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

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

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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