Definition
"A" size or "A" series is a set of paper sizes established by the International Standards Organization (ISO) that ranges from 2A0 (the largest) to A7 (the smallest). The size of the paper goes down as the number goes up, and each is half the size of the previous e.g. two A4 sheets make up an A3 piece and two A5 sheets make up an A4 sheet.
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"A" size
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size in millimetres
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approx inches
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2A0
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1,189 x 1,682 mm
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46,8 x 66,2 in
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A0
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841 x 1,189 mm
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33,1 x 46,8 in
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A1
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594 x 841 mm
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23,4 x 33,1 in
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A2
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420 x 594 mm
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16,5 x 23,4 in
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A3
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297 x 420 mm
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11,7 x 16,5 in
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A4
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210 x 297 mm
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8,3 x 11,7 in
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A5
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148 x 210 mm
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5,8 x 8,3 in
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A6
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105 x 148 mm
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4,1 x 5,8 in
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A7
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74 x 105 mm
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2,9 x 4,1 in
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A Series Formats
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B Series Formats
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C Series Formats
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4A0
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1682 × 2378
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–
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–
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–
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–
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2A0
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1189 × 1682
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–
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–
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–
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–
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A0
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841 × 1189
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B0
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1000 × 1414
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C0
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917 × 1297
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A1
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594 × 841
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B1
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707 × 1000
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C1
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648 × 917
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A2
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420 × 594
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B2
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500 × 707
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C2
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458 × 648
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A3
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297 × 420
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B3
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353 × 500
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C3
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324 × 458
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A4
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210 × 297
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B4
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250 × 353
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C4
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229 × 324
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A5
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148 × 210
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B5
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176 × 250
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C5
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162 × 229
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A6
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105 × 148
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B6
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125 × 176
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C6
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114 × 162
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A7
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74 × 105
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B7
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88 × 125
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C7
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81 × 114
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A8
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52 × 74
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B8
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62 × 88
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C8
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57 × 81
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A9
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37 × 52
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B9
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44 × 62
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C9
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40 × 57
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A10
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26 × 37
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B10
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31 × 44
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C10
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28 × 40
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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
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technical drawings, posters
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A1, A2
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flip charts
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A2, A3
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drawings, diagrams, large tables
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A4
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letters, magazines, forms, catalogs, laser printer and copying machine output
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A5
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note pads
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A6
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postcards
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B5, A5, B6, A6
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books
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C4, C5, C6
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envelopes for A4 letters: unfolded (C4), folded once (C5), folded twice (C6)
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B4, A3
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newspapers, supported by most copying machines in addition to A4
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B8, A8
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playing cards
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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:
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71%
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sqrt(0.5)
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A3 → A4
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84%
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sqrt(sqrt(0.5))
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B4 → A4
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119%
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sqrt(sqrt(2))
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A4 → B4 (also B5 → A4)
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141%
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sqrt(2)
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A4 → A3 (also A5 → A4)
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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.
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 used only ISO formats, then libraries would 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, both the European Union and the U.S. (!) passport have format B7, and library microfiches have format A6. In some countries (e.g., Germany) even many brands of toilet paper have format A6.
Further details
Calculating the dimensions
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:
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Format
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Width [m]
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Height [m]
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An
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2-1/4-n/2
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21/4-n/2
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Bn
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2-n/2
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21/2-n/2
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Cn
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2-1/8-n/2
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23/8-n/2
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The actual millimeter dimensions in the standard have been calculated by progressively rounding down any division-by-two result, as the small program iso-paper.c demonstrates. This guarantees that two A(n-1) pages together are never larger than an An page.
Aspect ratios other than sqrt(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:
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1/3 A4
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99 × 210
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1/4 A4
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74 × 210
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1/8 A4
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37 × 210
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1/4 A3
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105 × 297
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1/3 A5
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70 × 148
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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 and fit without folding into a DL envelope.
For postal purposes, ISO 269 and DIN 678 define the following envelope formats:
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Format
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Size [mm]
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Content Format
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C6
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114 × 162
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A4 folded twice = A6
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DL
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110 × 220
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A4 folded twice = 1/3 A4
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C6/C5
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114 × 229
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A4 folded twice = 1/3 A4
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C5
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162 × 229
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A4 folded once = A5
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C4
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229 × 324
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A4
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C3
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324 × 458
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A3
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B6
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125 × 176
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C6 envelope
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B5
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176 × 250
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C5 envelope
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B4
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250 × 353
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C4 envelope
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E4
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280 × 400
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B4
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The DL format is the most widely used business letter format. DL probably originally stood for "DIN lang" historically, but ISO 269 now explains this abbreviation more diplomatically as "Dimension Lengthwise" instead. Its size falls somewhat out of the system and equipment manufacturers have complained that it is slightly too small for reliable automatic enveloping. Therefore, DIN 678 introduced the C6/C5 format as an alternative for the DL envelope.
