International standard paper sizes

by Markus Kuhn

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

The ISO paper size concept

In the ISO paper size system, the height-to-width ratio of allpages is the square root of two (1.4142 : 1). In other words, thewidth and the height of a page relate to each other like the side andthe diagonal of a square. This aspect ratio is especially convenientfor a paper size. If you put two such pages next to each other, orequivalently cut one parallel to its shorter side into two equalpieces, then the resulting page will have again the same width/heightratio.

The ISO paper sizes are based on the metric system. Thesquare-root-of-two ratio does not permit both the height and width ofthe pages to be nicely rounded metric lengths. Therefore, the area ofthe pages has been defined to have round metric values. As paper isusually specified in g/m², this simplifies calculation of themass of a document if the format and number of pages are known.

ISO 216 defines the A series of paper sizes based on thesesimple principles:

• The height divided by the width of all formats isthe square root of two (1.4142).
• Format A0 has an area of one square meter.
• Format A1 is A0 cut into two equal pieces. In other words, theheight of A1 is the width of A0 and the width of A1 is half the heightof A0.
• All smaller A series formats are defined in the same way. If youcut format An parallel to its shorter side into two equalpieces of paper, these will have format A(n+1).
• The standardized height and width of the paper formats is arounded number of millimeters.

For applications where the ISO A series does not provide an adequateformat, the B series has been introduced to cover a wider range ofpaper sizes. The C series of formats has been defined for envelopes.

• The width and height of a Bn format are thegeometric mean between those of the An and thenext larger A(n−1) format. For instance, B1 is thegeometric mean between A1 and A0, that means the same magnificationfactor that scales A1 to B1 also scales B1 to A0.
• Similarly, the formats of the C series are the geometric meanbetween the A and B series formats with the same number. For example,an (unfolded) A4 size letter fits nicely into a C4 envelope, which in turnfits as nicely into a B4 envelope. If you fold this letter once to A5format, then it will fit nicely into a C5 envelope.
• B and C formats naturally are also square-root-of-two formats.

Note: The geometric mean of two numbersx and y is the square root of their product,(xy)^1/2, whereas their arithmetic meanis half their sum, (x+y)/2. For example, thegeometric mean of the numbers 2 and 8 is 4 (because 4/2 = 8/4), whereastheir arithmetic mean is 5 (because 5−2 = 8−5). The arithmetic mean ishalf-way between two numbers by addition, whereas the geometric meanis half-way between two numbers by multiplication.

By the way: The Japanese JIS P 0138-61 standarddefines the same A series as ISO 216, but a slightly different Bseries of paper sizes, sometimes called the JIS B or JB series. JIS B0has an area of 1.5 m², such that the area of JIS B pages isthe arithmetic mean of the area of the A series pages withthe same and the next higher number, and not as in the ISO B seriesthe geometric mean. For example, JB3 is 364 × 515, JB4is 257 × 364, and JB5 is 182 × 257 mm. Using the JIS Bseries should be avoided. It introduces additional magnificationfactors and is not an international standard.

The following table shows the width and height of all ISO A and Bpaper formats, as well as the ISO C envelope formats. The dimensionsare in millimeters:

A Series FormatsB Series FormatsC Series Formats4A01682 × 2378––––2A01189 × 1682–––– A0 841 × 1189B01000 × 1414C0917 × 1297 A1 594 × 841 B1 707 × 1000C1648 × 917 A2 420 × 594 B2 500 × 707 C2458 × 648 A3 297 × 420 B3 353 × 500 C3324 × 458A4210 × 297B4250 × 353C4229 × 324 A5 148 × 210 B5 176 × 250 C5162 × 229 A6 105 × 148 B6 125 × 176 C6114 × 162 A7 74 × 105 B7 88 × 125 C7 81 × 114 A8 52 × 74 B8 62 × 88 C8 57 × 81 A9 37 × 52 B9 44 × 62 C9 40 × 57A10 26 × 37 B10 31 × 44 C1028 × 40

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

Application examples

The ISO standard paper size system covers a wide range of formats, butnot all of them are widely used in practice. Among all formats, A4 isclearly the most important one for daily office use. Some mainapplications of the most popular formats can be summarized as:

A0, A1technical drawings, postersA1, A2flip chartsA2, A3drawings, diagrams, large tablesA4letters, magazines, forms, catalogs, laser printer andcopying machine outputA5note padsA6postcardsB5, A5, B6, A6booksC4, C5, C6envelopes for A4 letters: unfolded (C4), foldedonce (C5), folded twice (C6)B4, A3newspapers, supported by most copying machinesin addition to A4B8, A8playing cards

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

Example 1:

You are in a library and want to copy an article out of a journalthat has A4 format. In order to save paper, you want copy two journalpages onto each sheet of A4 paper. If you open the journal, thetwo A4 pages that you will now see together have A3 format. By settingthe magnification factor on the copying machine to 71% (that issqrt(0.5)), or by pressing the A3→A4 button that is availableon most copying machines, both A4 pages of the journal articletogether will fill exactly the A4 page produced by the copyingmachine. One reproduced A4 page will now have A5 format. No wastedpaper margins appear, no text has been cut off, and no experiments forfinding the appropriate magnification factor are necessary. The sameprinciple works for books in B5 or A5 format.

