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International standard newspaper sizes

by Markus Kuhn

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

The ISO paper size concept

In the ISO paper size organization, the tiptop-to-width ratio of all pages is the square root of two (1.4142 : 1). In other words, the width and the top of a page relate to each other similar the side and the diagonal of a square. This aspect ratio is peculiarly user-friendly for a paper size. If yous put ii such pages next to each other, or equivalently cut one parallel to its shorter side into ii equal pieces, then the resulting page will have once more the aforementioned width/height ratio.

A diagram demonstrating the sqrt(2) width/height ratio

The ISO newspaper sizes are based on the metric organisation. The square-root-of-two ratio does not permit both the height and width of the pages to exist nicely rounded metric lengths. Therefore, the area of the pages has been defined to accept round metric values. Equally paper is usually specified in g/m², this simplifies 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 based on these simple principles:

The peak divided by the width of all formats is the square root of ii (i.4142).
Format A0 has an area of 1 square meter.
Format A1 is A0 cutting into two equal pieces. In other words, the acme of A1 is the width of A0 and the width of A1 is one-half the height of A0.
All smaller A series formats are divers in the same way. If you cut format An parallel to its shorter side into two equal pieces of paper, these will have format A(north+1).
The standardized height and width of the newspaper formats is a rounded number of millimeters.

For applications where the ISO A series does non provide an adequate format, the B series has been introduced to comprehend a wider range of paper sizes. The C series of formats has been defined for envelopes.

The width and height of a Bdue north format are the geometric mean between those of the Anorthward and the adjacent larger A(n−ane) format. For instance, B1 is the geometric mean between A1 and A0, that ways the same magnification factor that scales A1 to B1 too scales B1 to A0.
Similarly, the formats of the C serial are the geometric mean between the A and B series formats with the aforementioned number. For case, an (unfolded) A4 size letter fits nicely into a C4 envelope, which in turn fits as nicely into a B4 envelope. If you fold this alphabetic character once to A5 format, and then it will fit nicely into a C5 envelope.
B and C formats naturally are too square-root-of-two formats.

Note: The geometric hateful of two numbers x and y is the square root of their product, (xy)^1/2, whereas their arithmetic hateful is half their sum, (x+y)/2. For example, the geometric mean of the numbers ii and 8 is iv (considering 4/two = 8/4), whereas their arithmetic mean is five (considering 5−2 = 8−five). The arithmetic mean is one-half-manner between two numbers by addition, whereas the geometric mean is half-way between two numbers by multiplication.

By the way: The Japanese JIS P 0138-61 standard defines the same A serial as ISO 216, simply a slightly dissimilar B series of newspaper sizes, sometimes called the JIS B or JB series. JIS B0 has an area of 1.5 m², such that the area of JIS B pages is the arithmetic hateful of the area of the A serial pages with the aforementioned and the next college number, and not as in the ISO B series the geometric hateful. For instance, JB3 is 364 × 515, JB4 is 257 × 364, and JB5 is 182 × 257 mm. Using the JIS B series should be avoided. It introduces boosted magnification factors and is not an international standard.

The post-obit table shows the width and height of all ISO A and B paper formats, too as the ISO C envelope formats. The dimensions are in millimeters:

A Series Formats		B Series Formats		C Series Formats
4A0	1682 × 2378	–	–	–	–
2A0	1189 × 1682	–	–	–	–
A0	841 × 1189	B0	1000 × 1414	C0	917 × 1297
A1	594 × 841	B1	707 × 1000	C1	648 × 917
A2	420 × 594	B2	500 × 707	C2	458 × 648
A3	297 × 420	B3	353 × 500	C3	324 × 458
A4	210 × 297	B4	250 × 353	C4	229 × 324
A5	148 × 210	B5	176 × 250	C5	162 × 229
A6	105 × 148	B6	125 × 176	C6	114 × 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 × 57
A10	26 × 37	B10	31 × 44	C10	28 × xl

The allowed tolerances are ±i.5 mm for dimensions upward to 150 mm, ±two mm for dimensions in a higher place 150 mm up to 600 mm, and ±iii mm for dimensions above 600 mm. Some national equivalents of ISO 216 specify tighter tolerances, for example DIN 476 requires ±1 mm, ±1.v mm, and ±2 mm respectively for the same ranges of dimensions.

Awarding examples

The ISO standard paper size arrangement covers a wide range of formats, but non all of them are widely used in practice. Amidst all formats, A4 is conspicuously the near important one for daily part use. Some chief 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	messages, magazines, forms, catalogs, laser printer and copying machine output
A5	notation pads
A6	postcards
B5, A5, B6, A6	books
C4, C5, C6	envelopes for A4 messages: 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 chief advantage of the ISO standard newspaper sizes becomes obvious for users of copying machines:

Example one:

You are in a library and want to copy an article out of a periodical that has A4 format. In order to save paper, yous want re-create two journal pages onto each canvas of A4 paper. If yous open the journal, the two A4 pages that you will now see together have A3 format. By setting the magnification cistron on the copying machine to 71% (that is sqrt(0.5)), or by pressing the A3→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 motorcar. 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 advisable magnification factor are necessary. The aforementioned principle works for books in B5 or A5 format.

