Ricoh coretech appendix4 isopapsize

International Standard Paper Sizes http://www.cl.cam.ac.uk/~mgk25/iso-paper.html

International Standard Paper Sizes

by Markus Kuhn

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

The ISO paper size concept

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

The ISO paper sizes are based on the metric system. The square root of two ratio rule
does not allow the height and width of the pages to be nicely rounded metric lengths.
Therefore, the area of the pages has been defined to have nice metric values. As paper is
usually specified in g/m², this allows easy calculation of the mass of a document if the
format and number of pages are known.

ISO 216 defines the A series of paper sizes as follows:

The height divided by the width of all formats is the square root of two (1.4142).
Format A0 has an area of one square meter.
Format A1 is A0 cut into two equal pieces, i.e. A1 is as high as A0 is wide and A1 is
half as wide as A0 is high.
All smaller A series formats are defined in the same way by cutting the next larger
format in the series parallel to its shorter side into two equal pieces.
The standardized height and width of the paper formats is a rounded number of
millimeters.

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

The width and height of a B series format is the geometric mean between the
corresponding A format and the next larger A format. For instance, B1 is the
geometric mean between A1 and A0, that means the magnification factor that scales
A1 to B1 also scales B1 to A0.
Similarly, the formats of the C series are the geometric mean between the A and B

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series formats with the same number. For example, an A4 letter fits nicely into a C4
envelope. If you fold this letter once to A5 format, then it will fit nicely into a C5
envelope.

[The Japanese JIS P 0138-61 standard defines the same A series as ISO 216, but a
slightly different B series of paper 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 mean of the area
of the A series pages with the same and the next higher number, and not as in the ISO B
series the geometric mean. For example JB3 is 364 × 515, JB4 is 257 × 364, and JB5 is
182 × 257 mm.]

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

A 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 × 40

The allowed tolerances are ±1.5 mm for dimensions up to 150 mm, ±2 mm for dimensions
above 150 mm up to 600 mm, and ±3 mm for dimensions above 600 mm. Some national
adaptions of ISO 216 specify smaller tolerances.

Application examples

The ISO standard paper size system covers a wide range of formats, but not all of them are
widely used in practice. Among all formats, A4 is clearly the most important one for daily
office use. Some main applications of the most popular formats can be summarized as:

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A0,A1 technical drawings, posters
A2,A3 drawings, diagrams, large tables

A4

letters, magazines, forms, catalogs, laser printer and copying machine

output
A5 note pads
A6 postcards
B5,A5,B6,A6 books
C4,C5,C6 envelopes for A4 letters: unfolded (C4), folded once (C5), folded twice (C6)
B4,A3 newspapers, supported by most copying machines in addition to A4

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

Example 1:

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

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

71% sqrt(0.5) A3 -> A4

84% sqrt(sqrt(0.5)) B4 -> A4
119% sqrt(sqrt(2)) A4 -> B4 (also B5 -> A4)
141% sqrt(2) A4 -> A3 (also A5 -> A4)

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

Example 2:

If you prepare a letter, you will have to know the weight of the content in order to determine
the postal fee. This can be very conveniently calculated with the ISO A series paper sizes.
Usual typewriter and laser printer paper weighs 80 g/m². An A0 page has an area of 1 m²,
and the next smaller A series page has half of this area. Therefore the A4 format has an
area of 1/16 m² and weighs with the common paper quality 5 g per page. If we estimate 20
g for a C4 envelope (including some safety margin), then you will be able to put 16 A4
pages into a letter before you reach the 100 g limit for the next higher postal fee.

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Calculation of the mass of books, newspapers, or packed paper is equally 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 in many applications. For
example, if all scientific journals use only ISO formats, then libraries will have to buy only
very few different sizes for the binders. Shelves can be designed such that standard
formats will fit in exactly without too much wasted shelf volume. The ISO formats are used
for surprisingly many things besides office paper: the German citizen ID card has format
A7, the European Union passport has format B7, library microfiches have format A6, and in
some countries even toilet paper has format A6.

