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 m² 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 m². 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 (). 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.
| 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
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:
| 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:
, but the other formats have not turned out to be particularly useful in practice and they have not caught on internationally.
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.
| 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 | ||||
| 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.
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).
| 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 |
| 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 |
| 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. |
"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).
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 |
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 |
| 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.
| 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.
| 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 |