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

71%	sqrt(0.5)	A3 → A4
84%	sqrt(sqrt(0.5))	B4 → A4
119%	sqrt(sqrt(two))	A4 → B4 (as well B5 → A4)
141%	sqrt(2)	A4 → A3 (too A5 → A4)

The magnification factors between all A sizes:

_from ^to	A0	A1	A2	A3	A4	A5	A6	A7	A8	A9	A10
A0	100%	71%	50%	35%	25%	xviii%	12.v%	eight.8%	6.2%	iv.four%	3.ane%
A1	141%	100%	71%	50%	35%	25%	18%	12.five%	viii.eight%	half dozen.two%	4.four%
A2	200%	141%	100%	71%	50%	35%	25%	18%	12.5%	8.8%	six.two%
A3	283%	200%	141%	100%	71%	50%	35%	25%	xviii%	12.v%	eight.8%
A4	400%	283%	200%	141%	100%	71%	50%	35%	25%	xviii%	12.5%
A5	566%	400%	283%	200%	141%	100%	71%	50%	35%	25%	18%
A6	800%	566%	400%	283%	200%	141%	100%	71%	l%	35%	25%
A7	1131%	800%	566%	400%	283%	200%	141%	100%	71%	l%	35%
A8	1600%	1131%	800%	566%	400%	283%	200%	141%	100%	71%	50%
A9	2263%	1600%	1131%	800%	566%	400%	283%	200%	141%	100%	71%
A10	3200%	2263%	1600%	1131%	800%	566%	400%	283%	200%	141%	100%

Non but the performance of copying machines in offices and libraries, but as well repro photography, microfilming, and printing are simplified by the 1:sqrt(2) aspect ratio of ISO paper sizes.

Case 2:

If you prepare a letter, you will take to know the weight of the content in club to determine the postal fee. This can be very conveniently calculated with the ISO A series newspaper sizes. Usual typewriter and laser printer paper weighs lxxx g/m². An A0 page has an area of 1 g², and the side by side smaller A series folio has one-half of this area. Therefore, the A4 format has an surface area of 1/sixteen m² and weighs with the common newspaper quality five one thousand per page. If we guess 20 g for a C4 envelope (including some safety margin), and then you will be able to put 16 A4 pages into a letter before you attain the 100 g limit for the next college postal fee.

Calculation of the mass of books, newspapers, or packed paper is equally fiddling. You probably will not demand such calculations often, but they nicely show the dazzler of the concept of metric newspaper sizes.

Using standard paper sizes saves coin and makes life simpler in many applications. For instance, if all scientific journals used only ISO formats, then libraries would have to buy only very few dissimilar sizes for the binders. Shelves tin be designed such that standard formats will fit in exactly without too much wasted shelf book. The ISO formats are used for surprisingly many things besides office paper: the German language denizen ID bill of fare has format A7, both the European Spousal relationship and the U.S. (!) passport have format B7, and library microfiches have format A6. In some countries (e.g., Germany) fifty-fifty many brands of toilet newspaper have format A6.

Further details

Computing the dimensions

The ISO newspaper sizes are specified in the standard in a table that states their width and height in millimeters. Following the principles described higher up, the dimensions could be calculated with the post-obit formulas:

Format	Width [chiliad]	Height [m]
A`n`	ii^{−i/iv−n/ii}	2^{one/four−n/ii}
B`due north`	2^{−northward/ii}	ii^{one/two−n/2}
C`due north`	2^−1/8−n/2	2^{3/viii−north/two}

However, the actual millimeter dimensions in the standard take been calculated instead by using the above values only at n = 0, and and then progressively dividing these values by 2 to obtain the smaller sizes, each time rounding the result to the next lower integer number of millimeters (floor role). This rounding to the adjacent lower integer guarantees that two A(north+1) pages together are never larger than an An page.

The following programs demonstrate this algorithm in several programming languages:

iso-newspaper.c – C version
iso-paper.py – Python version

Aspect ratios other than sqrt(ii)

Sometimes, paper formats with a different aspect ratio are required for labels, tickets, and other purposes. These should preferably be derived past cutting standard serial sizes into 3, 4, or 8 equal parts, parallel with the shorter side, such that the ratio betwixt the longer and shorter side is greater than the square root of two. Some case long formats in millimeters are:

1/iii A4	99 × 210
1/4 A4	74 × 210
i/eight A4	37 × 210
one/4 A3	105 × 297
1/iii A5	70 × 148

The 1/3 A4 format (99 × 210 mm) is also ordinarily practical for reduced letterheads for short notes that contain not much more than a one judgement bulletin and fit without folding into a DL envelope.

Envelope formats

For postal purposes, ISO 269 and DIN 678 ascertain the post-obit envelope formats:

Format	Size [mm]	Content Format
C6	114 × 162	A4 folded twice = A6
DL	110 × 220	A4 folded twice = 1/3 A4
C6/C5	114 × 229	A4 folded twice = 1/3 A4
C5	162 × 229	A4 folded once = A5
C4	229 × 324	A4
C3	324 × 458	A3
B6	125 × 176	C6 envelope
B5	176 × 250	C5 envelope
B4	250 × 353	C4 envelope
E4	280 × 400	B4

The DL format is the most widely used business concern letter format. DL probably originally stood for "DIN lang", but ISO 269 now explains this abridgement instead more diplomatically every bit "Dimension Lengthwise". Its size falls somewhat out of the system and equipment manufacturers take complained that information technology is slightly as well small for reliable automatic enveloping. Therefore, DIN 678 introduced the C6/C5 format equally an culling for the DL envelope.

