#### ISO Paper Sizes

based upon a text by Markus Kuhn, lecturer with the University of Cambridge Computer Laboratory. The ISO A4 paper size is today commonly used throughout the world. The following explains the ISO 216 paper size system and the principles behind the concept.

###### The ISO paper size concept

With the ISO paper size system, all sheet sizes have a width to height ratio of the square root of two (1:1.4142). By placing two sheets of A series paper next to each other, or by cutting one in half parallel to its shorter side, the resulting sheet will again have the same width to height ratio.

ISO paper sizes are based on the metric system. The square-root-of-two ratio does not allow the height and width of pages to be given simple whole metric sizes. The sizes therefore, are rounded to whole millimetre lengths. As the weight of paper in the metric system is specified in grams per square metre (gsm), a simple method of calculating the mass or weight of a publication is possible, where the size and number of pages is known.

ISO 216 defines the A series of paper sizes as follows: The height divided by the width of all formats is the square root of two (1.4142), hence an A3 sheet is approximately 141% larger than an A4 sheet. The base format A0 (841mm x 1189mm) has an area of one square metre. A1 is A0 cut into two equal halves, where the A1 sheet long dimension is the same as the short dimension of A0, and the A1 short dimension is half the A0 long dimension. Thus A0 measures 841mm x 1189mm and A1 measures 594mm x 841mm, where 594mm is half the length of 1189mm and rounded down to the nearest millimetre. All smaller A series formats are defined in the same way by cutting the next larger format parallel to its shorter side into two equal halves, so A2 measures 420mm x 594, where 420mm is half of 841mm, rounded down. For applications where the ISO A series does not provide an adequate range of sizes, the B series was created to provide a greater choice. The C series of formats has been defined for envelopes. The width and height of a B series format is the geometric mean between the corresponding A format and the next larger A format. For instance, B1 is the geometric mean falling between A1 and A0, in other words, the factor that scales A1 to B1 also scales B1 to A0. So where A0 has a length of 1189mm, B1 will have a length of 1000mm and A1 will have a length of 841mm, each is approximately an 84.1% reduction of the larger size, or a 118.9% enlargement of the smaller size. This percentage ration between sizes applies equally to the both the height and width dimensions of each sheet size. These percentages are demonstrated below when referring to photocopying machines. Similarly, the formats of the C series are the geometric mean between the A and B series formats with the same number. For example, an A4 letter fits into a C4 envelope, which in turn fits into a B4 envelope. Folding the A4 letter to A5 format, enables it to fit into a C5 envelope. The Japanese JIS P 0138-61 standard defines the same A series as ISO 216, but has a slightly different B series of paper sizes, sometimes called the JIS B or JB series. JIS B0 has an area of 1.5 sq m, such that the area of JIS B pages is the arithmetic mean of the area of the A series pages with the same and the next higher number, and not as in the ISO B series the geometric mean. For example JB3 is 364 x 515, JB4 is 257 x 364, and JB5 is 182 x 257 mm. Using the JIS B series should be avoided as it introduces additional magnification or reduction factors and is not a recognised international standard. The following table shows the width and height of all ISO A and B paper formats, as well as the ISO C envelope formats. The dimensions are in millimetres:

A Sizes (mm) B Sizes (mm) C Sizes (mm)
4A0 1682 x 2378
2A0 1189 x 1682
A0 841 x 1189 B0 1000 x 1414 C0 917 x 1297
A1 594 x 841 B1 707 x 1000 C1 648 x 917
A2 420 x 594 B2 500 x 707 C2 458 x 648
A3 297 x 420 B3 353 x 500 C3 324 x 458
A4 210 x 297 B4 250 x 353 C4 229 x 324
A5 148 x 210 B5 176 x 250 C5 162 x 229
A6 105 x 148 B6 125 x 176 C6 114 x 162
A7 74 x 105 B7 88 x 125 C7 81 x 114
A8 52 x 74 B8 62 x 88 C8 57 x 81
A9 37 x 52 B9 44 x 62 C9 40 x 57
A10 26 x 37 B10 31 x 44 C10 28 x 40

The allowed tolerances are ±1.5 mm for dimensions up to 150 mm, ±2 mm for dimensions above 150 mm up to 600 mm, and ±3 mm for dimensions above 600 mm. Some national equivalents of ISO 216 specify tighter tolerances, for example DIN 476 requires ±1 mm, ±1.5 mm, and ±2 mm respectively for the same ranges of dimensions.