Copying machines designed for ISO paper sizes usually providespecial keys for the following frequently needed magnificationfactors:

71%sqrt(0.5)A3 → A4 84%sqrt(sqrt(0.5))B4 → A4119%sqrt(sqrt(2))A4 → B4 (also B5 → A4)141%sqrt(2)A4 → A3 (also A5 → A4)

The magnification factors between all A sizes:

_from^toA0A1A2A3A4A5A6A7A8A9A10A0100%71%50%35%25%18%12.5%8.8%6.2%4.4%3.1%A1141%100%71%50%35%25%18%12.5%8.8%6.2%4.4%A2200%141%100%71%50%35%25%18%12.5%8.8%6.2%A3283%200%141%100%71%50%35%25%18%12.5%8.8%A4400%283%200%141%100%71%50%35%25%18%12.5%A5566%400%283%200%141%100%71%50%35%25%18%A6800%566%400%283%200%141%100%71%50%35%25%A71131%800%566%400%283%200%141%100%71%50%35%A81600%1131%800%566%400%283%200%141%100%71%50%A92263%1600%1131%800%566%400%283%200%141%100%71%A103200%2263%1600%1131%800%566%400%283%200%141%100%

Not only the operation of copying machines in offices andlibraries, but also repro photography, microfilming, and printing aresimplified 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 thecontent in order to determine the postal fee. This can be veryconveniently calculated with the ISO A series paper sizes. Usualtypewriter and laser printer paper weighs 80 g/m². An A0 page hasan area of 1 m², and the next smaller A series page has half ofthis area. Therefore, the A4 format has an area of 1/16 m² andweighs with the common paper quality 5 g per page. If we estimate 20 gfor a C4 envelope (including some safety margin), then you will beable to put 16 A4 pages into a letter before you reach the 100 g limitfor the next higher postal fee.

Calculation of the mass of books, newspapers, or packed paper isequally trivial. You probably will not need such calculations often,but they nicely show the beauty of the concept of metric paper sizes.

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

Further details

Calculating the dimensions

Although the ISO paper sizes are specified in the standard with thewidth and height given in millimeters, the dimensions can also becalculated with the following formulas:

FormatWidth [m]Height [m]An2^−1/4−n/22^1/4−n/2Bn2^−n/22^1/2−n/2Cn2^−1/8−n/22^3/8−n/2

The actual millimeter dimensions in the standard have beencalculated by progressively rounding down any division-by-two result,as the small program iso-paper.cdemonstrates. This guarantees that two A(n+1) pagestogether are never larger than an An page.

Aspect ratios other than sqrt(2)

Sometimes, paper formats with a different aspect ratio arerequired for labels, tickets, and other purposes. These shouldpreferably be derived by cutting standard series sizes into 3, 4, or 8equal parts, parallel with the shorter side, such that the ratiobetween the longer and shorter side is greater than the square root oftwo. Some example long formats in millimeters are:

1/3 A4 99 × 2101/4 A4 74 × 2101/8 A4 37 × 2101/4 A3105 × 2971/3 A5 70 × 148

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

Envelope formats

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

FormatSize [mm]Content FormatC6114 × 162A4 folded twice = A6DL110 × 220A4 folded twice = 1/3 A4C6/C5114 × 229A4 folded twice = 1/3 A4C5162 × 229A4 folded once = A5C4229 × 324A4C3324 × 458A3B6125 × 176C6 envelopeB5176 × 250C5 envelopeB4250 × 353C4 envelopeE4280 × 400B4

The DL format is the most widely used business letter format. DLprobably originally stood for “DIN lang”, but ISO 269 nowexplains this abbreviation instead more diplomatically as “DimensionLengthwise”. Its size falls somewhat out of the system andequipment manufacturers have complained that it is slightly too smallfor reliable automatic enveloping. Therefore, DIN 678 introduced theC6/C5 format as an alternative for the DL envelope.

Window envelopes, A4 letterheads, folding marksand standard layouts

There exists no international standard yet for window envelopes andmatching letterhead layouts. There are various incompatible nationalstandards, for example:

