Definitions

# Paper size

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 and its siblings) and the North American sizes.

## The international standard: ISO 216

The international paper size standard, ISO 216, is based on the German DIN 476 standard for paper sizes. Its unique quality is its scalalability: The height divided by the width of all formats is the square root of two (1.4142), so folding any sheet in half, the two halves have the same proportions, and any image can be reproduced on the half size paper by reducing it by about 70% (0,707 is the reciprocal of root 2). To double an image area, the multiplication factor is about 140% These options commonly appear on photocopiers and image projectors.

Within the ISO metric system, the base format is a sheet of paper measuring 1 in area (A0 paper size). Successive paper sizes in the series A1, A2, A3, and so forth, are defined by halving the preceding paper size parallel to its shorter side. The most frequently used paper size is A4 (210 × 297 mm). An advantage is that standard A4 sheets made from 80 grams/m² paper weighs 5 grams, allowing one to know the weight - and associated postage rate - by counting the number of sheets used.

This standard has been adopted by all countries in the world except the United States and Canada. In Mexico, Colombia, Chile and the Philippines, despite the ISO standard having been officially adopted, the U.S. "letter" format is still in common use. ISO paper sizes are all based on a single aspect ratio of the square root of 2, or approximately 1:1.4142. The advantages of basing a paper size upon this ratio were already noted in 1786 by the German scientist Georg Christoph Lichtenberg (in a letter to Johann Beckmann): if a sheet with aspect ratio √2 is divided into two equal halves parallel to its shortest side, then the halves will again have aspect ratio √2. In the beginning of the twentieth century, Dr Walter Porstmann turned Lichtenberg's idea into a proper system of different paper sizes. Porstmann's system was introduced as a DIN standard (DIN 476) in Germany in 1922, replacing a vast variety of other paper formats. Even today the paper sizes are called "DIN A4" in everyday use in Germany.

The DIN 476 standard spread quickly to other countries, and before the outbreak of World War II it had been adopted by the following countries:

During the war it was adopted by Uruguay (1942), Argentina (1943) and Brazil (1943); and directly afterwards the standard continued to spread to other countries:

By 1975 so many countries were using the German system that it was established as an ISO standard, as well as the official United Nations document format. By 1977 A4 was the standard letter format in 88 of 148 countries, and today only the U.S. and Canada have not adopted the system.

The largest standard size, A0, has an area of 1 . The length of the long side of the sheet in metres is the 4th root of 2—approximately 1.189 metres. The short side is the reciprocal of this number, approximately 0.841 metres. A1 is formed by cutting a piece of A0 into two equal area rectangles. Because of the choice of lengths, the aspect ratio is the same for A1 as for A0 (as it is for A2, A3, etc). This particular measurement system was chosen to allow folding of one standard size into another, which cannot be accomplished with traditional paper sizes.

Brochures are made by using material at the next size up i.e. material at A3 is folded to make A4 brochures. Similarly, material at A4 is folded to make A5 brochures.

It also allows scaling without loss of image from one size to another. Thus an A4 page can be enlarged to A3 and retain the exact proportions of the original document. Office photocopiers in countries that use ISO 216 paper often have one tray filled with A4 and another filled with A3. A simple method is usually provided (e.g. one button press) to enlarge A4 to A3 or reduce A3 to A4. This also allows two sheets of A4 (or any other size) to be scaled down and fit exactly 1 sheet without any cutoff or margins.

There is also a much less common B series. The area of B series sheets is the geometric mean of successive A series sheets. So, B1 is between A0 and A1 in size, with an area of 0.71 m² ($sqrt\left\{0.5\right\}$). As a result, B0 has one side 1-metre long, and other sizes in the B series have one side that is a half, quarter or eighth of a metre. While less common in office use, it is used for a variety of special situations. Many posters use B-series paper or a close approximation, such as 50 cm×70 cm; B5 is a relatively common choice for books. The B series is also used for envelopes and passports.

