INTERNATIONAL STANDARD PAPER SIZES

Standard paper sizes like ISO A4 are today widely used all over the world. This text explains the ISO 216 paper size system and the ideas behind its design.

The ISO paper size concept

In the ISO paper size system, all pages have a height-to-width ratio of square root of two (1:1.4142). This aspect ratio is especially convenient for a paper size. If you put two pages with this aspect ratio next to each other, or equivalently cut one parallel to its shorter side into two equal pieces, then the resulting page will have again the same width/height ratio.

The ISO paper sizes are based on the metric system. The square-root-of-two ratio does not allow the height and width of the pages to be nicely rounded metric lengths. Therefore, the area of the pages has been defined to have nice metric values. As paper is usually specified in grammes per square metre (gsm), this allows easy calculation of the mass of a document if the format and number of pages are 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).

Format A0 has an area of one square meter.

Format A1 is A0 cut into two equal pieces, i.e. A1 is as high as A0 is wide and A1 is half as wide as A0 is high.

All smaller A series formats are defined in the same way by cutting the next larger format in the series parallel to its shorter side into two equal pieces.

The standardized height and width of the paper formats is a rounded number of millimeters.

For applications where the ISO A series does not provide an adequate format, the B series has been introduced to cover a wider range of paper sizes. 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 between A1 and A0, that means the magnification factor that scales A1 to B1 also scales B1 to A0.
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 nicely into a C4 envelope, which in turn fits as nicely into a B4 envelope. If you fold this letter once to A5 format, then it will fit nicely into a C5 envelope.

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 millimeters:

A Sizes	mm	B Sizes	mm	C Sizes	mm
4AO	1682x2378	4BO	2000x2828
2AO	1189x1682	2BO	1414x2000
AO	841x1189	BO	1000x1414	CO	917x1297
A1	594x841	B1	707x1000	C1	917x1297
A2	420x594	B2	500x707	C2	458x648
A3	297x420	B3	353x500	C3	324x458
A4	210x297	B4	250x353	C4	229x324
A5	148x210	B5	176x250	C5	162x229
A6	105x148	B6	125x176	C6	114x162
A7	74x105	B7	88x125	C7	81x114
A8	52x74	B8	62x88	C8	57x81
A9	37x52	B9	44x62	C9	40x57
A10	26x37	B10	31X44	C10	28X40

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 instance DIN 476 requires ±1 mm, ±1.5 mm, and ±2 mm respectively for the same ranges of dimensions.

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 user or reader. Other ISO standards define the format serieses RA and SRA for untrimmed raw paper. These formats are only slightly larger than the corresponding A series formats. Sheets in these formats will be cut to the end format after 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 formats also follow the sqrt(2)-ratio and half-area rule, but the dimensions of the start format have been rounded to the full centimeter.

The common untrimmed paper formats, in millimeters, that printers order from the paper manufacturers are

RA Series Formats		SRA Series Formats
RA0	860x1220	SRA0	900x1280
RA1	610x860	SRA1	640x900
RA2	430x610	SRA2	450x640
RA3	305x430	SRA3	320x450
RA4	215x305	SRA4	225x320

Envelope formats

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

Format	Size (mm)	Content Format
C6	114x162	A4 folded twice = A6
DL	110x220	A4 folded twice = 1/3 A4
C6/C5	114x229	A4 folded twice = 1/3 A4
C5	162x229	A4 folded once = A5
C4	229x324	A4
C3	324x458	A3
B6	125x176	C6 envelope
B4	250x353	C4 envelope
E4	280x400	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 currently exists no ISO standard for envelopes with an address window, so let's have a look at the corresponding DIN standard. DIN 680 specifies that a transparent address window has to be 90 x 45 mm large and its left edge should be located 20 mm from the left edge of the envelope. For C6, DL, and C6/C5 envelopes, the bottom edge of the window should be 15 mm from the bottom edge of the envelope. For C4 envelopes, the top edge of the window should be either 27 or 45 mm from the top edge of the envelope.