• Germany: DIN 680 specifies that a transparent addresswindow is 90 × 45 mm large and its left edge should be located 20mm from the left edge of the envelope. For C6, DL, and C6/C5envelopes, the bottom edge of the window should be 15 mm from thebottom edge of the envelope. For C4 envelopes, the top edge of thewindow should be either 27 or 45 mm from the top edge of the envelope.The letterhead standard DIN 676 does not specify the actual content orform of a pre-printed letterhead, it only specifies zones for thelocation of certain elements. The letterhead format specified in DIN676 has a 85 × 45 mm large address field visible through thewindow, in which the top 5 mm are reserved for printing in a smallfont the sender’s address and the bottom 40 mm are for writing therecipient’s address. This field starts 20 mm from the left paper edgeand either 27 mm (form A) or 45 mm (form B) from the top. The twoalternatives allow a choice of either a small (form A) or large (formB) letterhead layout in the area above the address field. Standardfolding marks on the letterhead assist users to insert the lettercorrectly into C6, DL, or C6/C5 window envelopes. There is one foldingmark (for C6) on the top edge of the page, 148 mm from the left edge.There are also two folding marks on the left edge of the page, either105 and 210 mm from the bottom edge (form A) or 105 and 210 mm fromthe top edge (form B).
• United Kingdom: BS 4264 specifies that the transparentwindow on a DL envelope should be 93 × 39 mm large. Its top-leftcorner should be located 20 mm from the left margin and 53 mm from thetop margin of the envelope. BS 1808 specifies an 80 × 30 mm largeaddress panel on the letterhead. Its top-left corner is located 20 mmfrom the left margin and 51 mm from the top margin of the page. Theaddress panel is embedded inside a 91 × 48 mm large exclusionzone whose top left corner is located 20 mm from the left margin and42 mm from the top margin of the page. In other words, the area 9 mmabove and below and 11 mm right of the address panel should be keptclean of any other printing.
• Switzerland: The envelope window is 100 × 45 mm largeand located 12 mm either from the left or the right edge. The distanceto the top edge is 48 mm (for C6 and C5/C6) or 52 mm (for C5). The SNV010130 letterhead format places the recipient’s address into a 90× 40 mm large field 45 mm from the top and 8 mm from the rightedge of the A4 page. [from: H.R. Bosshard, 1980, ISBN 3-85584-010-5]
• Finland: SFS 2488:1994 specifies that for E seriesenvelopes the size of the window is 90 × 30 mm and for the Cseries 95 × 35 mm. In either case, the left margin is 18 mm andthe top margin 40 mm. SFS 2487:2000 (“Layout of document text area”)and SFS 2486:1999 (“Forms Layout”) specify that the area for therecipient’s address is 76.2 × 25.4 mm, located 20 mm from theleft, and 10±1 mm plus 25.4 mm from the top (the 25.4 mm are forthe sender’s information).

According to ISO 11180 and UniversalPostal Union standards, an international postal address should benot longer than 6 lines with up to 30 characters each. This requires amaximum area of 76.2 × 38.1 mm with the commonly used typewritercharacter width of 2.54 mm (1/10") and a baseline distance of 6.35 mm(1/4").

The Universal Postal Union LetterPost Regulations specify a standardposition of the address on the envelope, which is within 140 mmfrom the right edge, at least 40 mm from the top edge, and issurrounded by at least 15 mm unprinted envelope to the left, right andbelow of the address text.

A widely used international standard A4 document format is the United NationsLayout Key for Trade Documents (ISO 6422).

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 ensuresthat there remains a 20 mm single-layer margin for filing holes, thatthe page can be unfolded and folded again without being removed fromthe file, and that the label field at the bottom-left corner oftechnical drawings ends up in correct orientation on top of the foldedpage in the file.

Folder and file sizes

ISO 623 specifies the sizes of folders and files intended toreceive either A4 sheets or simple folders (without back) that are notdesigned for any particular filing system or cabinet. The sizesspecified are those of the overall rectangular surface when thefolders or files are folded, exclusive any margin or tabs. Simplefolders without back or mechanism are 220 × 315 mm large. Foldersand files with a very small back (less than 25 mm) with or withoutmechanism are 240 × 320 mm large. Files with wide back (exceeding25 mm) are 250 × 320 mm (without a mechanism) or 290 × 320mm if they include a mechanism. All these are maximum dimensions.Standardizing folder and file sizes helps to optimize shelf designsand provides a uniform look and handling even if folders fromvarious manufacturers are used.

Filing holes

ISO 838 specifies that, for filing purposes, two holes of 6±0.5mm diameter can be punched into the sheets. The centers of the twoholes are 80±0.5 mm apart and have a distance of 12±1 mm tothe nearest edge of the sheet. The holes are located symmetrically inrelation to the axis of the sheet or document. Any format that is atleast as large as A7 can be filed using this system.

Not specified in ISO 838, but also widely used, is an upwardscompatible 4-hole system. Its two middle holes correspond to ISO 838,plus there are two additional holes located 80 mm above and belowthese to provide for more stability. This way, sheets with fourpunched holes can also be filed in ISO 838 2-hole binders. This systemis also known under the nickname "888", presumably because the threegaps between the holes are all 8 cm wide. Some hole punches have ontheir paper guide not only markings for "A4", "A5", and "A6", but alsofor "888". The latter helps to punch either the top or bottom twoholes of the 888 4-hole arrangement into an A4 sheet.

Technical drawing pen sizes

Technical drawing pens follow the same size-ratio principle. Thestandard sizes differ by a factor sqrt(2): 2.00 mm, 1.40 mm,1.00 mm, 0.70 mm, 0.50 mm, 0.35 mm, 0.25 mm,0.18 mm, 0.13 mm. So after drawing with a 0.35 mm penon A3 paper and reducing it to A4, you can continue with the0.25 mm pen. (ISO 9175-1)

Ruled writing paper

There seems to be no international standard yet for ruled writingpaper. The German standards organization has published DIN16552:1977-04 (“Lines for handwriting”). That system is widely used,at least in Germany, by primary school teachers to specify whichschool exercise books pupils should use at which stage of learning howto write. Writing paper with fine gray 5 mm grid lines seems to bevery popular in many countries.