Window envelopes, A4 letterheads, folding marks and standard layouts

There exists no international standard yet for window envelopes and matching letterhead layouts. There are various incompatible national standards, for case:

Federal republic of germany: DIN 680 specifies that a transparent address window is 90 × 45 mm big and its left border 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 border of the envelope. The letterhead standard DIN 676 does not specify the actual content or class of a pre-printed letterhead, it only specifies zones for the location of certain elements. The letterhead format specified in DIN 676 has a 85 × 45 mm big address field visible through the window, in which the acme 5 mm are reserved for press in a small font the sender's address and the bottom xl mm are for writing the recipient'due south address. This field starts 20 mm from the left paper edge and either 27 mm (form A) or 45 mm (grade B) from the height. The two alternatives allow a choice of either a small-scale (form A) or large (grade B) letterhead layout in the area above the address field. Standard folding marks on the letterhead assist users to insert the letter of the alphabet correctly into C6, DL, or C6/C5 window envelopes. There is ane folding mark (for C6) on the tiptop border of the page, 148 mm from the left edge. There are besides two folding marks on the left border of the page, either 105 and 210 mm from the bottom edge (class A) or 105 and 210 mm from the meridian edge (form B).
United Kingdom: BS 4264 specifies that the transparent window on a DL envelope should exist 93 × 39 mm large. Its superlative-left corner should be located 20 mm from the left margin and 53 mm from the top margin of the envelope. BS 1808 specifies an fourscore × 30 mm large accost panel on the letterhead. Its peak-left corner is located 20 mm from the left margin and 51 mm from the top margin of the page. The address console is embedded within a 91 × 48 mm large exclusion zone whose top left corner is located 20 mm from the left margin and 42 mm from the acme margin of the folio. In other words, the area nine mm above and below and 11 mm correct of the accost panel should be kept clean of any other printing.
Switzerland: The envelope window is 100 × 45 mm large and located 12 mm either from the left or the right edge. The distance to the top edge is 48 mm (for C6 and C5/C6) or 52 mm (for C5). The SNV 010130 letterhead format places the recipient's address into a 90 × 40 mm large field 45 mm from the tiptop and eight mm from the right edge of the A4 page. [from: H.R. Bosshard, 1980, ISBN three-85584-010-5]
Finland: SFS 2488:1994 specifies that for E series envelopes the size of the window is 90 × 30 mm and for the C series 95 × 35 mm. In either case, the left margin is 18 mm and the summit margin twoscore mm. SFS 2487:2000 ("Layout of document text area") and SFS 2486:1999 ("Forms Layout") specify that the area for the recipient'due south address is 76.ii × 25.4 mm, located xx mm from the left, and 10±1 mm plus 25.4 mm from the top (the 25.4 mm are for the sender's information).

Co-ordinate to ISO 11180 and Universal Postal Spousal relationship standards, an international postal address should be not longer than 6 lines with up to 30 characters each. This requires a maximum expanse of 76.two × 38.1 mm with the ordinarily used typewriter graphic symbol width of two.54 mm (1/10") and a baseline distance of 6.35 mm (ane/4").

The Universal Postal Union Alphabetic character Post Regulations specify a standard position of the address on the envelope, which is within 140 mm from the right edge, at least 40 mm from the top edge, and is surrounded by at least 15 mm unprinted envelope to the left, right and below of the accost text.

A widely used international standard A4 document format is the Un Layout Cardinal 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 ensures that there remains a 20 mm single-layer margin for filing holes, that the folio can be unfolded and folded once more without being removed from the file, and that the label field at the bottom-left corner of technical drawings ends upwardly in correct orientation on top of the folded folio in the file.

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 arrangement or cabinet. The sizes specified are those of the overall rectangular surface when the folders or files are folded, sectional any margin or tabs. Simple folders without dorsum or machinery are 220 × 315 mm large. Folders and files with a very small-scale back (less than 25 mm) with or without mechanism are 240 × 320 mm large. Files with broad dorsum (exceeding 25 mm) are 250 × 320 mm (without a mechanism) or 290 × 320 mm if they include a machinery. All these are maximum dimensions. Standardizing folder and file sizes helps to optimize shelf designs and provides a uniform wait and handling even if folders from diverse manufacturers are used.

Filing holes

ISO 838 specifies that, for filing purposes, two holes of 6±0.5 mm diameter tin be punched into the sheets. The centers of the two holes are lxxx±0.5 mm autonomously and take a altitude of 12±1 mm to the nearest edge of the canvas. The holes are located symmetrically in relation to the axis of the sail or document. Whatever format that is at to the lowest degree as large as A7 tin can be filed using this system.

Non specified in ISO 838, only too widely used, is an upwards compatible iv-hole organization. Its 2 middle holes stand for to ISO 838, plus there are ii additional holes located fourscore mm to a higher place and beneath these to provide for more stability. This way, sheets with four punched holes can also be filed in ISO 838 two-pigsty binders. This organization is also known under the nickname "888", presumably because the 3 gaps between the holes are all 8 cm wide. Some hole punches have on their paper guide not but markings for "A4", "A5", and "A6", but also for "888". The latter helps to punch either the top or bottom 2 holes of the 888 iv-hole arrangement into an A4 sheet.

