# Paper size

There have been many standard sizes of paper at different times and in different countries.

## International paper sizes

File:A size illustration.png
A comparison of different paper sizes

International standard paper sizes are now used in all countries except the United States, Canada, and some other countries of the Americas.

The international standard is ISO 216, which defines amongst others, A4. ISO paper sizes are all based on a single aspect ratio of the square root of two, or approximately 1:1.4142. Basing paper upon this ratio was conceived by Georg Lichtenberg in the eighteenth century, made law in Germany in the 1920s, but did not reach its culmination until the prevalence of photocopy machines from the 1960s made having all paper with the same aspect ratio far more convenient in scaling than any other system.

The largest standard size, A0, has an area of 1 . A1 is formed by cutting a piece of A0 in half, which retains the aspect ratio. This particular measurement system was chosen in order 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. Thus an A4 brochure when open is A3 and can be placed on the copier and either printed directly onto the A3 paper or reduced to A4.

The ISO B series is a scaling of the A series; B1 is half way between A0 and A1 in area. The C series, defined in ISO 269, is half way between the A and B series of the same number; for instance, C0 is half way between A0 and B0. This way, C0 is slightly larger than A0, and B0 slightly larger than C0. This was intended to allow one to fit inside an envelope of the other. For instance, a letter written on A4 paper, the standard for this role, fits inside a C4 envelope. A C4 envelope can fit inside a B4 envelope.

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

The measurements in millimetres are more appropriate for determining the aspect ratio of paper than the less-accurate measurement of book sizes in centimetres. However, there is a tolerance factor that lengths of paper less than 150 mm can have plus-or-minus 1.5 mm and still qualify for the size designation. Lengths from 150 to 600 mm can have plus-or-minus 2 mm, while those over 600 can have plus-or-minus 3 mm.

ISO 216 does not define any sizes larger than A0 and B0, but the German standard DIN 476 puts a factor in front of these. Thus paper designated 2A0 is twice the size of A0, while 4A0 is four times A0.

Although A4 is the standard size in the rest of the world, it doesn't fit in US three-ring binders (and there is a different standard for hole-punched binders to go with the international papers as well). However, the rarer E5 paper is less than a millimetre taller than US Letter size, though it is about five-eighths of an inch narrower. Photocopies from A4 to E5 are simply reduced to 95%, while from E5 to A4 increased to 105%. And notice that, as A4 is the standard size for international firms, documents on their web sites (such as that of ISO itself) are designed to be printed on such paper of greater length. Printing them out without adjustment, on US Letter-size paper, prints the bottom of the page on a second sheet. Another problem with some computer printers and software, though less common than it was, is that their configuration often defaults to letter paper when new or reset, even in countries using the ISO 216 standard.

ISO/DIN paper sizes (in mm)
A B C
0 841 × 1189 1000 × 1414 917 × 1297
1 594 × 841 707 × 1000 648 × 917
2 420 × 594 500 × 707 458 × 648
3 297 × 420 353 × 500 324 × 458
4 210 × 297 250 × 353 229 × 324
5 148 × 210 176 × 250 162 × 229
6 105 × 148 125 × 176 114 × 162
7 74 × 105 88 × 125 81 × 114
8 52 × 74 62 × 88 57 × 81
9 37 × 52 44 × 62 40 × 57
10 26 × 37 31 × 44 28 × 40
ISO/DIN paper sizes (converted to rounded inch values)
A B C
0 33 × 46¾ 39¼ × 55¾ 36 × 51
1 23½ × 33 27¾ × 39¼ 25½ × 36
2 16½ × 23½ 19¾ × 27¾ 18 × 25½
3 11¾ × 16½ 14 × 19¾ 12¾ × 18
4 8¼ × 11¾ 9¾ × 14 9 × 12¾
5 5¾ × 8¼ 7 × 9¾ 6½ × 9
6 4¼ × 5¾ 5 × 7 4½ × 6½
7 3 × 4¼ 3½ × 5 3¼ × 4½
8 2 × 3 2½ × 3½ 2¼ × 3¼
9 1½ × 2 1¾ × 2½ 1½ × 2¼
10 1 × 1½ 1¼ × 1¾ 1 × 1½

## Current U.S. loose paper sizes

Current standard sizes of U.S. paper are a subset of the traditional sizes referred to below. Letter, legal, and ledger/tabloid are by far the most commonly used of these for everyday activities.