Untrimmed paper formats

All A and B series formats described so far are trimmed paper endsizes, i.e. these are the dimensions of the paper delivered to theuser or reader. Other ISO standards define the format series RA andSRA for untrimmed raw paper, where SRA stands for “supplementary rawformat A” (“sekundäres Rohformat A”). These formats are only slightlylarger than the corresponding A series formats. Sheets in theseformats will be cut to the end format after binding. The ISO RA0format has an area of 1.05 m² and the ISO SRA0 format has an areaof 1.15 m². These formats also follow the sqrt(2)-ratio andhalf-area rule, but the dimensions of the start format have beenrounded to the full centimeter. The common untrimmed paper formatsthat printers order from the paper manufacturers are

RA Series FormatsSRA Series FormatsRA0860 × 1220SRA0900 × 1280RA1610 × 860 SRA1640 × 900RA2430 × 610 SRA2450 × 640RA3305 × 430 SRA3320 × 450RA4215 × 305 SRA4225 × 320

The RA and SRA dimensions are also used as roll widths in rotatingprinting presses.

Overhead projectors

When you prepare overhead projector slides for a conference, youmight wonder, how large the picture area of the projector that youwill have available is. ISO 7943-1 specifies two standard sizes ofoverhead projector picture areas: Type A is 250 × 250 mm (cornersrounded with a radius less than 60 mm) and Type B is 285 × 285 mm(corners rounded with a radius less than 40 mm or cut off diagonallyno more than 40 mm). Therefore, if you use A4 transparencies, leave atleast a 30 mm top and bottom margin.

Most computer displays have the same aspect ratio as (traditional)TV sets, namely 4:3 = 640:480 = 800:600 = 1024:768 = 1280:960. If youprepare presentation slides, I recommend that you arrange your layoutinside a 280 × 210 mm field and make sure that you leave at least20 mm margin on the left and right side. This way, you plan for theaspect ratio of a TV/VGA projector and ensure at the same time thatyou can print on A4 transparencies such that every standard overheadprojector will show all parts of your slides.

Identification cards

ISO 7810 specifies three formats for identification cards:

• ID-1 = 85.60 × 53.98 mm (= 3.370 ×2.125 in)
• ID-2 = 105 × 74 mm (= A7)
• ID-3 = 125 × 88 mm (= B7)

ID-1 is the common format for banking cards (0.76 mm thick) and isalso widely used for business cards and driver’s licences. Some peopleprefer A8 (74 × 52 mm) for business cards. The standard passportformat is B7 (= ID-3), the German ID card has A7 (= ID-2) format andthe European Union driver’s licence is an ID-1 card.

History of the ISO paper formats

One of the oldest written records regarding the sqrt(2) aspectratio for paper sizes is a letter that the physics professorGeorgChristoph Lichtenberg (University of Göttingen, Germany,1742-1799) wrote 1786-10-25 to Johann Beckmann. In it, Lichtenbergexplains the practical and aesthetic advantages of the sqrt(2) aspectratio, and of his discovery that paper with that aspect ratio wascommonly available at the time. (There are also suggestions that thetask to find a paper format that is similar to itself after being cutin half appeared as a question in mathematics exams as early as 1755.)

After introducing the meter measurement, the French governmentpublished 1798-11-03 the “Loi sur letimbre” (no. 2136), a law on the taxation of paper that definedseveral formats that already correspond exactly to the modern ISOpaper sizes: “Grand registre” = ISO A2, “grand papier” = ISO B3,“moyen papier” = ISO A3, “petit papier” = ISO B4, “demi feuille” = ISOB5, “effets de commerce” = ISO 1/2 B5.

The French format series never became widely known and was quicklyforgotten again. The A, B, and C series paper formats, which are basedon the exact same design principles, were completely independentlyreinvented over a hundred years after the “Loi sur le timbre” inGermany by Dr. Walter Porstmann. They were adopted as the Germanstandard DIN 476 in 1922 as areplacement for the vast variety of other paper formats that had beenused before, in order to make paper stocking and document reproductioncheaper and more efficient. (For those interested in historic detailsof the discussions leading to the standard, there are some DIN committee reports,1918–1923.)

Porstmann’s DIN paper-format concept was convincing, and soonintroduced as a national standard in many other countries, forexample, Belgium (1924), Netherlands (1925), Norway (1926),Switzerland (1929), Sweden (1930), Soviet Union (1934), Hungary(1938), Italy (1939), Uruguay (1942), Argentina (1943), Brazil (1943),Spain (1947), Austria (1948), Romania (1949), Japan (1951), Denmark(1953), Czechoslovakia (1953), Israel (1954), Portugal (1954),Yugoslavia (1956), India (1957), Poland (1957), United Kingdom (1959),Venezuela (1962), New Zealand (1963), Iceland (1964), Mexico (1965),South Africa (1966), France (1967), Peru (1967), Turkey (1967), Chile(1968), Greece (1970), Simbabwe (1970), Singapur (1970), Bangladesh(1972), Thailand (1973), Barbados (1973), Australia (1974), Ecuador(1974), Columbia (1975) and Kuwait (1975). It finally became both aninternational standard (ISO 216) as well as the official UnitedNations document format in 1975 and it is today used in almost allcountries on this planet, leaving North America as the only remainingexception. In 1977, a large German car manufacturer performed a studyof the paper formats found in their incoming mail and concluded thatout of 148 examined countries, 88 already used the A series formatsthen. [Source: Helbig/Hennig 1988]

Note: The Lichtenberg Ratio – used by thestandard paper format series – is occasionally confused with the GoldenRatio (which Euclid referred to as the “extreme and mean ratio”).The Lichtenberg Ratio is defined by the equation a/b = 2b/a = sqrt(2),whereas the Golden Ratio is defined by a/b = (a+b)/a = b/(a−b) = (1 +sqrt(5))/2. While aesthetically pleasing properties have beenattributed to both, the Lichtenberg Ratio has the advantage ofpreserving the aspect ratio when cutting a page into two. The GoldenRatio, on the other hand, preserves the aspect ratio when cutting amaximal square from the paper, a property that seems not particularlyuseful for office applications. The Golden Ratio was for a while amore fashionable topic in the antique and renaissance arts literatureand it has a close connection to the Fibonacci sequence inmathematics.