The C series is used only for envelopes and is defined in ISO 269. The area of C series sheets is the geometric mean of the areas of the A and B series sheets of the same number; for instance, the area of a C4 sheet is the geometric mean of the areas of an A4 sheet and a B4 sheet. This means that C4 is slightly larger than A4, and B4 slightly larger than C4. The practical usage of this is that a letter written on A4 paper fits inside a C4 envelope, and a C4 envelope fits inside a B4 envelope.

The scalability also means that less paper (and hence money) is wasted by printing companies.

ISO paper sizes (plus rounded inch values)
Format A series B series C series
Size mm × mm in × in mm × mm in × in mm × mm in × in
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

The tolerances specified in the standard are

• ±1.5 mm (0.06 in) for dimensions up to 150 mm (5.9 in),
• ±2 mm (0.08 in) for lengths in the range 150 to 600 mm (5.9 to 23.6 in) and
• ±3 mm (0.12 in) for any dimension above 600 mm (23.6 in).

### German extensions

The German standard DIN 476 was published in 1922 and is the original specification of the A and B sizes. It differs in two details from its international successor:

DIN 476 provides an extension to formats larger than A0, denoted by a prefix factor. In particular, it lists the two formats 2A0, which is twice the area of A0, and 4A0, which is four times A0:

DIN 476 overformats
Name mm × mm in × in
4A0 1682 × 2378 66.2 × 93.6
2A0 1189 × 1682 46.8 × 66.2

DIN 476 also specifies slightly tighter tolerances:

• ±1 mm (0.04 in) for dimensions up to 150 mm (5.9 in),
• ±1.5 mm (0.06 in) for lengths in the range 150 mm to 600 mm (5.9 to 23.6 in) and
• ±2 mm (0.08 in) for any dimension above 600 mm (23.6 in).

### Swedish extensions

The Swedish standard SIS 014711 generalized the ISO system of A, B, and C formats by adding D, E, F, and G formats to it. Its D format sits between a B format and the next larger A format (just like C sits between A and the next larger B). The remaining formats fit in between all these formats, such that the sequence of formats A4, E4, C4, G4, B4, F4, D4 and H4. A3 is a geometric progression, in which the dimensions grow by a factor 21/8 from one size to the next. However, the SIS 014711 standard does not define any size between a D format and the next larger A format (called H in the previous example). Of these additional formats, G5 (169x239 mm) and E5 (155x220 mm) are popular in Sweden for printing dissertations , but the other formats have not turned out to be particularly useful in practice and they have not caught on internationally.

### Japanese B-series variant

The JIS defines two main series of paper sizes. The JIS A-series is identical to the ISO A-series, but with slightly different tolerances. The area of B-series paper is 1.5 times that of the corresponding A-paper, so the length ratio is approximately 1.22 times the length of the corresponding A-series paper. The aspect ratio of the paper is the same as for A-series paper. Both A- and B-series paper is widely available in Japan and most photocopiers are loaded with at least A4 and B4 paper.

There are also a number of traditional paper sizes, which are now used mostly only by printers. The most common of these old series are the Shiroku-ban and the Kiku paper sizes.

JIS paper sizes (plus rounded inch values)
Format B series Shiroku ban Kiku
Size mm × mm in × in mm × mm in × in mm × mm in × in
0 1030 × 1456 40.6 × 57.3
1 728 × 1030 28.7 × 40.6
2 515 × 728 20.3 × 28.7
3 364 × 515 14.3 × 20.3
4 257 × 364 10.1 × 14.3 264 × 379 10.4 × 14.9 227 × 306 8.9 × 12.0
5 182 × 257 7.2 × 10.1 189 × 262 7.4 × 10.3 151 × 227 5.9 × 8.9
6 128 × 182 5.0 × 7.2 189 × 262 7.4 × 10.3
7 91 × 128 3.6 × 5.0 127 × 188 5.0 × 7.4
8 64 × 91 2.5 × 3.6
9 45 × 64 1.8 × 2.5
10 32 × 45 1.3 × 1.8
11 22 × 32 0.9 × 1.3
12 16 × 22 0.6 × 0.9