Traditional Imperial paper formats

Size	Untrimmed inches	Folded Quarto Size inches
Pot	12 3/4 x 15 1/2	6 3/8 x 7 3/4
Crown	15 x 20	7 1/2 x 10
Double Crown	20 x 30	10 x 15
Quad Crown	30 x 40	15 x 20
Double Quad Crown	40 x 60	20 x 30
Demy	17 1/2 x 22 1/2	8 3/4 x 11 1/4
Small Demy	15 1/2 x 20	7 3/4 x 10
Double Demy (Music Demy)	22 1/2 x 35	11 1/4 x 17 1/2
Quad Demy	35 x 45	17 1/2 x 22 1/2
Small Foolscap	13 1/4 x 16 1/2	6 5/8 x 8 1/4
Double Foolscap	17 x 27	8 1/2 x 13 1/2
Foolscap	13 1/2 x 17	6 3/4 x 8 1/2
Quad Foolscap	27 x 34	13 1/2 x 17
Imperial	22 x 30	11 x 15
Medium	18 x 23	9 x 11 1/2
Double Medium	23 x 36	11 1/2 x 18
Post	15 1/2 x 19 1/4	7 3/4 x 9 5/8
Large Post	16 1/2 x 21	8 1/4 x 10 1/2
Sheet and 1/2 Post	19 1/2 x 23 1/2	9 3/4 x 11 3/4
Double Post	19 1/2 x 31 1/2	9 3/4 x 15 3/4
Double Large Post	21 x 33	10 1/2 x 16 1/2
Royal	20 x 25	10 x 12 1/2
Super Royal	20 x 27 1/2	10 x 13 3/4
Double Royal	25 x 40	12 1/2 x 20
Elephant	23 x 28	11 1/2 x 14

The common divisions and their abbreviations include:

Name	Folds	Pages
Folio	1	2
Quarto	2	4
Sexto or Sixmo	3	6
Octavo	3	8
Duodecimo or Twelvemo	4	12
Sextodecimo or Sixteenmo	4	16

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 important one for daily office use. Some main applications of the most popular formats can be summarized as:

A0,A1 technical drawings, posters
A1,A2 flip charts
A2,A3 drawings, diagrams, large tables
A4 letters, magazines, forms, catalogs, laser printer and copying machine output
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
B8,A8 playing cards

The main advantage of the ISO standard paper sizes becomes obvious for users of copying machines:

Example 1:

You are in a library and want to copy an article out of a journal that has A4 format. In order to save paper, you want copy two journal pages onto each sheet of A4 xerox paper. If you open the journal, the two A4 pages that you will now see together have A3 format. By setting the magnification factor on the copying machine to 71%, or by pressing the A3 to A4 button that is available on most copying machines, both A4 pages of the journal article together will fill exactly the A4 page produced by the copying machine. One reproduced A4 page will now have A5 format. No wasted paper margins appear, no text has been cut off, and no experiments for finding the appropriate magnification factor are necessary. The same principle works for books in B5 or A5 format.

Copying machines designed for ISO paper sizes usually provide special keys for the following frequently needed magnification factors:

71%	sqrt(0.5)	A3 > A4
84%	sqrt(sqrt(0.5))	B4 > A4
119%	sqrt(sqrt(2.0))	A4 > B4, or B5 > A4
141%	sqrt(2.0)	A4 > A3, or A5 > A4

Not only the operation of copying machines in offices and libraries, but also repro photography, microfilming, and printing are simplified by the 1:sqrt(2) aspect ratio of ISO paper sizes.

Example 2:

If you prepare a letter, you will have to know the weight of the content in order to determine the postal fee. This can be very conveniently calculated with the ISO A series paper sizes. Usual typewriter and laser printer 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 with the common paper quality 5 g per page. If we estimate 20 g for a C4 envelope (including some safety margin), then you will be able to put 16 A4 pages into a letter before you reach the 100 g limit for the next higher postal fee.

Using standard paper sizes saves money and makes life simpler in many applications. For example, if all scientific journals used only ISO formats, then libraries would have to buy only very few different sizes for the binders. Shelves can be designed such that standard formats will fit in exactly without too much wasted shelf volume. The ISO formats are used for surprisingly many things besides office paper: the German citizen ID card has format A7, both the European Union and the U.S. passport have format B7, and library microfiches have format A6. In some countries (e.g., Germany) even many brands of toilet paper have format A6.

Aspect ratios

Sometimes, paper formats with a different aspect ratio are required for labels, tickets, and other purposes. These should preferably be derived by cutting standard series sizes into 3, 4, or 8 equal parts, parallel with the shorter side, such that the ratio between the longer and shorter side is greater than the square root of two.