Technical drawing pen sizes

Technical drawing pens follow the aforementioned size-ratio principle. The standard sizes differ by a factor sqrt(2): two.00 mm, 1.40 mm, 1.00 mm, 0.seventy mm, 0.fifty mm, 0.35 mm, 0.25 mm, 0.18 mm, 0.13 mm. So later drawing with a 0.35 mm pen on A3 newspaper and reducing it to A4, you can continue with the 0.25 mm pen. (ISO 9175-ane)

Ruled writing newspaper

There seems to be no international standard however for ruled writing newspaper. The German standards system has published DIN 16552:1977-04 ("Lines for handwriting"). That system is widely used, at least in Deutschland, by primary school teachers to specify which school exercise books pupils should apply at which phase of learning how to write. Writing paper with fine gray five mm grid lines seems to be very popular in many countries.

Untrimmed paper formats

All A and B series formats described so far are trimmed paper end sizes, i.eastward. these are the dimensions of the newspaper delivered to the user or reader. Other ISO standards define the format series RA and SRA for untrimmed raw paper, where SRA stands for "supplementary raw format A" ("sekundäres Rohformat A"). These formats are only slightly larger than the corresponding A serial formats. Sheets in these formats will be cutting to the terminate format later binding. The ISO RA0 format has an expanse of 1.05 m² and the ISO SRA0 format has an area of 1.15 thousand². These formats also follow the sqrt(2)-ratio and half-area rule, but the dimensions of the beginning format take been rounded to the full centimeter. The common untrimmed paper formats that printers guild from the paper manufacturers are

RA Series Formats		SRA Series Formats
RA0	860 × 1220	SRA0	900 × 1280
RA1	610 × 860	SRA1	640 × 900
RA2	430 × 610	SRA2	450 × 640
RA3	305 × 430	SRA3	320 × 450
RA4	215 × 305	SRA4	225 × 320

The RA and SRA dimensions are also used every bit scroll widths in rotating printing presses.

Overhead projectors

When you lot set up overhead projector slides for a briefing, you might wonder, how big the picture show area of the projector that y'all will have available is. ISO 7943-1 specifies two standard sizes of overhead projector moving-picture show areas: Type A is 250 × 250 mm (corners rounded with a radius less than 60 mm) and Blazon B is 285 × 285 mm (corners rounded with a radius less than 40 mm or cut off diagonally no more than forty mm). Therefore, if y'all use A4 transparencies, leave at least a xxx mm top and bottom margin.

Most calculator displays have the same aspect ratio as (traditional) Television receiver sets, namely 4:3 = 640:480 = 800:600 = 1024:768 = 1280:960. If y'all prepare presentation slides, I recommend that yous arrange your layout within a 280 × 210 mm field and make sure that yous leave at least 20 mm margin on the left and correct side. This way, you programme for the aspect ratio of a Idiot box/VGA projector and ensure at the same time that you can print on A4 transparencies such that every standard overhead projector volition show all parts of your slides.

Identification cards

ISO 7810 specifies iii formats for identification cards:

ID-1 = 85.60 × 53.98 mm (= three.370 × 2.125 in)
ID-2 = 105 × 74 mm (= A7)
ID-3 = 125 × 88 mm (= B7)

ID-one is the common format for banking cards (0.76 mm thick) and is likewise widely used for business concern cards and driver's licences. Some people adopt A8 (74 × 52 mm) for business cards. The standard passport format is B7 (= ID-3), the German ID bill of fare has A7 (= ID-ii) format and the European Marriage driver's licence is an ID-one carte du jour.

History of the ISO paper formats

One of the oldest written records regarding the sqrt(two) aspect ratio for paper sizes is a letter that the physics professor Georg Christoph Lichtenberg (University of Göttingen, Deutschland, 1742-1799) wrote 1786-10-25 to Johann Beckmann. In it, Lichtenberg explains the applied and artful advantages of the sqrt(2) attribute ratio, and of his discovery that paper with that attribute ratio was unremarkably bachelor at the time. (There are also suggestions that the task to find a paper format that is like to itself afterwards being cut in half appeared every bit a question in mathematics exams as early on equally 1755.)

After introducing the meter measurement, the French government published 1798-eleven-03 the "Loi sur le timbre" (no. 2136), a police force on the taxation of paper that divers several formats that already correspond exactly to the modernistic ISO paper sizes: "Grand registre" = ISO A2, "thou papier" = ISO B3, "moyen papier" = ISO A3, "petit papier" = ISO B4, "demi feuille" = ISO B5, "effets de commerce" = ISO 1/two B5.

The French format series never became widely known and was quickly forgotten once more. The A, B, and C series paper formats, which are based on the exact aforementioned design principles, were completely independently reinvented over a hundred years after the "Loi sur le timbre" in Frg by Dr. Walter Porstmann. They were adopted equally the German standard DIN 476 in 1922 as a replacement for the vast diverseness of other paper formats that had been used before, in social club to make paper stocking and document reproduction cheaper and more than efficient. (For those interested in celebrated details of the discussions leading to the standard, there are some DIN committee reports, 1918–1923.)