[A more divine originof the A4 format has been suggested by Mr. Vernon Jenkins in aneffort to reduce unicity distance.]

Hints for North American paper users

The United States, Canada, and in part Mexico, are today the onlyindustrialized nations in which the ISO standard paper sizes are notyet widely used. In U.S. office applications, the paper formats“Letter” (216 × 279 mm), “Legal” (216 × 356 mm), “Executive”(190 × 254 mm), and “Ledger/Tabloid” (279 × 432 mm) arewidely used today. There exists also an American National StandardANSI/ASME Y14.1 for technical drawing paper sizes A (216 × 279mm), B (279 × 432 mm), C (432 × 559 mm), D (559 × 864mm), E (864 × 1118 mm), and there are many other unsystematicformats for various applications in use. The “Letter”, “Legal”,“Tabloid”, and other formats (although not these names) are defined inthe American National Standard ANSI X3.151-1987.

While all ISO paper formats have consistently the same aspect ratioof sqrt(2) = 1.414, the U.S. format series has two differentalternating aspect ratios 17/11 = 1.545 and 22/17 = 1.294. Therefore,you cannot reduce or magnify from one U.S. format to the next higheror lower without leaving an empty margin, which is ratherinconvenient.

The new American National Standard ANSI/ASME Y14.1m-1995 specifieshow to use the ISO A0−A4 formats for technical drawings in the U.S.Technical drawings usually have a fixed drawing scale (e.g., 1:100means that one meter is drawn as one centimeter), therefore it is noteasily possible to resize technical drawings between U.S. and standardpaper formats. As a result, internationally operating U.S.corporations increasingly find it more convenient to abandon the oldANSI Y14.1 formats and prepare technical drawings for ISO paper sizes,like the rest of the world does.

The historic origins of the 216 × 279 mm U.S. Letter format,and in particular its rationale, seem rather obscure. The earliestdocumented attempts to standardize U.S. paper format used a completelydifferent format. On 1921-03-28, the U.S. Secretary of Commerce(Hoover) declared a 203 × 267 mm format to be the standard forhis department, which was adopted on 1921-09-14 by the PermanentConference on Printing (established by General Dawes, first directorof the Bureau of the Budget) as the general U.S. government letterheadstandard. Independent of that, on 1921-08-30 a Committee on theSimplification of Paper Sizes consisting of printing industryrepresentatives was appointed to work with the Bureau of Standards. Itrecommended standard basic sizes of 432 × 559 mm (17 × 22in), 432 × 711 mm (17 × 28 in), 483 × 610 mm (19 ×24 in), 559 × 864 mm (22 × 34 in), 711 × 864 mm (28× 34 in), and 610 × 914 mm (24 × 36 in). What becamelater known as the U.S. Letter format is just the first of these basicsizes halved. Onehypothesis for the origin of this format series is that it wasderived from a then typical mold size used then in the production ofhand-made paper. “It does not appear, even in the selection of 8 1/2× 11 inch size paper, that any special analysis was made to provethat this provided an optimum size for a commercial letterhead” [Dunn,1972.]. It appears that this standard was just a commercial compromiseat the time to reduce inventory requirements without requiringsignificant changes to existing production equipment. The Hooverstandard remained in force until the government declared in1980-01 the 216 × 279 mm format to be the new official paperformat for U.S. government offices.

The Canadian standard CAN 2-9.60M “Paper Sizes for Correspondence”defines the six formats P1 (560 × 860 mm), P2 (430 × 560mm), P3 (280 × 430 mm), P4 (215 × 280 mm), P5 (140 ×215 mm), and P6 (107 × 140 mm). These are just the U.S. sizesrounded to the nearest half centimeter (P4 ~ U.S. Letter, P3 ~ U.S.Ledger). This Canadian standard was introduced in 1976, even thoughthe Ontario Government already had introduced the ISO A series formatsbefore in 1972. Even though these Canadian paper sizes look somewhatlike a pseudo-metric standard, they still suffer from the two majorinconveniences of the U.S. formats, namely they have no commonheight/width ratio and they differ significantly from what the rest ofthe world uses.

Note: It was proposed for an earlydraft of ISO 216 to recommended the special size 210 × 280 mm (aformat sometimes called PA4) as an interim measure for countries thatuse 215 × 280 mm paper and have not yet adopted the ISO A series.Some magazines and other print products that have to be printedeconomically on both A4 and U.S. Letter presses use the PA4 formattoday. Incidentally, this PA4 format has a width/height ratio of 3:4,the same as traditional TV screens and most computer monitors andvideo modes.