Some example long formats in millimeters are:

1/3 A4	99x120
1/4 A4	74x210
1/8 A4	37x210
1/4 A3	105x297
1/3 A3	70x148

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

Folding larger pages to A4 for filing

DIN 824 describes a method of folding A0, A1, etc. pages to A4 format for filing. This clever technique ensures that there remains a 20 mm single-layer margin for filing holes, that the page can be unfolded and folded again without being removed from the file, and that the label field at the bottom-left corner of technical drawings ends up in correct orientation on top of the folded page in the file.

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 upwards compatible 4-hole system. In it, the two middle holes correspond to ISO 838, plus there are two additional holes located 80 mm above and below these to provide for more stability. This way, sheets with four punched holes can also 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 back) 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, exclusive any margin or tabs. Simple folders without back or mechanism are 220 x 315 mm large. Folders and files with a very small back (less than 25 mm) with or without mechanism are 240 x 320 mm large. Files with wide back (exceeding 25 mm) are 250 x 320 mm (without a mechanism) or 290 x 320 mm if they include a mechanism. All these are maximum dimensions. Standardizing folder and file sizes allows to optimize shelf design and provides a uniform shelf look and handling even if folders from various manufacturers are used.

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 Gottingen, Germany, 1742-1799) in a letter that he wrote 1786-10-25 to Johann Beckmann. After introducing the meter measurement, the French government published 1794-11-03 the “Loi sur le timbre” (no. 2136), a law on the taxation of paper that defined several formats that correspond already exactly to the modern ISO paper sizes: “Grand registre” = ISO A2, “grand papier” = ISO B3, ”moyen papier” = ISO A”3, “petit papier” = ISO B4, “demi feuille” = ISO B5, “effets de commerce” = ISO 1/2 B5.

The French format series never became widely known and was quickly forgotten again. The A, B, and C series paper formats, which are based on the exact same design principles, were completely independently reinvented over a hundred years after the “Loi sur le timbre” in Germany by Dr. Walter Porstmann. They were adopted as the German standard DIN476 in 1922 as a replacement for the vast variety of other paper formats that had been used before, in order to make paper stocking and document reproduction cheaper and more efficient.

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 it is today used in almost all countries on this planet. 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]

The Lichtenberg Ratio used by the standard paper format series is occasionally confused with the Golden Ratio (Euclid referred to it as the "extreme and mean ratio"). The former is defined by the equation a/b = 2b/a = sqrt(2), whereas the latter is defined by a/b = (a+b)/a = b/(a-b) = (1 + sqrt(5))/2. While aesthetically pleasing properties have been attributed to both, the Lichtenberg Ratio has the advantage of preserving the aspect ratio when cutting a page into two. The Golden Ratio, on the other hand, preserves the aspect ratio when cutting a maximal square from the paper, a property that seems not particularly useful for office applications. The Golden Ratio was for a while a more fashionable topic in the antique and renaissance arts literature and it has a close connection to the Fibonacci sequence in mathematics.

North American paper formats

Name	Size inches	Size (mm)
Quarto	10 x 8	254 x 203
Foolscap	13 x 8	330 x 203
Letter	8 1/2 x 11	215 x 279
Government-Letter	8 x 10	203 x 254
Legal	8 1/2 x 14	215 x 355
Ledger	11 x 17	279 x 431
Executive	7 x 10 1/2	184 x 254
Post	15 1/2 x 19	393 x 488
Crown	15 x 20	381 x 508
Large post	16 1/2 x 21	419 x 533
Demy	17 1/2 x 22 1/2	444 x 571
Medium	18 x 23	457 x 584
Royal	20 x 25	508 x 635
Elephant	23 x 28	584 x 711
Double Demy	23 1/2 x 35	596 x 889
Quad Demy	35 x 45	889 x 1143
STMT	5 1/2 x 8 1/2	139 x 215
A	8 1/2 x 11	215 x 279
B	11 x 17	279 x 431
C	17 x 22	431 x 558
D	22 x 34	558 x 863
E	34 x 44	863 x 1117

ISO paper format standards are available from:

International Organization for Standardization
Case postale 56
1, rue de Varembé
CH-1211 Genève 20
Switzerland

Some of the above text is extracted from the paper ‘International StandardPaper Sizes‘ (ISO) by Markus Kuhn.

page top