View source for ISO 216

{{short description |International standard for paper sizes, including A4}}
{{Use British English |date=January 2024}}
{{Use dmy dates |date=August 2021}}
{{Lead too short|date=June 2023}}
[[File:PapierformateA0bisA8.jpg|thumb|right|Visualization with paper sizes in formats A0 to A8, exhibited at the science museum CosmoCaixa Barcelona]]
[[File:Schnellaktendeckel03.jpg|thumb|right|An A4 paper sheet folded into two A5 size pages]]
'''ISO 216''' is an [[International Organization for Standardization|international standard]] for [[paper size]]s, used around the world except in North America 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; the '''ISO 269''' "'''C'''" series is commonly listed alongside the A and B sizes.

All ISO 216, ISO 217 and ISO 269 paper sizes (except some envelopes) have the same [[aspect ratio]], [[square root of 2|{{math|{{sqrt|2}}:1}}]], within rounding to [[millimetres]]. 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.<ref>{{cite web |url=https://www.papersizes.org |website= Paper Sizes |title = International Paper Sizes & Formats|access-date=29 June 2020}}</ref>

== Dimensions of A, B and C series ==
<!-- [[Template:0]] adds a figure width space to keep the numbers aligned -->
{| class="wikitable"
|+ ISO paper sizes in [[millimetres]] and in [[inch]]es
! rowspan="2" | Size
! colspan="3" | A series formats
! colspan="3" | B series formats
! colspan="3" | C series formats
|- 
! name !! mm !! inches
! name !! mm !! inches
! name !! mm !! inches
|-
! −2
| 4A0 || 1682 × 2378 || 66.2 × 93.6 || || || || || ||
|-
! −1
| 2A0 || 1189 × 1682 || 46.8 × 66.2 || || || || || ||
|- 
! 0
| A0 || {{0}}841 × 1189 || 33.1 × 46.8
| B0 || 1000 × 1414 || 39.4 × 55.7
| C0 || {{0}}917 × 1297 || 36.1 × 51.1
|- 
! 1
| A1 || {{0}}594 × {{0}}841 || 23.4 × 33.1
| B1 || {{0}}707 × 1000 || 27.8 × 39.4
| C1 || {{0}}648 × {{0}}917 || 25.5 × 36.1
|- 
! 2
| A2 || {{0}}420 × {{0}}594 || 16.5 × 23.4
| B2 || {{0}}500 × {{0}}707 || 19.7 × 27.8
| C2 || {{0}}458 × {{0}}648 || 18.0 × 25.5
|- 
! 3
| A3 || {{0}}297 × {{0}}420 || 11.7 × 16.5
| B3 || {{0}}353 × {{0}}500 || 13.9 × 19.7
| C3 || {{0}}324 × {{0}}458 || 12.8 × 18.0
|- 
! 4
| A4 || {{0}}210 × {{0}}297 || {{0}}8.3 × 11.7
| B4 || {{0}}250 × {{0}}353 || {{0}}9.8 × 13.9
| C4 || {{0}}229 × {{0}}324 || {{0}}9.0 × 12.8
|- 
! 5
| A5 || {{0}}148 × {{0}}210 || {{0}}5.8 × {{0}}8.3
| B5 || {{0}}176 × {{0}}250 || {{0}}6.9 × {{0}}9.8
| C5 || {{0}}162 × {{0}}229 || {{0}}6.4 × {{0}}9.0
|- 
! 6
| A6 || {{0}}105 × {{0}}148 || {{0}}4.1 × {{0}}5.8
| B6 || {{0}}125 × {{0}}176 || {{0}}4.9 × {{0}}6.9
| C6 || {{0}}114 × {{0}}162 || {{0}}4.5 × {{0}}6.4
|- 
! 7
| A7 || {{0}}{{0}}74 × {{0}}105 || {{0}}2.9 × {{0}}4.1
| B7 || {{0}}{{0}}88 × {{0}}125 || {{0}}3.5 × {{0}}4.9 
| C7 || {{0}}{{0}}81 × {{0}}114 || {{0}}3.2 × {{0}}4.5 
|- 
! 8
| A8 || {{0}}{{0}}52 × {{0}}{{0}}74 || {{0}}2.0 × {{0}}2.9
| B8 || {{0}}{{0}}62 × {{0}}{{0}}88 || {{0}}2.4 × {{0}}3.5
| C8 || {{0}}{{0}}57 × {{0}}{{0}}81 || {{0}}2.2 × {{0}}3.2
|- 
! 9
| A9 || {{0}}{{0}}37 × {{0}}{{0}}52 || {{0}}1.5 × {{0}}2.0
| B9 || {{0}}{{0}}44 × {{0}}{{0}}62 || {{0}}1.7 × {{0}}2.4
| C9 || {{0}}{{0}}40 × {{0}}{{0}}57 || {{0}}1.6 × {{0}}2.2
|- 
! 10
| A10 || {{0}}{{0}}26 × {{0}}{{0}}37 || {{0}}1.0 × {{0}}1.5
| B10 || {{0}}{{0}}31 × {{0}}{{0}}44 || {{0}}1.2 × {{0}}1.7
| C10 || {{0}}{{0}}28 × {{0}}{{0}}40 || {{0}}1.1 × {{0}}1.6
|- valign="bottom"
| <!-- The size illustrations are to scale with each other. -->
| colspan="3" | [[Image:A size illustration2.svg|250px]]
| colspan="3" | [[Image:B size illustration2.svg|297px]]
| colspan="3" | [[Image:C size illustration2.svg|273px]]
|}
[[Image:Comparison SIS 014711 paper sizes.svg|thumb|Comparison of ISO 216 paper sizes between A4 and A3 and Swedish extension [[SIS 014711]] sizes]]