Both the “Letter” and “Legal” format could easily be replaced byA4, “Executive” (if it is really needed) by B5, and “Ledger/Tabloid”by A3. Similarly, the A–E formats can be replaced by A4–A0. It can behoped and expected that with the continuing introduction of the metricsystem in the United States, the ISO paper formats will eventuallyreplace non-standard paper formats also in North America. Conversionto A4 as the common business letter and document format in NorthAmerica would not be too difficult, as practically all modernsoftware, copying machines, and laser printers sold today in the U.S.already support A4 paper as a standard feature.

Users of photocopiers outside the U.S. and Canada usually take itfor granted that the machine is able to enlarge A4 → A3 orreduce A3 → A4, the two paper formats usually kept in machineswith two paper trays. When they use a copier in North America, itoften comes as a disappointing surprise when they find out thatmagnifying an entire page is not a function available there. Theabsence of this useful capability is a direct result of theunfortunate design of the U.S. paper formats. North American copiersusually also have two or more paper trays, but these are mostly usedfor the two very similar “Letter” and “Legal” formats, wasting theopportunity of offering a highly useful magnifying capability. Anyenlarging of a “Letter” page onto “Legal” paper will always chop offmargins and is therefore of little use. The Legal format itself isquite rarely used, the notion that it is for “legal” work is a popularmyth; the vast majority of U.S. legal documents are actually using the“Letter” format. Some copiers also offer in addition or instead thenext larger “Ledger” format, but that again has a different aspectratio and will therefore change the margins of a document duringmagnification or reduction.

Based on the experience from the introduction of ISO paper formatsin other industrialized countries at various points during the 20thcentury, it becomes clear that this process needs to be initiated by apolitical decision to move all government operation to the new paperformat system. History shows that the commercial world then graduallyand smoothly adopts the new government standard for office paperwithin about 10–15 years. It would not be a major operation to dothis in the U.S. and Canada as well, especially considering that moststandard software and office machines are already prepared for A4.However, such a project can succeed only if the national executive hasthe political will to accomplish this. The transition period of abouta decade is necessary to avoid expensive equipment replacement costsfor printers, especially those with older large rotary presses thatwere not yet designed to be easily retooled for ISO paper sizes.

If you purchase new office or printing equipment in North America,it might be wise to pay attention whether the equipment is suitablefor use with A4 paper. When you make inquiries, best indicate tovendors that ISO 216 compatibility of equipment is of concern to you.

If you live in the U.S. and have never been abroad, you might notbe aware that paper and accessories in the North-American sizes arenot commonly available outside the U.S. or Canada. They are verydifficult to obtain in any other country and the only practical way toget U.S. “Letter” there is to cut one of the next larger availablesizes (usually B4, A3 or RA4). Therefore, do not expect anyone to sendyou documents in “Letter” format from abroad. If you send documents toany other country, your use of A4 will greatly ease the handling andfiling of your documents for the recipient. If you design softwarethat might be used globally, please keep in mind that the vastmajority of laser printer users will print onto A4 paper. Therefore,always make A4 the default setting and the first selection choice inyour printing user interface. Remember that it is the paper formatused by about 95% of the people on this planet.

Due to popular demand, I have prepared an unofficial table with theISO sizes in inch fractions. Each listed inch fraction has thesmallest denominator that keeps the value within the ISO 216 tolerancelimits. Product designers should use the official millimeter valuesinstead. There is also a table inPostScript points.

A Series FormatsB Series FormatsC Series Formats4A066 1/4 × 93 5/8––––2A046 3/4 × 66 1/4–––– A0 33 × 46 3/4 B0 39 3/8 × 55 3/4C036 × 51 A1 23 3/8 × 33 B1 27 3/4 × 39 3/8 C125 1/2 × 36 A2 16 1/2 × 23 3/8 B2 19 3/4 × 27 3/4 C218 × 25 1/2 A3 11 3/4 × 16 1/2 B3 13 7/8 × 19 3/4 C312 3/4 × 18 A48 1/4 × 11 3/4 B4 9 7/8 × 13 7/8 C4 9 × 12 3/4 A5 5 7/8 × 8 1/4 B5 7 × 9 7/8 C5 6 3/8 × 9 A6 4 1/8 × 5 7/8 B6 4 7/8 × 7 C6 4 1/2 × 6 3/8 A7 2 7/8 × 4 1/8 B7 3 1/2 × 4 7/8 C7 3 3/16 × 4 1/2 A8 2 × 2 7/8 B8 2 1/2 × 3 1/2 C8 2 1/4 × 3 3/16 A9 1 1/2 × 2 B9 1 3/4 × 2 1/2 C9 1 5/8 × 2 1/4 A10 1 × 1 1/2B10 1 1/4 × 1 3/4C10 1 1/8 × 1 5/8

The dominance of the “Letter” format instead of ISO A4 as thecommon laser-printer paper format in North America causes a lotof problems in daily international document exchange with the USA andCanada. ISO A4 is 6 mm less wide but 18 mm higher than the U.S.“Letter” format. Word processing documents with an A4 layout can oftennot be printed without loss of information on “Letter” paper orrequire you to reformat the text, which will change the pagenumbering. “Letter” format documents printed outside North Americaeither show too much white space on the top or bottom of the page orthe printer refuses to operate as “Letter” format paper has beenselected by the software but is not available. A4 size documents haveto be copied or printed with a 94% magnification factor to fit on the6% less tall “Letter” paper, and “Letter” documents have to be printedwith 97% size to fit on the 3% less wide A4 format.