## North American paper sizes

### Loose sizes

Current standard sizes of U.S. paper are a subset of the traditional sizes referred to below. "Letter", "legal", "ledger", and "tabloid" are by far the most commonly used of these for everyday activities. The origins of the exact dimensions of "letter" size paper (8½ in × 11 in, 215.9 mm × 279.4 mm) are lost in tradition and not well documented. The American Forest and Paper Association argues that the dimension originates from the days of manual paper making, and that the 11 inch length of the page is about a quarter of "the average maximum stretch of an experienced vatman's arms. However, this does not explain the width or aspect ratio.

North American paper sizes
Size in × in mm × mm
Letter 8.5 × 11 216 × 279
Legal 8.5 × 14 216 × 356
Ledger 17 × 11 432 × 279
Tabloid 11 × 17 279 × 432

There is an additional paper size, to which the name "government-letter" was given by the IEEE Printer Working Group: the 8 in × 10½ in (203.2 mm × 266.7 mm) paper that is used in the United States for children's writing. It was prescribed by Herbert Hoover when he was Secretary of Commerce to be used for U.S. government forms, apparently to enable discounts from the purchase of paper for schools. In later years, as photocopy machines proliferated, citizens wanted to make photocopies of the forms, but the machines did not generally have this size paper in their bins. Ronald Reagan therefore had the U.S. government switch to regular letter size (8½ in × 11 in). The 8 in × 10½ in size is still commonly used in spiral-bound notebooks and the like.

An alternative explanation in the past for the difference between "government size" (as government-letter size was referred to at the time) and letter size paper was that the slightly smaller sheet used less paper, and therefore saved the government money in both paper and filing space. However, when Reagan prescribed the change to letter size, it was commonly stated that U.S. paper manufacturers had standardized their production lines for letter size, and were meeting government orders by trimming ½" each from two sides of letter-size stock; thus the government was allegedly paying more for its smaller paper size before Reagan abolished it. The different paper size also reportedly restricted the government's ability to take advantage of modular office furniture designs, common in the 1980s, whose cabinets were designed for letter size paper.

U.S. paper sizes are currently standard in the United States, the Philippines and Chile. The latter two use U.S. "letter", but the Philippine and Chilean "legal" size is 8½ in × 13 in (215.9 mm × 330.2 mm). ISO sizes are available, but not widely used, in both the U.S. and the Philippines.

In Canada, U.S. paper sizes are a de facto standard. The government, however, uses a combination of ISO paper sizes, and CAN 2-9.60M "Paper Sizes for Correspondence" specifies P1 through P6 paper sizes, which are the U.S. paper sizes rounded to the nearest 5 mm.

Mexico has adopted the ISO standard, but U.S. "letter" format is still the system in use throughout the country. It is virtually impossible to encounter ISO standard papers in day-to-day uses, with "Carta 216 mm × 279 mm" (letter), "Oficio 216 mm × 340 mm" (legal) and "Doble carta" (ledger/tabloid) being nearly universal. U.S. sizes are also widespread and in common use in Colombia

See switching costs, network effects and standardization for possible reasons for differing regional adoption rates of the ISO standard sizes.

#### ANSI paper sizes

In 1995, the American National Standards Institute adopted ANSI/ASME Y14.1 which defined a regular series of paper sizes based upon the de facto standard 8½ in × 11 in "letter" size which it assigned "ANSI A". This series also includes "ledger"/"tabloid" as "ANSI B". This series is somewhat similar to the ISO standard in that cutting a sheet in half would produce two sheets of the next smaller size. Unlike the ISO standard, however, the arbitrary aspect ratio forces this series to have two alternating aspect ratios. The ANSI series is shown below.