== History ==
{{Redirect|Lichtenberg ratio|<math display="inline">\sqrt{2}</math>|Square root of 2}}

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]].<ref name="Beck">{{cite web |first=Georg Christoph |last=Lichtenberg
|title=Lichtenberg's letter to Johann Beckmann |translator-first=Markus |translator-last=Kuhn |translator-link=Markus Kuhn (computer scientist) |language=de, en |orig-year=Written 25 October 1786 |date=7 February 2006 |publisher=[[University of Cambridge]] |url=http://www.cl.cam.ac.uk/~mgk25/lichtenberg-letter.html |access-date=10 May 2016}} Published in {{cite book 
|last = Lichtenberg |first = Georg Christoph |title = Briefwechsel |trans-title=Correspondence |editor1-first=Ulrich |editor1-last=Joost |editor2-first=Albrecht |editor2-last=Schöne |editor-link2=Albrecht Schöne
|publisher = Beck |location = Munich |date = 1990 |volume=III (1785–1792)
|language=de |pages= 274–75
|url={{Google books |iz8cwXux3B0C |page=274 |plainurl=yes}} |access-date=10 May 2016 |isbn = 3-406-30958-5}}</ref> 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 ({{langx|fr|Loi sur le timbre (Nº 2136)}}) that was based in part on page sizes.<ref name="B237">{{cite journal |title=Loi sur le timbre (Nº 2136) |trans-title=Stamp Act (No. 2136) |date=3 November 1798 |journal=Bulletin des Lois de la République |issue=237 |pages=1–2 |language=fr |publisher=Republic of France |location=Paris |url=http://www.cl.cam.ac.uk/~mgk25/loi-timbre.html |url-status=live |access-date=2024-01-20 |archive-url=https://web.archive.org/web/20090426170239/http://www.cl.cam.ac.uk/~mgk25/loi-timbre.html |archive-date=26 April 2009 |via=Markus Kuhn }}</ref>
[[Image:Comparison_paper_sizes.svg|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 [[Die Brücke (institute)|the Bridge]] association ({{langx|de|Die Brücke}}), 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,<ref name="B237" /> a global standard{{snd}}a [[Die Brücke (institute)#Weltformat - World Standard|world format]] ({{lang|de|Weltformat}}){{snd}}for paper sizes based on the ratio <math display="inline">\sqrt{2}</math>, referring to the argument advanced by Lichtenberg's 1786 letter, but linking this to the [[metric system]] using {{convert|1|cm|lk=in}} as the width of the base format. {{ill |Walter Porstmann |de}} argued in a long article published in 1918, that a firm basis for the system of paper formats, which deal with surfaces, ought not be the length but the area; that is, linking the system of paper formats to the metric system using the square metre rather than the centimetre, constrained by <math display="inline">\tfrac{x}{y}=\sqrt{2}</math> and area <math display="inline">a = x \times y = 1</math> square metre, where <math display="inline">x</math> is the length of the shorter side and <math display="inline">y</math> is the length of the longer side, for the second equation both in metres. Porstmann also argued that formats for ''containers'' of paper, such as envelopes, should be 10% larger than the paper format itself.