Universities in the U.S. increasingly use A4 size paper in laserprinters and library copying machines, because most conferencesoutside North America require papers to be submitted in A4 format andmany journals and conference proceedings are printed in A4 format.

The three-hole 108-mm filing system widely used in the U.S. is notcompatible with the two-hole 80-mm ISO system used in most othercountries. The three-hole system could of course also be used on A4pages, but many files with a three-hole mechanism are only designedfor U.S. “Letter” sheets and are not tall enough to reliably protectA4 pages. Another disadvantage of the three-hole system is that it isnot suitable for storing formats smaller than U.S. “Letter”.

The U.S. Postal Service standard-size range for first-class orsingle piece third-class mail weighing up to 28 g includes ISO C6 andDL envelopes. The U.S. currently use quite a large number of envelopeformats.

The U.S. paper industry has managed to come up with a truly bizarre wayof specifying the density of paper. Instead of providing you withthe obvious quotient of mass per area (e.g., in grams per squaremeter, ounces per square yard, whatever), they specify the total massM of a ream of N pages of some sizeX×Y. This means, you have to know four (!)values in order to understand how to calculate the (scalar) density ofthe paper. For example “20 lb paper” can mean that a ream of 500 pagesin format 24×36 in has a total mass of 20 pounds. These reamsizes of 500 × 24 in × 36 in = 278.70912 m² aresomewhat typical in newsprint applications but not universal, as17×22 in, 25×38 in and other reference sheet sizes are usedas well! With 453.59237 g/lb and 278.70912 m²/ream, we getroughly 1 lb/ream = 1.63  g/m² for this particular reamsize. It is a big pain if you have to do these conversions yourselfand you really should complain to paper suppliers who still do notmanage to communicate the proper g/m² values (commonly called“grammage” in both English and French) for their products.

And before I forget it, readers fascinated by the idea of CentralEuropeans using A6 as a toilet paper size might also be interested tohear that the U.S. have for the same application field a standardsquare format of 4.5×4.5 in = 114×114 mm, which isfor instance documented in NewJersey Specification No. 7572-01 (May 1997), section 2.3.

Below follow some links to various other on-line locations thatwill help you to enter the ISO paper format world.

• The Guide toInternational Paper Sizes by EDS Inc. describes ISO, JIS, andnon-metric paper formats
• Brian Forté: A4 vsUS Letter and Papersizes for screenplay presentation
• MakingPostscript and Acrobat Files International by Jacob Palme explainsthe problems caused by the difference between U.S. Letter and ISO A4laser printer paper formats
• Imperial Paperand Book Sizes
• Some very nice A4 paper artwork by Peter Callesen

Although it is still rarely advertised,ISO A4 laser printer and copying paper, as well as suitable files andfolders, are available today from many U.S. office supplycompanies. A4 paper and supplies have been regularly ordered in theU.S. for many years, especially by companies and organizations with alot of international correspondence, including patent lawyers,diplomats, universities, and some government agencies.

Many of the larger stationery chains do offer at least one type ofA4 paper in their catalogues. Often the only type of A4 paperavailable is a higher-quality brand: the type of paper one mightprefer for important documents, such as international patentapplications.

The U.S.-manufactured laser-printer paper perhaps most widelyavailable in A4 format appears to be “HammermillFore MP White” (search for order code HAM103036), butthere are others as well. If the shop assistant is unfamiliar with “A4paper”, try asking for “210 mm × 297 mm”, “8 1/4 in × 11 3/4 in”,“international size”, or “European size” paper.

When I first wrote this page in 1996 while I lived in the U.S.,most shops there did not keep A4 paper on stock routinely and mighthave to order it first. Many were only able to order entire boxes of10 reams (5000 sheets) and many shop assistants were unfamiliar withthe ISO paper-size system. I am being told that the situation hasimproved quite a bit during the last decade and that A4 paper andaccessories are now a lot easier to obtain, but are still consideredspecialty items.

If you still cannot find any supply for A4 paper in your area, thentry for example the following vendors, who have confirmed to have A4paper or related articles on stock for fast delivery:

• Empire Imports Inc.,[e-mail],European Office Supplies, P.O. Box 2728, Amherst, MA 01004-2728, phone[phone], fax [phone], has a very good selection of A4filebinders, ISOhole punches, A4paper, etc. Try their A4starter kit.
• European Office Solutions Inc., 6103 Silken Laumann Way,Mississauga, Ontario L5V 1A1, Canada, phone [phone], sells A4copier paper and many accessories.
• Office Depot sells HammermillFore DP Paper, 8 1/4" x 11 3/4", 20 Lb., 96 Brightness, Ream Of 500Sheets, Item #: 261782, $6.29
• Staples has recently startedto offer A4 paper (e.g., "HammerMill Fore MP Premium Multi-FunctionPaper A4-Size", item no. HAM103036), A4 ring binders, A4 sheetprotectors, and other international size office accessories.
• OfficeMax also sells HammermillFore Multipurpose Paper, A4 (11-3/4" x 8-1/4"). Item # 20120174, Style# HPG103036.
• Xpedx operate a chain of paper storesin the U.S. (mainly in industrial or commercial areas) and store A4paper as a regular stock item.
• IKEA has been reported to sell in itsU.S. stores not only filing cabinets that are designed for both A4 andU.S. Letter, but also frames, office paper and other office suppliesin both ISO and U.S. format.
• HammermillFore MP White Office Paper, 20-lb.Sub., 210mm x 297mm, Internat’lA4
• Xerox, phone [phone],sells A4 paper (e.g., "PremiumMultipurpose 4024, a-4 size", order no. 3R2594) for laser printersand copying machines.
• Southworth Company, 265Main Street, Agawam, MA 01001, phone [phone] is a producer offine cotton andinkjet A4 paper and matching DL envelopes in various colors andtextures. These are now also distributed in the U.S. to resellers, forexample via S.P. Richards.
• Carstens [e-mail], phone[phone], sells A4 ringbinders.
• Keysan, [e-mail], PO Box 5146Pittsburgh, PA 15206, phone [phone], sell A4ringbinders.
• Metro Paper, [e-mail], phone[phone].
• Boise Cascade now alsosells A4 paper in the U.S. (catalog number P110303-6)
• GRAYTEX PAPERS, phone[phone], are another US supplier of A3, A4, and A5 papers.
• Sunrise Paper Inc., phone [phone], are an American owned wholesale export broker of A4,offset, and coated paper grades from China.
• more on-line paper vendors can easily be found via the Yahoo!Internet directory.