With care, documents can be prepared so that the text and images fit on either ANSI or their equivalent ISO sheets at 1:1 reproduction scale.

Name in × in mm × mm Ratio Alias Similar ISO A size
ANSI A 8½ × 11 216 × 279 1.2941 Letter A4
ANSI B 17 × 11
11 × 17
432 × 279
279 × 432
1.5455 Ledger
Tabloid
A3
ANSI C 17 × 22 432 × 559 1.2941 A2
ANSI D 22 × 34 559 × 864 1.5455 A1
ANSI E 34 × 44 864 × 1118 1.2941 A0

Other, larger sizes continuing the alphabetic series illustrated above exist, but it should be noted that they are not part of the series per se, because they do not exhibit the same aspect ratios. For example, Engineering F size (28 in × 40 in, 711.2 mm × 1016.0 mm) also exists, but is rarely encountered, as are G, H, … N size drawings. G size is 22½ in (571.5 mm) high, but variable width up to 90 in (2286 mm) in increments of 8½ in, i.e., roll format. H and larger letter sizes are also roll formats. Such sheets were at one time used for full-scale layouts of aircraft parts, wiring harnesses and the like, but today are generally not needed, due to widespread use of computer-aided design (CAD) and computer-aided manufacturing (CAM).

#### Architectural sizes

In addition to the ANSI system as listed above, there is a corresponding series of paper sizes used for architectural purposes. This series also shares the property that bisecting each size produces two of the size below. It may be preferred by North American architects because the aspect ratios (4:3 and 3:2) are ratios of small integers, unlike their ANSI (or ISO) counterparts. Furthermore, the aspect ratio 4:3 matches the traditional aspect ratio for computer displays. The architectural series, usually abbreviated "Arch", is shown below:

Name in × in mm × mm Ratio
Arch A 9 × 12 229 × 305 4:3
Arch B 12 × 18 305 × 457 3:2
Arch C 18 × 24 457 × 610 4:3
Arch D 24 × 36 610 × 914 3:2
Arch E 36 × 48 914 × 1219 4:3
Arch E1 30 × 42 762 × 1067 7:5

#### Other sizes

Name in × in mm × mm Ratio
Statement, Half Letter, Memo 5.5 × 8.5 140 × 216 1.
Quarto 9 × 11 229 × 279 1.
Executive, Monarch 7.25 × 10.5 184 × 267 ~1.4483
Government-Letter 8 × 10.5 203 × 267 1.3125
Letter 8.5 × 11 216 × 279 ~1.2941
Foolscap, Folio 8.27 × 13 210 × 330 1.625
Government-Legal 8.5 × 13 216 × 330 ~1.5294
Legal 8.5 × 14 216 × 356 ~1.6067
Ledger, Tabloid 11 × 17 279 × 432 1.
Super-B 13 × 19 330 × 483 ~1.4615
Post 15.5 × 19.5 394 × 489 ~1.2581
Crown 15 × 20 381 × 508 1.
Large Post 16.5 × 21 419 × 533 1.
Demy 17.5 × 22.5 445 × 572 ~1.2857
Medium 18 × 23 457 × 584 1.2
Broadsheet 18 × 24 457 × 610 1.
Royal 20 × 25 508 × 635 1.25
Elephant 23 × 28 584 × 711 ~1.2174
Double Demy 22.5 × 35 572 × 889 1.
Quad Demy 35 × 45 889 × 1143 ~1.2857

Name in × in mm × mm Ratio
Index card 3 × 5 76 × 127 1.
Index card 4 × 6 102 × 152 1.5
Index card 5 × 8 127 × 203 1.6
International business card * 2⅛ × 3.37 53.98 × 85.6 1.586
US business card 2 × 3.5 51 × 89 1.75
Japanese business card ~2.165 × ~3.583 55 × 91 ~1.65

• This is the same size as the smallest rectangle containing a credit card. However, credit card size, as defined in ISO 7810, also specifies rounded edges and a thickness.