Porstmann's DIN paper-format concept was disarming, and soon introduced equally a national standard in many other countries, for case, Kingdom of belgium (1924), Netherlands (1925), Norway (1926), Switzerland (1929), Sweden (1930), Soviet Union (1934), Hungary (1938), Italia (1939), Uruguay (1942), Argentina (1943), Brazil (1943), Kingdom of spain (1947), Austria (1948), Romania (1949), Japan (1951), Denmark (1953), Czechoslovakia (1953), State of israel (1954), Portugal (1954), Yugoslavia (1956), India (1957), Poland (1957), United Kingdom (1959), Venezuela (1962), New Zealand (1963), Iceland (1964), United mexican states (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 an international standard (ISO 216) besides every bit the official United nations certificate format in 1975 and it is today used in almost all countries on this planet, with the exception of N America. In 1977, a big German car manufacturer performed a report of the paper formats constitute in their incoming mail and concluded that out of 148 examined countries, 88 already used the A series formats so. [Source: Helbig/Hennig 1988]

Notation: The Lichtenberg Ratio – used by the standard newspaper format series – is occasionally confused with the Golden Ratio (which Euclid referred to as the "extreme and mean ratio"). The Lichtenberg Ratio is defined by the equation a/b = 2b/a = sqrt(ii), whereas the Gilt Ratio is defined by a/b = (a+b)/a = b/(a−b) = (one + sqrt(5))/two. While aesthetically pleasing properties have been attributed to both, the Lichtenberg Ratio has the reward of preserving the aspect ratio when cutting a folio into ii. The Aureate Ratio, on the other manus, preserves the aspect ratio when cutting a maximal square from the paper, a holding that seems not particularly useful for office applications. The Golden Ratio was for a while a more than fashionable topic in the antique and renaissance arts literature and it has a close connexion to the Fibonacci sequence in mathematics.

Hints for North American newspaper users

The United States, Canada, and in function Mexico, are today the merely industrialized nations in which the ISO standard paper sizes are not yet widely used. In U.Due south. function applications, the paper formats "Letter of the alphabet" (216 × 279 mm), "Legal" (216 × 356 mm), "Executive" (190 × 254 mm), and "Ledger/Tabloid" (279 × 432 mm) are widely used today. There exists also an American National Standard ANSI/ASME Y14.ane for technical drawing newspaper sizes A (216 × 279 mm), B (279 × 432 mm), C (432 × 559 mm), D (559 × 864 mm), East (864 × 1118 mm), and in that location are many other unsystematic formats for various applications in use. The "Letter", "Legal", "Tabloid", and other formats (although not these names) are defined in the American National Standard ANSI X3.151-1987.

While all ISO newspaper formats accept consistently the same aspect ratio of sqrt(ii) = ane.414, the U.South. format serial has ii different alternating attribute ratios 17/11 = 1.545 and 22/17 = ane.294. Therefore, you cannot reduce or magnify from 1 U.Due south. format to the next higher or lower without leaving an empty margin, which is rather inconvenient.

American National Standard ANSI/ASME Y14.1m-1995 specifies how to use the ISO A0−A4 formats for technical drawings in the U.S. Technical drawings normally take a fixed drawing calibration (e.grand., one:100 means that 1 meter is drawn as 1 centimeter), therefore it is non easily possible to resize technical drawings betwixt U.S. and standard paper formats. As a result, internationally operating U.S. corporations increasingly find it more user-friendly to abandon the sometime ANSI Y14.1 formats and prepare technical drawings for ISO paper sizes, like the rest of the world does.

The celebrated origins of the 216 × 279 mm U.South. Letter format, and in particular its rationale, seem rather obscure. The earliest documented attempts to standardize U.Southward. paper format used a completely dissimilar format. On 1921-03-28, the U.S. Secretary of Commerce (Hoover) declared a 203 × 267 mm format to be the standard for his department, which was adopted on 1921-09-14 by the Permanent Conference on Printing (established by General Dawes, starting time director of the Agency of the Budget) every bit the general U.Due south. government letterhead standard. Independent of that, on 1921-08-30 a Committee on the Simplification of Paper Sizes consisting of printing industry representatives was appointed to work with the Bureau of Standards. It recommended standard basic sizes of 432 × 559 mm (17 × 22 in), 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 became later known as the U.S. Letter format is just the starting time of these basic sizes halved. 1 hypothesis for the origin of this format series is that information technology was derived from a then typical mold size used then in the production of paw-made paper. "It does not appear, even in the pick of 8 one/2 × 11 inch size newspaper, that whatever special analysis was made to prove that this provided an optimum size for a commercial letterhead" [Dunn, 1972.]. It appears that this standard was just a commercial compromise at the time to reduce inventory requirements without requiring significant changes to existing production equipment. The Hoover standard remained in forcefulness until the authorities declared in 1980-01 the 216 × 279 mm format to be the new official newspaper format for U.S. government offices.

The Canadian standard Tin can 2-ix.60M "Paper Sizes for Correspondence" defines the six formats P1 (560 × 860 mm), P2 (430 × 560 mm), P3 (280 × 430 mm), P4 (215 × 280 mm), P5 (140 × 215 mm), and P6 (107 × 140 mm). These are simply the U.South. sizes rounded to the nearest half centimeter (P4 ~ U.Southward. Alphabetic character, P3 ~ U.Southward. Ledger). This Canadian standard was introduced in 1976, even though the Ontario Government already had introduced the ISO A series formats before in 1972. Fifty-fifty though these Canadian newspaper sizes look somewhat like a pseudo-metric standard, they still suffer from the 2 major inconveniences of the U.S. formats, namely they have no mutual height/width ratio and they differ significantly from what the rest of the world uses.