This is just a small arbitrary collection of paper vendors thatoffer ISO format paper. Please mail me if you know otheruseful hints and net resources about working with ISO paper sizes. Iespecially want to invite North American vendors of ISO paper formatrelated products (paper, envelopes, filing material, office furniture,etc.) to contact me so that I can collect pointers to these companieshere.

If you want to purchase cheap A4 paper and accessories in the U.S.but still have difficulties finding any locally, please do take thetime to inform the purchasing department of your usual office supplycompany about your needs. Point them to this web page if they are notfamiliar with the paper size system used by >90% of the people on thisplanet.

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References

This text summarizes and explains the content of the followinginternational standards:

• ISO 216:1975, Writing paper and certain classes of printed matter— Trimmed sizes — A and B series.
• ISO 269:1985, Correspondence envelopes — Designation and sizes.
• ISO 623:1974, Paper and board — Folders and files — Sizes.
• ISO 838:1974, Paper — Holes for general filing purposes —Specifications.
• ISO 7943-1:1987, Overhead Projectors — Projection stages —Dimensions

The following standards contain related information but are notcovered here completely:

• ISO 217:1995, Paper — Untrimmed sizes — Designation andtolerances for primary and supplementary ranges, and indication ofmachine direction.
• ISO 328:1974, Picture postcards and lettercards — Size.
• ISO 353:1975, Processed writing paper and certain classes ofprinted matter — Method of expression of dimensions.
• ISO 416:1974, Picture postcards — Area reserved for the address.
• ISO 478:1974, Paper — Untrimmed stock sizes for the ISO-A Series— ISO primary range.
• ISO 479:1975, Paper — Untrimmed sizes — Designation andtolerances.
• ISO 593:1974, Paper — Untrimmed stock sizes for the ISO-A Series— ISO supplementary range.
• ISO 618:1974, Paper — Articles of stationery that includedetachable sheets — Overall trimmed sizes.

These standards are available from

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

phone: [phone]
fax: [phone]
web: www.iso.org

The most comprehensive source of information about the ISO andNorth American paper formats and many related standards, as well astheir respective histories, is the book

• Max Helbig, Winfried Hennig: DIN-Format A4 – Ein Erfolgssystem inGefahr. Beuth-Kommentare, Deutsches Institut für Normung, Beuth Verlag, 1988, 144 pages, ISBN3-410-11878-0, ~17 EUR.

DIN also produced a brief German prospectus with information about thehistory of the DIN paper sizes:

• DieGeschichte der Papierformate

Here are a few more references for those interested in theintroduction of ISO paper sizes in North America:

• Arthur D. Dunn: Notes onthe standardization of paper sizes. Ottawa, Canada, 54 pages,1972. (out of print, available via inter-library loan from National Library of Canada, TS 1118S5 D4, AMICUS No. 73886)
• Response from Michael F. DiMario,U.S. Public Printer, on my request for information about theintroduction of ISO 216 paper formats in U.S. government agencies.
• Ad HocCommittee Report – Metric Usage in Federal Printing, a study donein 1992 by the U.S. government that shows that migration tointernational standard paper formats is feasible and, with fewexceptions, would not cause significant costs.

Some related media coverage:

• Thelogic behind metric paper sizes. Slashdot, 2004-05-14.

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If you have any questions or suggestions about how this text mightbe improved, please contact me byemail. I wish to thank for helpful suggestions Gary Brown, GeneFornario, Don Hillger, Arild Jensen, Joseph B. Reid, Bruce Naylor,Ryan Park, Terry Simpson, Karl Kleine, Jukka Korpela, David Cantrell,Oliver Baptiste, Mark Weyer, Benoit Rittaud, Frank Dabelstein, andothers. Special thanks go also to the German-American FulbrightCommission for the scholarship that allowed me to spend a year atPurdue University, Indiana, where this text was born, along with myinterest in U.S. metrication.

Hypertext links to this text are very welcome. You may freely reuseany part of this text in your own publications. If you do, I wouldappreciate a free copy.

You might also be interested in the Metrictypographic units and Internationalstandard date and time notation web pages, or in the discussionson the USENET group misc.metric-system.

Markus Kuhn