###### Application examples

The ISO standard paper size system covers a wide range of formats, but not all of them are widely used in practice. Among all formats, A4 is clearly the most convenient for daily office use. Some main applications of the most popular formats can be summarized as:

 A0,A1 technical drawings, posters A2,A3 drawings, diagrams, large tables A4 letters, magazines, forms, catalogues, laser printer and photocopying machines A5 note pads A6 postcards B5,A5,B6,A6 books C4,C5,C6 envelopes for A4 letters: unfolded (C4), folded once (C5), folded twice (C6) B4,A3 newspapers, supported by most copying machines in addition to A4

One of the main advantages of the ISO standard paper sizes becomes apparent when using photocopying machines:

###### Example 1:

When copying an article from an A4 publication, you can copy two A4 pages on to a single sheet of A4 paper. By exposing two A4 pages (double page spread), and setting the reduction factor to 71%, or by selecting the pre-set A3 to A4 reduction facility, both A4 pages will be reproduced side-by-side on a single A4 sheet. Each of the original A4 pages will have been reduced in size to A5. No large blank margins appear, no text disappears, and there is no need to experiment to find the appropriate magnification or reduction factor. The same principle works for books in B5 or A5 format.

Copying machines designed for ISO paper sizes usually provide special keys or pre-sets for the following frequently used magnification or reduction factors:

 71.00% A3 > A4 84.00% B4 > A4 119.00% A4 > B4 (also B5 > A4) 141.00% A4 > A3 (also A5 > A4)
###### Example 2:

When preparing a letter, knowing the weight of the paper helps when calculating the cost of mailings. This can be very conveniently calculated with the ISO A series paper sizes. Standard stationery paper weighs 80 gsm. An A0 page has an area of 1 sq m, and the next smaller A series page has half of this area. Therefore the A4 format has an area of 1/16 sq m and weighs 5 grams per page. Allowing an estimate of 20 grams for a C4 envelope, 16 A4 pages can be included before the initial 100 gram limit is reached.

The ISO formats are used for surprisingly many things besides office paper: the German citizen ID card has format A7, and the European Union passport uses the B7 format, library microfiches use the A6 format.

###### Aspect ratios

There are occasions when paper sizes other than the standard A series are required, such as labels, tickets etc. These can be achieved by cutting standard series sizes into 3, 4, or 8 equal parts, parallel to the shorter side, in order that the ratio between the longer and shorter side is greater than the square root of two. Some example long formats in millimetres are:

 1/3 A4 99 x 210 1/4 A4 74 x 210 1/8 A4 37 x 210 1/4 A3 105 x 297 1/3 A5 70 x 148

The 1/3 A4 format (99 x 210 mm) is also commonly used for reduced letterheads or compliment slips, or for short notes that contain not much more than a single sentence message and fit without folding into a DL envelope.

###### Envelope formats

For postal purposes, ISO 269 and DIN 678 define the following envelope formats:

Format Size (mm) Content Format
C6 114 x 162 A4 folded twice = A6
DL 110 x 220 A4 folded twice = 1/3 A4
C6/C5 114 x 229 A4 folded twice = 1/3 A4
C5 162 x 229 A4 folded once = A5
C4 229 x 324 A4
C3 324 x 458 A3
B6 125 x 176 C6 envelope
B5 176 x 250 C5 envelope
B4 250 x 353 C4 envelope
E4 280 x 400 B4

The DL format is the most widely used business letter format. Its size falls somewhat out of the system and equipment manufacturers have complained that it is slightly too small for the reliable automatic enveloping, therefore DIN 678 introduced the C6/C5 format as an alternative for DL.

There is no current ISO standard for envelopes with an address window, there is however a corresponding DIN standard. DIN 680 specifies that a transparent address window should measure 90mm x 45 mm with its left side 20 mm from the left edge of the envelope. For C6, DL, and C6/C5 envelopes, the bottom of the window should be 15 mm from the bottom edge of the envelope. For C4 envelopes, the top of the window should be either 27 or 45 mm from the top edge of the envelope.