Note: It was proposed for an early draft of ISO 216 to recommended the special size 210 × 280 mm (a format sometimes called PA4) every bit an interim measure for countries that employ 215 × 280 mm newspaper and have non yet adopted the ISO A serial. Some magazines and other impress products that have to be printed economically on both A4 and U.South. Letter of the alphabet presses use the PA4 format today. Incidentally, this PA4 format has a width/peak ratio of 3:4, the same as traditional Boob tube screens and most estimator monitors and video modes.

Both the "Letter" and "Legal" format could hands be replaced past A4, "Executive" (if it is actually needed) by B5, and "Ledger/Tabloid" past A3. Similarly, the A–East formats can exist replaced by A4–A0. It can be hoped and expected that with the continuing introduction of the metric system in the United States, the ISO newspaper formats will eventually supersede not-standard paper formats as well in N America. Conversion to A4 as the common business letter of the alphabet and document format in North America would non be too difficult, as practically all modern software, copying machines, and laser printers sold today in the U.Due south. already support A4 paper as a standard feature.

Users of photocopiers outside the U.S. and Canada ordinarily accept information technology for granted that the automobile is able to overstate A4 → A3 or reduce A3 → A4, the 2 paper formats usually kept in machines with ii paper trays. When they use a copier in North America, information technology oftentimes comes as a disappointing surprise when they detect out that magnifying an entire page is non a part available there. The absence of this useful capability is a direct result of the unfortunate design of the U.Southward. paper formats. North American copiers usually as well have 2 or more paper trays, simply these are mostly used for the ii very like "Letter" and "Legal" formats, wasting the opportunity of offer a highly useful magnifying capability. Whatever enlarging of a "Alphabetic character" page onto "Legal" newspaper will always chop off margins and is therefore of little use. The Legal format itself is quite rarely used, the notion that information technology is for "legal" piece of work is a pop myth; the vast majority of U.S. legal documents are actually using the "Letter" format. Some copiers as well offer in addition or instead the next larger "Ledger" format, merely that again has a different aspect ratio and will therefore alter the margins of a certificate during magnification or reduction.

Based on the experience from the introduction of ISO newspaper formats in other industrialized countries at various points during the 20th century, it becomes articulate that this process needs to be initiated past a political determination to motion all government operation to the new paper format organisation. History shows that the commercial world then gradually and smoothly adopts the new government standard for office newspaper within about 10–15 years. It would not be a major operation to do this in the U.S. and Canada also, especially considering that most standard software and role machines are already prepared for A4. However, such a project can succeed merely if the national executive has the political will to accomplish this. The transition menses of about a decade is necessary to avoid expensive equipment replacement costs for printers, especially those with older big rotary presses that were non nonetheless designed to be easily retooled for ISO paper sizes.

If you purchase new office or printing equipment in N America, information technology might be wise to pay attention whether the equipment is suitable for use with A4 newspaper. When yous brand inquiries, best bespeak to vendors that ISO 216 compatibility of equipment is of concern to you.

If y'all live in the U.Southward. and have never been away, you might not exist aware that newspaper and accessories in the Northward-American sizes are not commonly available outside North America. They are very difficult to obtain in most other countries and the only applied way to get U.South. "Letter" at that place is to cut ane of the next larger available sizes (unremarkably B4, A3 or RA4). Therefore, practise not expect anyone to send you documents in "Letter" format from abroad. If you send documents to whatever other country, your apply of A4 will greatly ease the handling and filing of your documents for the recipient. If yous blueprint software that might be used globally, delight keep in mind that the vast majority of laser printer users volition print onto A4 paper. Therefore, ever make A4 the default setting and the start selection choice in your printing user interface. Remember that information technology is the paper format used by almost 95% of the people on this planet.

Due to popular demand, I take prepared an unofficial table with the ISO sizes in inch fractions. Each listed inch fraction has the smallest denominator that keeps the value inside the ISO 216 tolerance limits. Product designers should apply the official millimeter values instead. In that location is also a table in PostScript points.

A Serial Formats		B Series Formats		C Serial Formats
4A0	66 1/4 × 93 five/8	–	–	–	–
2A0	46 3/4 × 66 1/4	–	–	–	–
A0	33 × 46 3/4	B0	39 iii/eight × 55 iii/4	C0	36 × 51
A1	23 3/viii × 33	B1	27 3/4 × 39 3/8	C1	25 one/2 × 36
A2	16 one/2 × 23 3/8	B2	xix 3/iv × 27 3/4	C2	eighteen × 25 1/2
A3	11 iii/4 × 16 1/2	B3	13 vii/eight × xix iii/4	C3	12 three/four × 18
A4	8 1/four × 11 3/four	B4	nine 7/8 × 13 7/8	C4	ix × 12 3/four
A5	5 vii/viii × eight i/4	B5	seven × ix 7/viii	C5	6 3/8 × 9
A6	4 1/8 × 5 vii/eight	B6	4 7/eight × seven	C6	4 ane/ii × 6 three/8
A7	ii vii/eight × iv 1/8	B7	3 one/two × four 7/8	C7	3 3/16 × four one/2
A8	two × two vii/8	B8	ii 1/2 × 3 i/2	C8	ii 1/4 × 3 3/16
A9	ane ane/2 × 2	B9	1 three/4 × 2 i/2	C9	one 5/8 × two 1/4
A10	1 × i i/2	B10	1 1/4 × 1 iii/4	C10	1 1/viii × one 5/viii