Photograph sizes
Name in × in mm × mm Ratio
2R 2.5 × 3.5 64 × 89 1.4
- 3 × 5 76 × 127 1.
LD, DSC 3.5 × 4.67 89 × 119 1. (4:3)
3R, L 3.5 × 5 89 × 127 ~1.4286
LW 3.5 × 5.25 89 × 133 1.5 (3:2)
KGD 4 × 5.33 102 × 136 1. (4:3)
4R, KG 4 × 6 102 × 152 1.5
2LD, DSCW 5 × 6.67 127 × 169 1. (4:3)
5R, 2L 5 × 7 127 × 178 1.4
2LW 5 × 7.5 127 × 190 1.5 (3:2)
8R 8 × 10 203 × 254 1.25
12R 8 × 12 203 × 305 1.5
14R 11 × 14 279 × 356 1.

### Tablet sizes

The sizes listed above are for paper sold loosely in reams. There are many sizes of tablets of paper, that is, sheets of paper kept from flying around by being bound at one edge, usually by a strip of plastic or hardened PVA adhesive. Often there is a pad of cardboard (also known as chipboard or greyboard) at the bottom of the stack. Such a tablet serves as a portable writing surface, and the sheets often have lines printed on them, usually in blue, to make writing in a line easier. An older means of binding is to have the sheets stapled to the cardboard along the top of the tablet; there is a line of perforated holes across every page just below the top edge from which any page may be torn off. Lastly, a pad of sheets each weakly stuck with adhesive to the sheet below, trademarked as "Post-It" or "Stick-Em" and available in various sizes, serve as a sort of tablet.

"Letter pads" are of course 8½ by 11 inches, while the term "legal pad" is often used by laymen to refer to pads of various sizes including those of 8½ by 14 inches. There are "steno pads" (used by stenographers) of 6 by 9 inches.

Of course, in countries where the ISO sizes are standard, most notebooks and tablets are sized to ISO specifications (for example, most newsagents in Australia stock A4 and A3 tablets).

Traditionally, a number of different sizes were defined for large sheets of paper, and paper sizes were defined by the sheet name and the number of times it had been folded. Thus a full sheet of "royal" paper was 25 × 20 inches, and "royal octavo" was this size folded three times, so as to make eight sheets, and was thus 10 by 6¼ inches.

Imperial sizes were used in the United Kingdom and its territories. Some of the base sizes were as follows:

Name in × in mm × mm Ratio
Emperor 48 × 72 1219 × 1829 1.5
Antiquarian 31 × 53 787 × 1346 1.7097
Grand eagle 28.75 × 42 730 × 1067 1.4609
Double elephant 26.75 × 40 678 × 1016 1.4984
Atlas* 26 × 34 660 × 864 1.3077
Colombier 23.5 × 34.5 597 × 876 1.4681
Double demy 22.5 × 35.5 572 × 902 1.5(7)
Imperial* 22 × 30 559 × 762 1.3636
Double large post 21 × 33 533 × 838 1.5713
Elephant* 23 × 28 584 × 711 1.2174
Princess 21.5 × 28 546 × 711 1.3023
Cartridge 21 × 26 533 × 660 1.2381
Royal* 20 × 25 508 × 635 1.25
Sheet, half post 19.5 × 23.5 495 × 597 1.2051
Double post 19 × 30.5 483 × 762 1.6052
Super royal 19 × 27 483 × 686 1.4203
Medium* 17.5 × 23 470 × 584 1.2425
Demy* 17.5 × 22.5 445 × 572 1.2857
Large post 16.5 × 21 419 × 533 1.(27)
Copy draught 16 × 20 406 × 508 1.25
Large post 15.5 × 20 394 × 508 1.2903
Post* 15.5 × 19.25 394 × 489 1.2419
Crown* 15 × 20 381 × 508 1.(3)
Pinched post 14.75 × 18.5 375 × 470 1.2533
Foolscap* 13.5 × 17 343 × 432 1.2593
Small foolscap 13.25 × 16.5 337 × 419 1.2453
Brief 13.5 × 16 343 × 406 1.1852
Pott 12.5 × 15 318 × 381 1.2
* The sizes marked with an asterisk are still in use in the United States.