###### Untrimmed paper formats

All A and B series formats described so far are trimmed paper end sizes, i.e. these are the dimensions of the paper delivered to the end user. Other ISO standards define the RA and SRA formats for untrimmed raw paper. These formats are only slightly larger than the corresponding A formats. Sheets in these formats are cut to the final size format after printing and binding. The ISO RA0 format has an area of 1.05 sq m and the ISO SRA0 format has an area of 1.15 sq m. These also follow the square root of 2 ratio and the half-area rule, but the dimensions of the base format have been rounded to the full centimetre. The common untrimmed paper formats printers order from the paper manufacturers or merchants are:

RA Series Formats SRA Series Formats
RA0 860 x 1220 SRA0 900 x 1280
RA1 610 x 860 SRA1 640 x 900
RA2 430 x 610 SRA2 450 x 640
RA3 305 x 430 SRA3 320 x 450
RA4 215 x 305 SRA4 225 x 320
###### Punched holes for filing

ISO 838 specifies that for filing purposes, two holes of 6±0.5 mm diameter can be punched into the sheets. The centers of the two holes are 80±0.5 mm apart and have a distance of 12±1 mm to the nearest edge of the sheet. The holes are located symmetrically in relation to the axis of the sheet or document. Any format that is at least as large as A7 can be filed using this system. Not specified in ISO 838, but also widely used, is an upwardly compatible 4-hole system. The two middle holes correspond to ISO 838, and the two additional holes are positioned 80 mm above and below these to give greater stability. Sheets with four punched holes corresponding to the ISO 838 standard, can be filed in ISO 838 2-hole binders.

###### Folder and file sizes

ISO 623 specifies the sizes of folders and files intended to receive either A4 sheets or simple folders (without spine) that are not designed for any particular filing system or cabinet. The sizes specified are those of the overall rectangular surface when the folders or files are folded, excluding any margin or tabs. Simple folders without a spine or binding mechanism are 220 x 315 mm large. Folders and files with a very small spine (less than 25 mm) with or without a binding mechanism are 240 x 320 mm large. Files with a wide spine (exceeding 25 mm) are 250 x 320 mm (without a mechanism) or 290 x 320 mm if they include a binding mechanism. All are maximum dimensions. Standardizing folder and file sizes allows the optimization of shelf design.

ISO 7943-1 specifies two standard sizes of overhead projector picture areas: Type A is 250 x 250 mm (round corners with a radius less than 60 mm) and Type B is 285 x 285 mm (round corners with a radius less than 40 mm or cut off diagonally no more than 40 mm). Therefore, when using A4 transparencies, leave at least a 30 mm top and bottom margin.

###### Identification cards

ISO 7810 specifies identification cards and defines the following three standard formats: ID-1 = 85.60 x 53.98 mm (= 3.370 x 2.125 in), ID-2 = 105 x 74 mm (= A7), and ID-3 = 125 x 88 mm (= B7). ID-1 is the common format for banking cards (0.76 mm thick) and is also widely used for business cards and driver's licences. The standard passport format is B7 (= ID-3).

###### History of the ISO paper formats

The practical and aesthetic advantages of the square root of 2 aspect ratio for paper sizes were probably first noted by the physics professor Georg Christoph Lichtenberg (University of Göttingen, Germany, 1742-1799) in a letter he wrote in 1786 to Johann Beckmann. After introducing the meter measurement, the French government published in 1794 the "Loi sur le timbre" (no. 2136), a law on the taxation of paper defining several formats corresponding exactly to modern ISO paper sizes: "Grand registre" = ISO A2, "grand papier" = ISO B3, "moyen papier" = ISO A3, "petit papier" = ISO B4, "demi feuille" = ISO B5 and "effets de commerce" = ISO 1/2 B5.

The French format was never widely adopted and soon disappeared. The modern A, B, and C series paper formats, based on the exactly same design principles as the French system, were reinvented over a hundred years later in Germany by Dr. Walter Porstmann. They were adopted as the German standard DIN 476 in 1922 to replace the huge variety of other paper sizes in use until then, and to make paper stocking and reproduction methods cheaper and more efficient.

The DIN paper formats were soon also introduced in many other countries, for example Belgium (1924), Netherlands (1925), Norway (1926), Switzerland (1929), Sweden (1930), Soviet Union (1934), Hungary (1938), Italy (1939), Uruguay (1942), Argentina and Brazil (1943), Spain (1947), Austria (1948), Romania (1949), Japan (1951), Denmark and Czechoslovakia (1953), Israel and Portugal (1954), Yugoslavia (1956), India and Poland (1957), United Kingdom (1959), Venezuela (1962), New Zealand (1963), Iceland (1964), Mexico (1965), South Africa (1966), France/Peru/Turkey (1967), Chile (1968), Greece/Zimbabwe/Singapore (1970), Bangladesh (1972), Thailand and Barbados (1973), Australia and Ecuador (1974), Columbia and Kuwait (1975). Porstmann's DIN paper format system finally became both an international standard (ISO 216) as well as the official United Nations document format in 1975 and is today used in almost all countries. 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 used already the A series formats then. [Source: Helbig/Hennig 1988]