widths increase by a factor of , so that particular pens can be used on particular sizes of paper, and then the next smaller or larger size can be used to continue the drawing after it has been reduced or enlarged, respectively.

:{| class="wikitable"

!style="text-align:left"| Line Width (mm)

|colspan=2| 0.10

|colspan=2| 0.13

|colspan=2| 0.18

|colspan=2| 0.25

|colspan=2| 0.35

|colspan=2| 0.50

|colspan=2| 0.70

|colspan=2| 1.0

|colspan=2| 1.4

|colspan=2| 2.0

!style="text-align:left"| Colour

|width="2%" style="background:brown"| ||Maroon

|width="2%" style="background:darkmagenta"| ||Violet

|width="2%" style="background:crimson"| ||Red

|width="2%" style="background:white"| ||White

|width="2%" style="background:gold"| ||Yellow

|width="2%" style="background:saddlebrown"| ||Brown

|width="2%" style="background:steelblue"| ||Blue

|width="2%" style="background:chocolate"| ||Orange

|width="2%" style="background:lightseagreen"| ||Turquoise

|width="2%" style="background:silver"| ||Gray

thumb|upright=.5|Micronorm logo The earlier DIN 6775 standard upon which ISO 9175-1 is based also specified a term and symbol for easy identification of pens and drawing templates compatible with the standard, called Micronorm, which may still be found on some technical drafting equipment.

Overformats

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:

{| class="wikitable"

|+ DIN 476 overformats (with rounded inch values)

! Name !! mm × mm !! inch × inch

! 4A0

! 2A0

While not formally defined, ISO 216:2007 notes them 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." 2A0 is also known by other unofficial names like "A00".

References

External links

International standard paper sizes: ISO 216 details and rationale
ISO 216 at iso.org
Articles by Wilhelm Ostwald referencing Lichtenberg's letter, and W. Porstmann specifying a metric system of norms for formats for lengths, surfaces (planes), and volumes, laying the ground for the DIN-Series, in German
Explanation of paper sizes

Dimensions of A, B and C series

History

Properties

A series

B series

C series

Tolerances

Application

Matching technical pen widths

Overformats

See also

References

External links