Traditional sizes for writing paper in the United Kingdom , :

Name in × in
Quarto 11 × 9
Imperial 9 × 7
Kings 8 × 6.5
Dukes 7 × 5.5
The common divisions and their abbreviations include:
Name Abbr. Folds Leaves Pages
Folio fo, f 1 2 4
Quarto 4to 2 4 8
Sexto, sixmo 6to, 6mo 3 6 12
Octavo 8vo 3 8 16
Duodecimo, twelvemo 12mo 4 12 24
Sextodecimo, sixteenmo 16mo 4 16 32

Foolscap folio is often referred to simply as 'folio' or 'foolscap'. Similarly, 'quarto' is more correctly 'copy draught quarto'.

Many of these sizes were only used for making books (see bookbinding), and would never have been offered for ordinary stationery purposes.

## Transitional paper sizes

### PA series

PA4-based series
Name mm × mm Ratio
PA0 840 × 1120 3:4
PA1 560 × 840 2:3
PA2 420 × 560 3:4
PA3 280 × 420 2:3
PA4 210 × 280 3:4
PA5 140 × 210 2:3
PA6 105 × 140 3:4
PA7 70 × 105 2:3
PA8 52 × 70 ≈3:4
PA9 35 × 52 ≈2:3
PA10 26 × 35 ≈3:4

A transitional size called PA4 (210 mm × 280 mm, 8¼ in × 11 in) was proposed for inclusion into the ISO 216 standard in 1975. It has the height of Canadian P4 paper (215 mm × 280 mm, about 8½ in × 11 in) and the width of international A4 paper (210 mm × 297 mm). The table to the right shows how this format can be generalized into an entire format series.

The PA formats did not end up in ISO 216, because the committee felt that the set of standardized paper formats should be kept to the minimum necessary. However, PA4 remains of practical use today. In landscape orientation, it has the same 4:3 aspect ratio as the displays of traditional TV sets, some computer displays and data projectors. PA4, with appropriate margins, is therefore a good choice as the format of presentation slides. At the same time, PA4 is the largest format that fits on both A4 and US/Canadian Letter paper without resizing.

PA4 is used today by many international magazines, because it can be printed easily on equipment designed for either A4 or US Letter.

### Antiquarian

Although the movement is towards the international standard metric paper sizes, on the way there from the traditional ones there has been at least one new size just a little larger than that used internationally. British architects and industrial designers once used a size called "Antiquarian" as listed above, but given in the New Metric Handbook (Tutt & Adler 1981) as 813 mm × 1372 mm. This is a little larger than the A0 size. So for a short time, a size called A0a (1000 mm × 1370 mm) was used in Britain.

### F4

F4 (210 mm × 330 mm) is common in Southeast Asia and Australia, and is sometimes called "foolscap". It has the same width as A4, but is longer.

## Other metric sizes

Name mm × mm in × in
DL 110 × 220 4.3 × 8.7
F4 210 × 330 8.3 × 13.0
RA0 860 × 1220 33.9 × 48.0
RA1 610 × 860 24.0 × 33.9
RA2 430 × 610 16.9 × 24.0
RA3 305 × 430 12.0 × 16.9
RA4 215 × 305 8.5 × 12.0
SRA0 900 × 1280 35.4 × 50.4
SRA1 640 × 900 25.2 × 35.4
SRA2 450 × 640 17.7 × 25.2
SRA3 320 × 450 12.6 × 17.7
SRA4 225 × 320 8.9 × 12.6
A3+ 329 × 483 12.9 × 19.0