The dominance of the "Letter" format instead of ISO A4 every bit the common light amplification by stimulated emission of radiation-printer paper format in North America causes a lot of problems in daily international document exchange with the U.s.a. and Canada. ISO A4 is half-dozen mm less wide merely eighteen mm higher than the U.South. "Letter" format. Word processing documents with an A4 layout can often not exist printed without loss of information on "Letter" newspaper or require you to reformat the text, which will change the folio numbering. "Letter of the alphabet" format documents printed outside N America either prove as well much white space on the top or bottom of the page or the printer refuses to operate as "Letter" format paper has been selected by the software but is not available. A4 size documents have to be copied or printed with a 94% magnification gene to fit on the 6% less tall "Letter" newspaper, and "Letter" documents have to exist printed with 97% size to fit on the 3% less wide A4 format.

Universities in the U.S. increasingly use A4 size paper in laser printers and library copying machines, because almost conferences outside N America require papers to be submitted in A4 format and many journals and briefing proceedings are printed in A4 format.

The three-hole 108-mm filing system widely used in the U.Southward. is non compatible with the two-hole 80-mm ISO organization used in almost other countries. The three-pigsty system could of course too be used on A4 pages, but many files with a 3-hole machinery are only designed for U.S. "Letter" sheets and are non tall enough to reliably protect A4 pages. Some other disadvantage of the iii-pigsty system is that it is not suitable for storing formats smaller than U.S. "Letter".

The U.S. Mail service standard-size range for first-class or unmarried piece third-form mail weighing up to 28 g includes ISO C6 and DL envelopes. The U.S. currently employ quite a big number of envelope formats.

The U.S. paper industry has managed to come upwardly with a truly bizarre way of specifying the density of paper. Instead of providing you with the obvious caliber of mass per expanse (east.one thousand., in grams per square meter, ounces per square yard, whatever), they specify the total mass M of a ream of N pages of some size X×Y. This ways, you lot accept to know four (!) values in society to empathise how to calculate the (scalar) paper density M/(N×X×Y). The problem is that N×Ten×Y depend on the type of paper, but are rarely stated explicitly.

Example: "20 lb newspaper" can mean that a reference ream of 500 pages in format 24×36 in has a total mass of twenty pounds. The item reference ream size of 24 in × 36 in × 500 pages = 278.70912 m²/ream is often used in news-print applications. With 453.59237 chiliad/lb and 278.70912 m²/ream, we get a conversion factor of about i lb/ream = 1.63 g/m². But that gene applies only for the news-impress reference ream size 24×36 in, which is past no ways universal!

Example: If you look instead at U.S. "Letter" office paper, "20 lb paper" means something very unlike. Hither, the reference ream size is usually 17 in × 22 in × 500 pages = 120.6449 m²/ream, which corresponds to four bodily reams. And and then the conversion factor becomes i lb/ream = 3.7597 thousand/m², meaning that for example 20 lb/ream = 75.19 one thousand/thousand² and 24 lb/ream = 90.23 g/grand².

Information technology is a large pain if you have to practice these conversions yourself and you actually should complain to paper suppliers who notwithstanding do not manage to communicate simple chiliad/m² values (commonly called "grammage" in both English and French) for their products.

Earlier I forget it: readers fascinated past the idea of some Europeans using A6 equally a toilet paper size might likewise exist interested to hear that the U.S. take for the same application field a standard square format of 4.five×iv.5 in = 114×114 mm, which is for instance documented in New Jersey Specification No. 7572-01 (May 1997), section 2.3.

Below follow some links to various other on-line locations that volition assistance y'all to enter the ISO paper format world.

The Guide to International Newspaper Sizes past EDS Inc. describes ISO, JIS, and non-metric paper formats
Brian Forté: A4 vs United states Alphabetic character and Paper sizes for screenplay presentation
Making Postscript and Acrobat Files International by Jacob Palme explains the problems caused by the departure between U.Southward. Letter and ISO A4 laser printer paper formats
Imperial Newspaper and Book Sizes
Some very overnice A4 newspaper artwork past Peter Callesen

Although it is nonetheless rarely advertised, ISO A4 laser printer and copying paper, also as suitable files and folders, are bachelor today from many U.South. office supply companies. A4 newspaper and supplies take been regularly ordered in the U.S. for many years, especially past companies and organizations with a lot of international correspondence, including patent lawyers, diplomats, universities, and some regime agencies.

Many of the larger stationery chains do offering at least one type of A4 paper in their catalogues. Often the only type of A4 paper available is a college-quality make: the type of paper one might prefer for important documents, such as international patent applications.

The U.S.-manufactured light amplification by stimulated emission of radiation-printer paper perhaps most widely bachelor in A4 format appears to be "Hammermill Fore MP White" (search for gild code HAM103036), but there are others as well. If the shop assistant is unfamiliar with "A4 paper", try asking for "210 mm × 297 mm", "eight 1/4 in × 11 three/4 in", "international size", or "European size" newspaper.

