maths behind paper sizes

8/12/2019 MATHS Behind Paper Sizes

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International standard paper sizes

Standard paper sizes like ISO A4

are widely used all over the world

today.

We are going to see about

The ISO paper size concept

Series of Papers

Usage Of Paper Sizes


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In the ISO paper size system, the height-to-widthratio of all pages is the square root of two (1.4142 : 1).

In other words, the width and the height of a pagerelate to each other like the side and the diagonal ofa square.

This aspect ratio is especially convenient for a papersize. If you put two such pages next to each other, orequivalently cut one parallel to its shorter side intotwo equal pieces, then the resulting page will have

again the same width/height ratio.

THE ISO PAPER SIZE CONCEPT


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Types Of Series.

A Series(Sizes for A Series Paper - A0, A1, A2, A3, A4, A5,

A6, A7 and A8)

B Series(Sizes for B Series Paper - B0, B1, B2, B3, B4, B5,

B6, B7 and B8)

C Series(Sizes for C Series Envelopes - C0, C1, C2, C3, C4,

C5, C6, C7 and C8)
http://www.papersizes.org/a-paper-sizes.htmhttp://www.papersizes.org/a-paper-sizes.htmhttp://www.papersizes.org/b-paper-sizes.htmhttp://www.papersizes.org/b-paper-sizes.htmhttp://www.papersizes.org/c-envelope-sizes.htmhttp://www.papersizes.org/c-envelope-sizes.htmhttp://www.papersizes.org/c-envelope-sizes.htmhttp://www.papersizes.org/c-envelope-sizes.htmhttp://www.papersizes.org/c-envelope-sizes.htmhttp://www.papersizes.org/c-envelope-sizes.htmhttp://www.papersizes.org/c-envelope-sizes.htmhttp://www.papersizes.org/b-paper-sizes.htmhttp://www.papersizes.org/b-paper-sizes.htmhttp://www.papersizes.org/b-paper-sizes.htmhttp://www.papersizes.org/b-paper-sizes.htmhttp://www.papersizes.org/b-paper-sizes.htmhttp://www.papersizes.org/a-paper-sizes.htmhttp://www.papersizes.org/a-paper-sizes.htmhttp://www.papersizes.org/a-paper-sizes.htmhttp://www.papersizes.org/a-paper-sizes.htmhttp://www.papersizes.org/a-paper-sizes.htm


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A Series Paper Sizes

The height divided by thewidth of all formatsis 2or 1.4142. (We takeheight > width)

All smaller A series formatsare defined in the same way bycutting the next larger formatin the series parallel to itsshorter side into two equalpieces. A(n) = 2 A(n+1)

The standardized height andwidth of the paper formats is arounded number inmillimetres.


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The width and height of A(n)

paper are given by:

If n is even,

If n is odd,

Can you verify the table on the

left hand side?

General formulasA series paper width x height (mm)

A0 841 1189

A1 594 841

A2 420 594

A3 297 420A4 210 297

A5 148 210

A6 105 148A7 74 105

A8 52 74

A9 37 52

A10 26 37


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Extensions - B Series Paper Sizes

The B series paper standards are also basedaround the 1:2 aspect ratio, but in order toprovide sizes not covered by the A series, thelength and width of size B(n) are defined asbeing the geometric mean of size A(n) andsize A(n-1).

Note: The geometric mean of two numbers is

the square root of the product of those twonumbers. e.g. The geometric mean of 6 and 4 is(6x4) or 24.


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B Series paper

The width and height of a Bseries format is thegeometric mean betweenthe corresponding A formatand the next larger Aformat.

Let W(n) and H(n) be thewidth and height of

B(n). w(n) and h(n) be thatof A(n).

Then

B series paper width x height (mm)

B1 707 1000

B2 500 707

B3 353 500

B4 250 353

B5 176 250

B6 125 176

B7 88 125

B8 62 88

B9 44 62

B10 31 44


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The C Series Envelope Sizes

The C series sizes were introduced to definethe sizes of envelopes suitable for the A seriespaper sizes.

This is also based on the 2 aspect ratio.

The size of a C(n) envelope is defined as thegeometric mean of paper sizes A(n) and B(n).

This leads to a C(n) envelope which nicelyholds a sheet of A(n) paper unfolded.


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Size Width x Height (mm) Width x Height (in)

C0 917 x 1297 mm 36.1 x 51.5 in

C1 648 x 917 mm 25.5 x 36.1 in

C2 458 x 648 mm 18.0 x 25.5 in

C3 324 x 458 mm 12.8 x 18.0 in

C4 229 x 324 mm 9.0 x 12.8 in

C5 162 x 229 mm 6.4 x 9.0 in

C6 114 x 162 mm 4.5 x 6.4 in

C7 81 x 114 mm 3.2 x 4.5 in

C8 57 x 81 mm 2.2 x 3.2 in

C9 40 x 57 mm 1.6 x 2.2 in

C10 28 x 40 mm 1.1 x 1.6 in


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A C4 envelope will hold a sheet of A4 paper unfolded, a C5envelope will hold a sheet of A4 paper folded in half once parallel toits shortest sides and a C6 envelope will hold the same piece of

paper folded twice.This is the reason that you will sometimes see these envelopesizes being referred to as A4 envelope size, A5 envelope size and A6envelope size.

C6 EnvelopeC4 Envelope C5 Envelope


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SIZES USAGESA0, A1 Technical drawings, Posters

A1, A2 Flip charts

A2, A3 Drawings, Diagrams, Large tables

A4 Letters, Magazines, Forms, Catalogues, LaserPrinter and Copying Machine Output

A5 Note pads

A6 Postcards

B5, A5, B6, A6 Books

C4, C5, C6Envelopes for A4 letters: unfolded (C4),folded once (C5), folded twice (C6)

B4, A3Newspapers, supported by most copyingmachines in addition to A4

B8, A8 Playing cards

USAGES OF PAPER SIZES


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