Further details

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

Format Width [m] Height [m]

An
Bn
Cn

-1/4-n/2

2

-n/2

2

-1/8-n/2

2

2

2

2

1/4-n/2

1/2-n/2

3/8-n/2

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

1/3 A4 99 × 210
1/4 A4 74 × 210
1/8 A4 37 × 210
1/4 A3 105 × 297
1/3 A5 70 × 148

All formats described so far are trimmed paper end sizes, i.e. these are the dimensions of
the paper delivered to the user or reader. Other ISO standards define the format serieses
RA and SRA for untrimmed raw paper. These formats are only slightly larger than the
corresponding A series formats. Sheets in these formats will be cut to the end format after
binding. The ISO RA0 format has an area of 1.05 m² and the ISO SRA0 format has an area
of 1.15 m². These formats also follow the sqrt(2) ratio and half area rule, but the
dimensions of the start format have been rounded to the full centimeter. The common
untrimmed paper formats that printers order from the paper manufacturers are

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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

ISO 838 specifies that for filing purposes, two holes of 6±0.5 mm diameter can be punched
into the sheets. The centers of the two holes are 80±0.5 mm apart and have a distance of
12±1 mm to the nearest edge of the sheet. The holes are located symmetrically in relation
to the axis of the sheet or document.

ISO 623 specifies the sizes of folders and files intended to receive either A4 sheets or
simple folders (without back) that are not designed for any particular filing system or
cabinet. The sizes specified are those of the overall rectangular surface when the folders or
files are folded, exclusive any margin or tabs. Simple folders without back or mechanism
are 220 × 315 mm large. Folders and files with a very small back (less than 25 mm) with or
without mechanism are 240 × 320 mm large. Files with wide back (exceeding 25 mm) are
250 × 320 mm (without a mechanism) or 290 × 320 mm if they include a mechanism. All
these are maximum dimensions. Standardizing folder and file sizes allows to optimize shelf
design and provides a uniform shelf look and handling even if folders from various
manufacturers are used.

When you prepare overhead projector slides for a conference, you might wonder, how
large the picture area of the projector that you will have available will be. ISO 7943-1
specifies two standard sizes of overhead projector picture areas: Type A is 250 × 250 mm
(corners rounded 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 diagonally no more than 40 mm).

The ISO DL envelope format has the dimensions 110 × 220 mm and an A4 business letter
folded twice to 1/3 A4 format fits nicely into it. The 1/3 A4 format (99 × 210 mm) is also
commonly applied for reduced letterheads for short notes that contain not much more than
a one sentence message.

ISO 7810 specifies identification cards and defines the following three standard formats:
ID-1 = 85.60 × 53.98 mm (= 3.370 × 2.125 in), ID-2 = 105 × 74 mm (= A7), and ID-3 = 125
× 88 mm (= B7). ID-1 is the common format for banking cards (0.76 mm thick) and is also
widely used for business cards and drivers licences. The standard passport format is B7 (=
ID-3).

The ISO standard paper sizes were first proposed by the German standards organization

DIN around 1920 as a replacement for the vast variety of other paper formats that had

been used before, in order to make paper stocking and document reproduction cheaper
and more efficient. This paper format system became an international standard (ISO 216)
in 1975 and is today used in almost all countries.

Hints for North American paper users

The United States and Canada are today the only industrialized nations, where the ISO

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standard paper sizes are not yet widely used. In office applications, the different but very
similar paper formats "Letter" (216 × 279 mm), "Legal" (216 × 356 mm), "Executive" (190 ×
254 mm), and "Ledger/Tabloid" (279 × 432 mm) are widely used today in these two
countries. There exists also an American National Standard ANSI/ASME Y14.1 for
technical drawing paper sizes A (216 × 279 mm), B (279 × 432 mm), C (432 × 559 mm), D
(559 × 864 mm), E (864 × 1118 mm), and there 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. The new
American National Standard ANSI/ASME Y14.1m-1995 specifies now the ISO A0-A4
formats for technical drawings.

Both the "Letter" and "Legal" letter format could easily be replaced by A4, "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 be expected that with the continuing introduction of the metric

system in the United States, the ISO paper formats will eventually replace non-standard

paper formats also in North America.
The dominance of the "Letter" format instead of ISO A4 as the common laser printer paper

format in North America causes a lot of problems in daily international document exchange
with the USA and Canada. 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 often not be printed
without loss of information on "Letter" paper or require you to reformat the text, which will
change the page numbering. "Letter" format documents printed outside North America
either show too 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
documents have to be copied or printed with a 94% magnification factor to fit on the 6%
less tall "Letter" paper, and "Letter" documents have to be printed with 97% size to fit on
the 3% less wide A4 format.