In 1921, after a long discussion and another intervention by Porstmann, the Standardisation Committee of German Industry ({{lang|de|Normenausschuß der deutschen Industrie}}, or NADI in short), which is the [[Deutsches Institut für Normung|German Institute for Standardisation]] ({{lang|de|Deutsches Institut für Normung}}, or DIN in short) today, published German standard ''DI Norm 476'' the specification of four series of paper formats with ratio <math display="inline">\sqrt{2}</math>, with series A as the always preferred formats and basis for the other series. All measures are rounded to the nearest millimetre. A0 has a surface area of {{convert|1|m2}} up to a [[rounding error]], with a width of {{convert|841|mm}} and height of {{convert|1189|mm}}, so an actual area of {{convert|0.999949|m2}}; A4 is recommended as standard paper size for business, administrative and government correspondence; and A6 for postcards. Series B is based on B0 with width of {{convert|1|m}}, C0 is {{convert|917|×|1297|mm}}, and D0 {{convert|771|×|1090|mm}}. Series C is the basis for envelope formats.

The DIN paper-format concept was soon introduced as a national standard in many other countries, for example, Belgium (1924), Netherlands (1925), Norway (1926), Switzerland (1929), Sweden (1930), Soviet Union (1934), Hungary (1938), Italy (1939), Finland (1942), Uruguay (1942), Argentina (1943), Brazil (1943), Spain (1947), Austria (1948), Romania (1949), Japan (1951), Denmark (1953), Czechoslovakia (1953), Israel (1954), Portugal (1954), Yugoslavia (1956), India (1957), Poland (1957), United Kingdom (1959), Venezuela (1962), New Zealand (1963), Iceland (1964), Mexico (1965), South Africa (1966), France (1967), Peru (1967), Turkey (1967), Chile (1968), Greece (1970), Zimbabwe (1970), Singapore (1970), Bangladesh (1972), Thailand (1973), Barbados (1973), Australia (1974), Ecuador (1974), Colombia (1975) and Kuwait (1975).

It finally became both an international standard ([[ISO]] 216) as well as the official [[United Nations]] document format in 1975, and it is today used in almost all countries in the world, with the exception of several countries in the Americas.

In 1977, a large German car manufacturer performed a study of the paper formats found in their incoming mail and concluded that out of 148 examined countries, 88 already used the A series formats.<ref name=":0" />

==Advantages==
The main advantage of this system is its scaling. [[Rectangle|Rectangular]] paper with an aspect ratio of <math display="inline">\sqrt{2}</math> has the unique property that, when cut in two across the midpoints of the longer sides, each half has the same <math display="inline">\sqrt{2}</math> aspect ratio as the whole sheet before it was divided. Equivalently, if one lays two same-sized sheets of paper with an aspect ratio of <math display="inline">\sqrt{2}</math> side by side along their longer side, they form a larger rectangle with the aspect ratio of <math display="inline">\sqrt{2}</math> and double the area of each individual sheet.

The ISO system of paper sizes exploits these properties of the <math display="inline">\sqrt{2}</math> aspect ratio. In each series of sizes (for example, series A), the largest size is numbered 0 (so in this case A0), and each successive size (A1, A2, etc.) has half the area of the preceding sheet and can be cut by halving the length of the preceding size sheet. The new measurement is rounded down{{contradictory inline |reason=The rest of this article says to nearest, not down to, so which is it? |date=January 2024}} to the nearest millimetre. A folded [[brochure]] can be made by using a sheet of the next larger size (for example, an A4 sheet is folded in half to make a brochure with size A5 pages). An office [[photocopier]] or printer can be designed to reduce a page from A4 to A5 or to enlarge a page from A4 to A3. Similarly, two sheets of A4 can be scaled down to fit one A4 sheet without excess empty paper.

