ISO 216

**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 (ISO) paper sizes used in most countries in the world today. The Millimetre ( American spelling: millimeter, symbol mm) is a unit of Length in the Metric system, equal to The Millimetre ( American spelling: millimeter, symbol mm) is a unit of Length in the Metric system, equal to The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International 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 (A4 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. Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. Deutsches Institut für Normung eV ( DIN; in English, the German Institute for Standardization) is the German national organization for Some of the formats contained therein were independently invented in France during its revolution and later forgotten. This article is about the country For a topic outline on this subject see List of basic France topics. [1] The aspect ratio used by this norm was mentioned in a letter by the German Georg Christoph Lichtenberg written 1786-10-25. Georg Christoph Lichtenberg ( 1 July 1742 – 24 February 1799) was a German Scientist, Satirist and Year 1786 ( MDCCLXXXVI) was a Common year starting on Sunday (link will display the full calendar of the Gregorian calendar (or a Common Events 1147 - The Portuguese, under Afonso I, and Crusaders from England and Flanders conquer Lisbon after a [2]

ISO 216:1975, defines two series of paper sizes: A and B
ISO 269:1985, defines a C series for envelopes
ISO 217:1995, defines two untrimmed series of raw paper sizes: RA and SRA

1 A series
2 B series
3 C series
4 Tolerances
5 A, B, C comparison
6 Application
7 See also
8 External links

A series

A size chart illustrating the ISO A series. The ISO 2171995 standard defines the RA and SRA paper formats

Paper in the A series format has a $1:\sqrt{2}$ 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. M^2 redirects here For other uses see M². CM2 redirects here 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 Paper size Letter is the most common Paper size for office use in the United States, Canada, Mexico, Chile, and a few

The geometrical rationale behind the square root of 2 being the aspect ratio is that a half of a rectangle in which this is the proportion between sides is a smaller rectangle having the same proportion between sides. The square root of 2, also known as Pythagoras' Constant, often denoted by \sqrt{2} or √2 This guarantees that for example, at the same time two A4 sheet placed side-by-side have the same size of an A3 sheet, while the A4 and A3 sheets have exactly the same ratio between long and short sides.

The formula that gives the larger border of the paper size A $n$ in metres and without rounding off is the geometric sequence: $a n = 2 1 / 4 - n / 2$ . In Mathematics, a geometric progression, also known as a geometric sequence, is a Sequence of Numbers where each term after the first is found The paper size A $n$ thus has the dimension $a n$ × $a n + 1$ .

The exact millimetre measurement of the long side of A $n$ is given by $\left \lfloor 1000/(2^{(2n-1)/4})+0.2 \right \rfloor$ .

B series

A size chart illustrating the ISO B series.

The B series formats are geometric means between the A series format with the same number and the A series format with one lower number. 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 For example, B1 is a geometric mean between A1 and A0. The sides of B0 are 1 m to $\sqrt{2}$ m.

There is also an incompatible Japanese B series defined by the JIS. This article is about Japanese Industrial Standards in general see JIS encoding for the character encoding used in representing the Japanese language for computer software 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 $n$ is given by $\left \lfloor 1000/(2^{(n-1)/2})+0.2 \right \rfloor$ .

C series

The C series formats are geometric means between the B series format with the same 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 $n$ is given by $\left \lfloor 1000/(2^{(4n-3)/8})+0.2 \right \rfloor$ .

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 inches
	A Series Formats		B Series Formats		C Series Formats
size	mm	inches	mm	inches	mm	inches
0	841 × 1189	33. The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International Inches redirects here To see the Les Savy Fav album see Inches. 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 $1:\sqrt{2}$ ; 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. The United States of America —commonly referred to as the Country to "Dominion of Canada" or "Canadian Federation" or anything else please read the Talk Page 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 (A4 (Canada uses a P-series of sizes, which are the US paper sizes rounded to metric dimensions. )

Rectangular sheets of paper with the ratio $1:\sqrt{2}$ are popular in paper folding, where they are sometimes called "A4 rectangles" or "silver rectangles". In Geometry, a rectangle is defined as a Quadrilateral where all four of its angles are Right angles A rectangle with vertices ABCD would be denoted as Paper folding is the Art of folding Paper; it is known in many societies that use paper [3] (Confusingly, "silver rectangle" can also refer to a rectangle in the proportion $1:(1+\sqrt{2})$ ), known as the silver ratio. The silver ratio is a mathematical Constant. Its name is an allusion to the Golden ratio; analogously to the way the golden ratio is the limiting ratio )

External links

International standard paper sizes: ISO 216 details and rationale
A4 paper artwork
ISO 216 at iso.org

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 (A4 The Paper size Letter is the most common Paper size for office use in the United States, Canada, Mexico, Chile, and a few

Dictionary

-noun

the international standard for paper sizes

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