Conversion to A4 as the common business letter and document format in North America
would not cause any significant cost. Practically all software, copying machines, and laser
printers are also sold outside North America and have therefore been designed for
handling A4 paper and sometimes even other ISO formats for many years. The only
necessary investment is usually a new A4 paper tray, which costs for example 45 US$ for a

HP LaserJet III printer and can be ordered easily from your local vendor. Recent laser

printers can even handle A4 paper without replacing paper trays, because the U.S.
government is now considering to switch to A4 paper and office supply manufacturers do
not want to miss this market.

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

The three-hole filing system widely used in the U.S. is not compatible with the two-hole ISO
system used in most other countries. The three-hole system could of course also be used
on A4 pages, but many files with a three-hole mechanism are only designed for U.S.
"Letter" sheets and are not tall enough to reliably protect A4 pages.

The U.S. Postal Service standard-size range for first-class or single piece third-class mail
weighing up to 28 g includes ISO C6 and DL envelopes. Unfortunately, the height limit for
standard size mail is currently 7 mm too small for C5 envelopes, therefore C5 and C4
envelopes count as nonstandard-size mail and require a surcharge.

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

Guide to A4 Paper Setup for Windows or WordPerfect by NIST

The Guide to International Paper Sizes by EDS Inc. describes ISO, JIS, and
non-metric paper formats

Making Postscript and Acrobat Files International by Jacob Palme explains the

problems caused by the difference between U.S. Letter and ISO A4 laser printer
paper formats

Although it is rarely advertised, ISO A4 laser printer and xerox paper as well as suitable
files and folders are already available today from many U.S. office supply companies. ISO
A4 paper is regularly ordered in the U.S., especially by companies with a lot of international
correspondence, by universities, and by government agencies that have already switched
to the metric system. If you cannot find any supply for ISO A4 paper in your area, then try
for example the following vendors, that have confirmed to have A4 paper 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 good selection of A4 filebinders, ISO hole punches, A4 paper, etc.

Hammermill Papers, produces A4 paper (Fore DP, Laser Print)
Xerox, phone [phone], sells A4 paper for laser printers and copying

machines.

Carstens [e-mail], phone [phone], sells A4 ringbinders.
ComStar Company.
Metro Paper, [e-mail], phone [phone].

more on-line paper vendors can easily be found via the Yahoo! Internet directory.

This is just a small arbitrary collection of paper vendors that offer ISO format paper. Please

mail me if you know other useful hints and net resources about working with ISO paper

sizes. I especially want to invite North American vendors of ISO paper format related
products (paper, filing material, replacement paper trays, etc.) to contact me so that I can
collect pointers to these companies here.

References

This text summarizes and explains the content of the following international 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

[Note: There is a new 1996 revision draft of ISO 216 which I have not yet seen. Contact me
if you have more information.]

The following standards contain related information but are not covered here completely:

ISO 217:1995, Paper -- Untrimmed sizes -- Designation and tolerances for primary

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and supplementary ranges, and indication of machine 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, Paper -- Untrimmed sizes -- Designation and tolerances.
ISO 593:1974, Paper -- Untrimmed stock sizes for the ISO-A Series -- ISO
supplementary range.
ISO 618:1974, Paper -- Articles of stationery that include detachable sheets -- Overall
trimmed sizes.

These standards are available from

International Organization for Standardization

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

phone: [phone]
fax: [phone]
email: [e-mail]

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

Response from Michael F. DiMario, U.S. Public Printer, on my request for information

about the introduction of ISO 216 paper formats in U.S. government agencies.

Ad Hoc Committee Report - Metric Usage in Federal Printing, a study done by the

U.S. government that shows that migration to international standard paper formats is
feasible and, with few exceptions, would not cause significant costs.

If you have any suggestions about how this text might be improved, please contact me by

email. I wish to thank for helpful suggestions Gary Brown, Gene Fornario, Don Hilger, Arild
Jensen, Joseph B. Reid, Bruce Naylor, Ryan Park, and others.

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

You might also be interested in the Metric Typographic Units and International Standard

Date and Time Notation Web pages.

Markus Kuhn <[e-mail]>

created 1996-10-29 -- last modified 1999-05-07 -- http://www.cl.cam.ac.uk/~mgk25/iso-paper.html

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