This system also simplifies calculating the weight of paper. Under [[ISO 536]], paper's [[grammage]] is defined as a sheet's mass in [[gram]]s (g) per area in [[square metre]]s (unit symbol g/m<sup>2</sup>; the nonstandard abbreviation "gsm" is also used).<ref name="ISO 536">{{Cite web
|url=https://www.iso.org/obp/ui/#iso:std:iso:536:ed-4:v1:en
|access-date=8 June 2021
|author=International Organization for Standardization |author-link=International Organization for Standardization
|title=ISO 536:2019(en): Paper and board — Determination of grammage
|edition=4 |at=§&nbsp;3.1 note 1.
|work=ISO Browsing Platform
|date=November 2019}}</ref>  One can derive the grammage of other sizes by [[Division (mathematics)|arithmetic division]]. A standard A4 sheet made from {{Nowrap|80 g/m<sup>2</sup>}} paper weighs {{convert|5|g}}, as it is {{frac|1|16}} (four halvings, ignoring rounding) of an A0 page. Thus the weight, and the associated [[mail#postage|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 {{math|{{sqrt|2}}}} (≈ 1.414, when rounded). A0 is defined so that it has an area of {{cvt|1|m2|ft2|lk=on}} before rounding to the nearest {{convert|1|mm}}. Successive paper sizes in the series (A1, A2, A3, etc.) are defined by halving the area of the preceding paper size and rounding down, so that the long side of {{Nowrap|A(''n'' + 1)}} is the same length as the short side of A''n''. Hence, each next size is nearly exactly half the area of the prior size. So, an A1 page can fit two A2 pages inside the same area.

The most used of this series is the size A4, which is {{cvt|210|x|297|mm|sigfig=3}} and thus almost exactly {{convert|1/16|m2|m2 sqin|4}} in area. For comparison, the [[Letter (paper size)|letter]] paper size commonly used in North America ({{convert|8+1/2|x|11|in|sigfig=3|abbr=on|disp=semicolon}}) is about {{Nowrap|6 mm}} ({{Nowrap|0.24 in}}) wider and {{Nowrap|18 mm}} ({{Nowrap|0.71 in}}) shorter than A4. Then, the size of A5 paper is half of A4, i.e. {{Nowrap|148 mm}} × {{Nowrap|210 mm}} ({{Nowrap|5.8 in}} × {{Nowrap|8.3 in}}).<ref>{{cite web |title= A Paper Sizes – A0, A1, A2, A3, A4, A5, A6, A7, A8, A9 |url= https://www.papersizes.org/a-paper-sizes.htm |website= papersizes.org |access-date= 2 August 2018 }}</ref><ref>{{cite web |title= International Paper Sizes, Dimensions, Format & Standards |url= https://papersize.co/ |website= PaperSize |access-date= 5 October 2018 }}</ref>

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, {{sfrac|''x''|''y''}}, will be the same as that of a rectangle half its size, {{sfrac|''y''|''x''/2}}, which means that {{math|1={{sfrac|''x''|''y''}} = {{sfrac|''y''|''x''/2}}}}, which reduces to {{math|1={{sfrac|''x''|''y''}} = {{sqrt|2}}}}; in other words, an aspect ratio of {{math|1:{{sqrt|2}}}}.