There is an additional paper size to which the name "government-letter" was given by the IEEE Printer Working Group: the 8-by-10½ inch paper that is used in America for children's writing and was prescribed by Herbert Hoover when he was Secretary of Commerce to be used for U.S. governmental forms. Apparently this would enable discounts from purchase of paper for schools. As photocopy machines later proliferated, citizens wanted to make photocopies of the forms, but as the machines did not generally have this size paper in their bins, they could not do so, thus Ronald Reagan had the U.S. government switch to letter size. 8" × 10½" is still commonly used in spiral-bound notebooks and the like.

U.S. paper sizes are currently standard in the United States, Mexico, 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 half-centimeter [1].

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

Name Inches mm Ratio
Quarto 10 × 8 254 × 203 1.25
Foolscap 13 × 8 330 × 203 1.625
Executive 10½ × 7¼ 267 × 184 1.4483
Government-Letter 10½ × 8 267 × 203 1.3125
Letter 11 × 8½ 279 × 216 1.2941
Legal 14 × 8½ 356 × 216 1.6471
Ledger, Tabloid 17 × 11 432 × 279 1.5455
Post 19¼ × 15½ 489 × 394 1.2419
Crown 20 × 15 508 × 381 1.3333
Large Post 21 × 16½ 533 × 419 1.2727
Demy 22½ × 17½ 572 × 445 1.2857
Medium 23 × 18 584 × 457 1.2778
Royal 25 × 20 635 × 508 1.25
Elephant 28 × 23 711 × 584 1.2174
Double Demy 35 × 23½ 889 × 597 1.4894
Quad Demy 45 × 35 1143 × 889 1.2857
Statement 8½ × 5½ 216 × 140 1.5455
A 11 × 8½ 279 × 216 1.2941
B 17 × 11 432 × 279 1.5455
C 22 × 17 559 × 432 1.2941
D 34 × 22 864 × 559 1.5455
E 44 × 34 1118 × 864 1.2941

## Current U.S. paper sizes for tablets

The sizes listed above are for paper sold loosely in reams. There are a large number of 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. Often there is a pad of cardboard (or greyboard) at the bottom of the stack. Such a tablet serves as a portable writing surface, and the sheets 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, the pad of sheets each weakly stuck with adhesive to the sheet below, trade-marked as "Stick-Em's," serve as a sort of tablet. Their size is 3 inches square.

The significance of taking separate note of these sizes is that their contents are just as likely to be photocopied and enlarged, of course onto loose paper, as are the more standardized international sizes of paper.

"Letter pads" are of course 8½ by 11 inches, but the term "Legal pad" is often used for pads of this size besides those of 8½ by 14 inches. There are "Steno pads" (used by stenographers) of 6 by 9 inches, and pads for pre-school children of twice and four times this size, but which have lines going the long way across the paper: 9 by 12 inches and 12 by 18 inches. For the latter use, there are also pads 10¾ by 13½ inches.

For varied commercial purposes, all sorts of sizes have been recently observed: 4 by 5½ inches; 5 by 8 inches; 5-3/8 by 8-1/4 inches; 6 by 9½ inches; 7¼ by 9½ inches; and 7¾ by 9-7/8 inches.

The only "metric" paper in the shops where this observation was taken are a few Chinese-made "composition books" for children which are 190 mm by 247 mm, a slight modification from the 7¾ by 9¾ inch ones. But the holes in the sheets of any of theses tablets fit American-standard binders.

## Japanese paper sizes

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 Shiroko-ban and the Kiku paper sizes.