When I first wrote this page in 1996 while I lived in the U.Due south., well-nigh shops there did non proceed A4 paper on stock routinely and might take to order it first. Many were only able to guild entire boxes of 10 reams (5000 sheets) and many shop assistants were unfamiliar with the ISO newspaper-size system. I am being told that the situation has improved quite a bit during the final decade and that A4 paper and accessories are at present a lot easier to obtain, but are still considered specialty items.

If yous all the same cannot find any supply for A4 paper in your surface area, then attempt for case the post-obit vendors in North America, who have confirmed to have A4 paper or related articles on stock for fast delivery:

Empire Imports Inc., European Office Supplies, P.O. Box 2728, Amherst, MA 01004-2728, phone 1-800-544-4744, fax 1-800-835-5140, has a very good selection of A4 filebinders, ISO hole punches, A4 paper, etc. Try their A4 starter kit.
European Office Solutions Inc., 6103 Silken Laumann Manner, Mississauga, Ontario L5V 1A1, Canada, phone i-877-929-9713, sells A4 copier newspaper and many accessories.
Office Depot sells Hammermill Fore DP Paper, 8 ane/4" 10 eleven 3/4", 20 Lb., 96 Brightness, Ream Of 500 Sheets, Detail #: 261782
Staples has recently started to offer A4 paper (e.g., "HammerMill Fore MP Premium Multi-Function Paper A4-Size", item no. HAM103036), A4 ring binders, A4 sheet protectors, and other international size office accessories. (Y'all can select "Paper size 8.27" x 11.69"" on the U.S. web site to detect A4 products.)
OfficeMax sells X-ix Multiuse Re-create Paper, 92 Bright, 500 Sheets/Ream, A4, 20 lb..
Xpedx operate a chain of paper stores in the U.S. (mainly in industrial or commercial areas) and store A4 newspaper equally a regular stock item.
IKEA has been reported to sell in its U.Due south. stores not only filing cabinets that are designed for both A4 and U.S. "Letter", but also frames, part paper and other role supplies in both ISO and U.South. format.
Hammermill Fore MP White Office Paper, 20-lb.Sub., 210mm x 297mm, Internat'l A4
Xerox, sells A4 paper (e.grand., "Premium Multipurpose 4024, A4" or "Business concern 4200, A4", order no. 3R2594) for laser printers and copying machines.
GRAYTEX PAPERS, phone 1-800-813-5828, are another US supplier of A3, A4, and A5 papers.
Keepfiling in Sturtevant, Wisconsin sell A4 3-ring binders and matching A4 canvass protectors
more on-line paper vendors can easily be found via the Yahoo! Internet directory.

This is just a small, arbitrary collection of some Northward American newspaper vendors that offer ISO format paper or related supplies.

References

This text summarizes and explains the content of the following international standards:

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

The post-obit standards incorporate related information but are not covered here completely:

ISO 217:1995, Paper — Untrimmed sizes — Designation and tolerances for primary and supplementary ranges, and indication of car direction.
ISO 328:1974, Picture postcards and lettercards — Size.
ISO 353:1975, Processed writing paper and certain classes of printed 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, Newspaper — Untrimmed sizes — Designation and tolerances.
ISO 593:1974, Paper — Untrimmed stock sizes for the ISO-A Series — ISO supplementary range.
ISO 618:1974, Newspaper — Articles of jotter that include detachable sheets — Overall trimmed sizes.

These standards are available from

The most comprehensive source of information nearly the ISO and North American paper formats and many related standards, as well as their respective histories, is the volume

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

DIN also produced a cursory German language prospectus with information near the history of the DIN paper sizes:

Dice Geschichte der Papierformate

Here are a few more references for those interested in the introduction of ISO paper sizes in N America:

Arthur D. Dunn: Notes on the standardization of paper sizes. Ottawa, Canada, 54 pages, 1972. (out of print, available via inter-library loan from National Library of Canada, TS 1118 S5 D4, AMICUS No. 73886)
Response from Michael F. DiMario, U.S. Public Printer, on my request for data nigh the introduction of ISO 216 paper formats in U.South. government agencies.
Ad Hoc Committee Report – Metric Usage in Federal Printing, a report done in 1992 by the U.S. government that shows that migration to international standard paper formats is feasible and, with few exceptions, would not crusade significant costs.

Some related media coverage:

The logic behind metric paper sizes. Slashdot, 2004-05-14.

If yous accept any questions or suggestions nigh how this text might be improved, please contact me by email, but delight do not ship me whatsoever requests to add links to your own web pages. I wish to thank for helpful suggestions Gary Brown, Gene Fornario, 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, and others. Special thanks go likewise to the German-American Fulbright Commission for the scholarship that immune me to spend a year at Purdue University, Indiana, where this text was born, along with my interest in U.Due south. metrication.

You might besides be interested in the Metric typographic units and International standard appointment and time notation web pages, or in the discussions on the USENET group misc.metric-system.

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Markus Kuhn

created 1996-10-29 – last modified 2018-07-13 – https://www.cl.cam.air-conditioning.united kingdom/~mgk25/iso-newspaper.html

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