Any {{math|A''n''}} paper can be defined as {{math|1=A''n'' = ''S'' × ''L''}}, where (measuring in metres)

:<math>\text{A}_n = \begin{cases}
S = \left(\sqrt{\frac{1}{2}}\right)^{n + \frac{1}{2}}\\
L = \left(\sqrt{\frac{1}{2}}\right)^{n - \frac{1}{2}}
\end{cases}</math>

Therefore

:<math>\text{A0} = \begin{cases}
S = \left(\sqrt{\frac{1}{2}}\right)^{0 + \frac{1}{2}} \approx 0.841\,\text{m}\\
L = \left(\sqrt{\frac{1}{2}}\right)^{0 - \frac{1}{2}} \approx 1.189\,\text{m}
\end{cases}</math>, {{pad}} <math>\text{A1} = \begin{cases}
S = \left(\sqrt{\frac{1}{2}}\right)^{1 + \frac{1}{2}} \approx 0.595\,\text{m}\\
L = \left(\sqrt{\frac{1}{2}}\right)^{1 - \frac{1}{2}} \approx 0.841\,\text{m}
\end{cases}</math> {{pad}} <math>\text{A2} = \begin{cases}
S = \left(\sqrt{\frac{1}{2}}\right)^{2 + \frac{1}{2}} \approx 0.420\,\text{m}\\
L = \left(\sqrt{\frac{1}{2}}\right)^{2 - \frac{1}{2}} \approx 0.595\,\text{m}
\end{cases}</math> {{pad}} Etc.

===B series===
The B series is defined in the standard as follows: "A subsidiary series of sizes is obtained by placing the [[Geometric mean|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 {{math|{{sqrt|2}}}}, 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 [[Japanese Industrial Standard|JIS]] defines to have 1.5 times the area of the corresponding JIS A series (which is identical to the ISO A series).<ref>{{cite web|url=http://www.paper-sizes.com/uncommon-paper-sizes/japanese-b-series-paper-size|title=Japanese B Series Paper Size|access-date=18 April 2010}}</ref> Thus, the lengths of JIS B series paper are {{math|{{sqrt|1.5}}}} ≈ 1.22 times those of A-series paper. By comparison, the lengths of ISO B series paper are {{math|{{sqrt|2|4}}}} ≈ 1.19 times those of A-series paper.

Any {{math|B''n''}} paper (according to the ISO standard) can be defined as {{math|1=B''n'' = ''S'' × ''L''}}, where (measuring in metres)

:<math>\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>\text{B0} = \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>, {{pad}} <math>\text{B1} = \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> {{pad}} <math>\text{B2} = \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> {{pad}} 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 {{math|{{sqrt|2}}}} 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 {{math|{{sqrt|2|8}}}}, though there is no size half-way between B''n'' and {{Nowrap|A(''n'' − 1)}}: A4, C4, B4, "D4", A3, ...; there is such a D-series in the [[Paper size#Swedish extensions|Swedish extensions]] to the system. The lengths of ISO C series paper are therefore {{math|{{sqrt|2|8}}}} ≈ 1.09 times those of A-series paper.

The C series formats are used mainly for [[envelope]]s. 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 {{math|C''n''}} paper can be defined as {{math|1=C''n'' = ''S'' × ''L''}}, where (measuring in metres)

:<math>\text{C}_n = \begin{cases}
S = \left(\sqrt{\frac{1}{2}}\right)^{n + \frac{1}{4}}\\
L = \left(\sqrt{\frac{1}{2}}\right)^{n - \frac{3}{4}}
\end{cases}</math>

Therefore

:<math>\text{C0} = \begin{cases}
S = \left(\sqrt{\frac{1}{2}}\right)^{0 + \frac{1}{4}} \approx 0.917\,\text{m}\\
L = \left(\sqrt{\frac{1}{2}}\right)^{0 - \frac{3}{4}} \approx 1.297\,\text{m}
\end{cases}</math>, {{pad}} <math>\text{C1} = \begin{cases}
S = \left(\sqrt{\frac{1}{2}}\right)^{1 + \frac{1}{4}} \approx 0.648\,\text{m}\\
L = \left(\sqrt{\frac{1}{2}}\right)^{1 - \frac{3}{4}} \approx 0.917\,\text{m}
\end{cases}</math> {{pad}} <math>\text{C2} = \begin{cases}
S = \left(\sqrt{\frac{1}{2}}\right)^{2 + \frac{1}{4}} \approx 0.458\,\text{m}\\
L = \left(\sqrt{\frac{1}{2}}\right)^{2 - \frac{3}{4}} \approx 0.648\,\text{m}
\end{cases}</math> {{pad}} Etc.