JIS paper sizes (in mm)
B- Shiroko ban
4x6/
Kiku
-0 1030 x 1456
-1 728 x 1030
-2 515 x 728
-3 364 x 515
-4 257 x 364 264 x 379 227 x 306
-5 182 x 257 189 x 262 151 x 227
-6 128 x 182 189 x 262
-7 91 x 128 127 x 188
-8 64 x 91
-9 45 x 64
-10 32 x 45
-11 22 x 32
-12 16 x 22

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 3 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 inches mm Ratio
Emperor 72 × 48 1829 × 1219 1.5
Antiquarian 53 × 31 1346 × 787 1.7097
Grand Eagle 42 × 28¾ 1067 × 730 1.4609
Colombier 34½ × 23½ 876 × 597 1.4681
Atlas* 34 × 26 864 × 660 1.3077
Imperial* 30 × 22 762 × 559 1.3636
Pinched Post 28½ × 14¾ 724 × 375 1.9322
Elephant* 28 × 23 711 × 584 1.2174
Princess 28 × 21½ 711 × 546 1.3023
Cartridge 26 × 21 660 × 533 1.2381
Royal* 25 × 20 635 × 508 1.25
Sheet and Half Post 23½ × 19½ 597 × 495 1.2051
Medium* 23 × 18 584 × 457 1.2778
Demy* 22½ × 17½ 572 × 445 1.2857
Large Post 21 × 16½ 533 × 419 1.2727
20 × 15½ 508 × 394 1.2903
Copy Draught 20 × 16 508 × 406 1.25
Crown* 20 × 15 508 × 381 1.3333
Post* 19¼ × 15½ 489 × 394 1.2419
Foolscap* 17 × 13½ 432 × 343 1.2593
Small Foolscap 16½ × 13¼ 419 × 337 1.2453
Brief 16 × 13½ 406 × 343 1.1852
Pott 15 × 12½ 381 × 318 1.2
• The sizes marked with an asterisk are used in the US.

The common divisions and their abbreviations include:

Name(s) Abbr. Folds Pages
Folio fo/f 1 2
Quarto 4to 2 4
Sexto or Sixmo 6to/6mo 3 6
Octavo 8vo 3 8
Duodecimo or Twelvemo 12mo 4 12
Sextodecimo or Sixteenmo 16mo 4 16

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

Although the movement is toward 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 "New Metric Handbook," (Tutt & Adler 1981) as 813 by 1372 mm. This is a bit larger than the A0 size. So for a short time, a size called A0a was used in Britain, being 1000 mm by 1370 mm, to get that extra 100 mm on the longer side, write Tutt & Adler.

Also, the E5 size might become transitional for the U.S., though no hint of this is present.

## Paper thickness and density

### Grammage

Throughout the world, except in regions using US paper sizes, the product of thickness and density of paper is expressed in grams per square metre (g/m²). This quantity is commonly called grammage in both English and French (ISO 536).

Typical office paper has a grammage of 80 g/m², therefore a typical A4 sheet (1/16 m²) weighs 5 g.

The unofficial unit symbol "gsm" instead of the official "g/m²" is also occasionally encountered in English speaking countries. This may be a result of typists not knowing how to enter a superscript 2, a character not labeled on standard US and UK keyboards.

### Uncut ream weight

In countries using US paper sizes, the weight in pounds for an uncut ream (500 sheets) is used, so to compute the weight per area, one must know three (or four) quantities:

1. The weight of a ream.
2. The number of sheets in a ream.
3. The uncut dimensions of a sheet of paper.
4. The conversion factors between avoirdupois pound and gram (1 lb ≈ 454 g) and between square inch and square metre (1 m² ≈ 1550 in²): 1 lb/in² ≈ 7037 g/m².

For example, a "20 pound ream of Letter paper" has a weight of only 5 pounds because uncut dimensions are twice the cut dimensions. Since the cut dimensions are 8½ in × 11 in, the uncut dimensions are 17 in × 22 in. Therefore paper weight per area of this type of Letter is:

$\frac {20\ \frac{\mathrm{lb}}{\mathrm{ream}} \times 1\ \mathrm{sheet}} {17\ \mathrm{in} \times 22\ \mathrm{in} \times 500\ \frac{\mathrm{sheet}}{\mathrm{ream}}} = 1.06951872 \times 10^{-4}\ \frac{\mathrm{lb}}{\mathrm{in^2}} \approx 75.25\ \frac{\mathrm{g}}{\mathrm{m^2}}$