==Tolerances==
The tolerances specified in the standard are:
* [[±]]1.5&nbsp;mm for dimensions up to 150&nbsp;mm,
* ±2.0&nbsp;mm for dimensions in the range 150 to 600&nbsp;mm, and
* ±3.0&nbsp;mm for dimensions above 600&nbsp;mm.

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

==Application==

The ISO 216 formats are organized around the ratio 1:{{math|{{sqrt|2}}}}; 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 [[Paper size#North American paper sizes|North American paper sizes]]. Although they have also officially adopted the ISO 216 paper format, Mexico, Panama, Peru, Colombia, the Philippines, and Chile also use mostly U.S. paper sizes.

[[Rectangle|Rectangular]] sheets of paper with the ratio 1:{{math|{{sqrt|2}}}} are popular in [[paper folding]], such as [[mathematics of paper folding|origami]], where they are sometimes called "A4 rectangles" or "silver rectangles".<ref name="Lister">{{cite web|url=http://www.britishorigami.info/academic/lister/a4.php|title=The A4 rectangle|last=Lister|first=David|work=The Lister List|publisher=British Origami Society|location=England|access-date=6 May 2009}}</ref>  In other contexts, the term "silver rectangle" can also refer to a rectangle in the proportion 1:(1&nbsp;+&nbsp;{{math|{{sqrt|2}}}}), known as the [[silver ratio]].

==Matching technical pen widths==
[[File:Rotring Rapidograph Technical Pens 0.1–2.0 mm.svg|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&nbsp;mm on an A0-sized sheet, 0.5&nbsp;mm on an A1 sheet, and 0.35&nbsp;mm on A2, A3, or A4.<ref>{{cite web|url=http://www.metrication.com/drafting/lines.html|title=Pen Sizes and Line Types|last1=Bell|first1=Steven|website=Metrication.com|access-date=30 August 2017}}</ref>

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&nbsp;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 {{math|{{sqrt|2}}}}, 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.<ref name=":0">{{cite web|url=https://www.cl.cam.ac.uk/~mgk25/iso-paper.html|title=International standard paper sizes|last1=Kuhn|first1=Markus|access-date=30 August 2017}}</ref><ref>{{cite web|url=https://www.designingbuildings.co.uk/wiki/Technical_drawing_pen_sizes|title=Technical drawing pen sizes|website=Designing Buildings Wiki|access-date=30 August 2017}}</ref>

:{| class="wikitable"
|-
!style="text-align:left"| Linewidth (mm)
|width="9%" colspan=2| 0.10
|width="9%" colspan=2| 0.13
|width="9%" colspan=2| 0.18
|width="9%" colspan=2| 0.25
|width="9%" colspan=2| 0.35
|width="9%" colspan=2| 0.50
|width="9%" colspan=2| 0.70
|width="9%" colspan=2| 1.0
|width="9%" colspan=2| 1.4
|width="9%" 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"| ||Green
|width="2%" style="background:silver"| ||Gray
|}

[[File:Micronorm.svg|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
| {{size|1682|2378}}
|-
! 2A0
| {{size|1189|1682}}
|}

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".<ref>{{cite web | url=https://pixel2print.co.uk/print/posters-(new)/large-format-posters/a00/ | title=A00 }}</ref>

==See also==
* [[ANSI/ASME Y14.1]]
* [[Envelope sizes#International standard sizes|International standard envelope sizes]]
* [[Paper density]]

==References==
{{Reflist}}

==External links==
{{Commons category|DIN EN ISO 216}}
* [http://www.cl.cam.ac.uk/~mgk25/iso-paper.html International standard paper sizes]: ISO 216 details and [[Design rationale|rationale]]
* [http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=36631 ISO 216 at iso.org]
* [https://www.cl.cam.ac.uk/~mgk25/volatile/DIN-A4-origins.pdf 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]
*[https://www.cl.cam.ac.uk/~mgk25/iso-paper.html Explanation of paper sizes]
{{ISO standards}}
{{Deutsches Institut für Normung}}

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[[Category:ISO standards|#00216]]
[[Category:Stationery]]
[[Category:Metrication]]
[[Category:Technical specifications]]