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International standard paper sizes
Mau 发表于 2007-12-24 10:28:06
by Markus Kuhn
Standard paper sizes like ISO A4 are widely used all over the world today. 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, the height-to-width ratio of all pages is the square root of two (1.4142 : 1). In other words, the width and the height of a page relate to each other like the side and the diagonal of a square. This aspect ratio is especially convenient for a paper size. If you put two such pages 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 does not permit both the height and width of the pages to be nicely rounded metric lengths. Therefore, the area of the pages has been defined to have round metric values. As 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 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. In other words, the height of A1 is the width of A0 and the width of A1 is half the height of A0.
- All smaller A series formats are defined 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(n+1).
- 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 Bn format are the geometric mean between those of the An and the next larger A(n−1) format. For instance, B1 is the geometric mean between A1 and A0, that means the same 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 series formats with the same number. For example, 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 letter once to A5 format, then it will fit nicely into a C5 envelope.
- B and C formats naturally are also square-root-of-two formats.
Note: The geometric mean of two numbers x and y is the square root of their product, (xy)1/2, whereas their arithmetic mean is half their sum, (x+y)/2. For example, the geometric mean of the numbers 2 and 8 is 4 (because 4/2 = 8/4), whereas their arithmetic mean is 5 (because 5−2 = 8−5). The arithmetic mean is half-way 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 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. Using the JIS B series should be avoided. It introduces additional magnification factors and is not an international standard.
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 equivalents of ISO 216 specify tighter tolerances, for instance DIN 476 requires ±1 mm, ±1.5 mm, and ±2 mm respectively for the same ranges of dimensions.
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:
| A0, A1 | technical drawings, posters |
| A1, A2 | flip charts |
| 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 |
| B8, A8 | playing cards |
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 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) |
The magnification factors between all A sizes:
| fromto | A0 | A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 | A10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| A0 | 100% | 71% | 50% | 35% | 25% | 18% | 12.5% | 8.8% | 6.2% | 4.4% | 3.1% |
| A1 | 141% | 100% | 71% | 50% | 35% | 25% | 18% | 12.5% | 8.8% | 6.2% | 4.4% |
| A2 | 200% | 141% | 100% | 71% | 50% | 35% | 25% | 18% | 12.5% | 8.8% | 6.2% |
| A3 | 283% | 200% | 141% | 100% | 71% | 50% | 35% | 25% | 18% | 12.5% | 8.8% |
| A4 | 400% | 283% | 200% | 141% | 100% | 71% | 50% | 35% | 25% | 18% | 12.5% |
| A5 | 566% | 400% | 283% | 200% | 141% | 100% | 71% | 50% | 35% | 25% | 18% |
| A6 | 800% | 566% | 400% | 283% | 200% | 141% | 100% | 71% | 50% | 35% | 25% |
| A7 | 1131% | 800% | 566% | 400% | 283% | 200% | 141% | 100% | 71% | 50% | 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% |
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:
| Format | Width [m] | Height [m] |
|---|---|---|
| An | 2−1/4−n/2 | 21/4−n/2 |
| Bn | 2−n/2 | 21/2−n/2 |
| Cn | 2−1/8−n/2 | 23/8−n/2 |
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:
| 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 |
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.
Envelope formats
For postal purposes, ISO 269 and DIN 678 define the following 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 letter format. DL probably originally stood for “DIN lang”, but ISO 269 now explains this abbreviation instead more diplomatically as “Dimension Lengthwise”. 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.
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 example:
- Germany: DIN 680 specifies that a transparent address window is 90 × 45 mm large and its left edge 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 edge of the envelope. The letterhead standard DIN 676 does not specify the actual content or form 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 large address field visible through the window, in which the top 5 mm are reserved for printing in a small font the sender’s address and the bottom 40 mm are for writing the recipient’s address. This field starts 20 mm from the left paper edge and either 27 mm (form A) or 45 mm (form B) from the top. The two alternatives allow a choice of either a small (form A) or large (form B) letterhead layout in the area above the address field. Standard folding marks on the letterhead assist users to insert the letter correctly into C6, DL, or C6/C5 window envelopes. There is one folding mark (for C6) on the top edge of the page, 148 mm from the left edge. There are also two folding marks on the left edge of the page, either 105 and 210 mm from the bottom edge (form A) or 105 and 210 mm from the top edge (form B).
- United Kingdom: BS 4264 specifies that the transparent window on a DL envelope should be 93 × 39 mm large. Its top-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 80 × 30 mm large address panel on the letterhead. Its top-left corner is located 20 mm from the left margin and 51 mm from the top margin of the page. The address panel is embedded inside a 91 × 48 mm large exclusion zone whose top left corner is located 20 mm from the left margin and 42 mm from the top margin of the page. In other words, the area 9 mm above and below and 11 mm right of the address 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 top and 8 mm from the right edge of the A4 page. [from: H.R. Bosshard, 1980, ISBN 3-85584-010-5]
- 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 top margin 40 mm. SFS 2487:2000 (“Layout of document text area”) and SFS 2486:1999 (“Forms Layout”) specify that the area for the recipient’s address is 76.2 × 25.4 mm, located 20 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).
According to ISO 11180 and Universal Postal Union standards, an international postal address should be not longer than 6 lines with up to 30 characters each. This requires a maximum area of 76.2 × 38.1 mm with the commonly used typewriter character width of 2.54 mm (1/10") and a baseline distance of 6.35 mm (1/4").
The Universal Postal Union Letter 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 address text.
A widely used international standard A4 document format is the United Nations Layout Key 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 page can be unfolded and folded again without being removed from the file, and that the label field at the bottom-left corner of technical drawings ends up in correct orientation on top of the folded page 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 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 helps to optimize shelf designs and provides a uniform look and handling even if folders from various manufacturers are used.
Filing holes
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. Any format that is at least as large as A7 can be filed using this system.
Not specified in ISO 838, but also widely used, is an upwards compatible 4-hole system. Its two middle holes correspond to ISO 838, plus there are two additional holes located 80 mm above and below these to provide for more stability. This way, sheets with four punched holes can also be filed in ISO 838 2-hole binders. This system is also known under the nickname "888", presumably because the three gaps between the holes are all 8 cm wide. Some hole punches have on their paper guide not only markings for "A4", "A5", and "A6", but also for "888". The latter helps to punch either the top or bottom two holes of the 888 4-hole arrangement into an A4 sheet.
Technical drawing pen sizes
Technical drawing pens follow the same size-ratio principle. The standard sizes differ by a factor sqrt(2): 2.00 mm, 1.40 mm, 1.00 mm, 0.70 mm, 0.50 mm, 0.35 mm, 0.25 mm, 0.18 mm, 0.13 mm. So after drawing with a 0.35 mm pen on A3 paper and reducing it to A4, you can continue with the 0.25 mm pen. (ISO 9175-1)
Ruled writing paper
There seems to be no international standard yet for ruled writing paper. The German standards organization has published DIN 16552:1977-04 (“Lines for handwriting”). That system is widely used, at least in Germany, by primary school teachers to specify which school exercise books pupils should use at which stage of learning how to write. Writing paper with fine gray 5 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.e. these are the dimensions of the paper 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 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
| 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 as roll widths in rotating printing presses.
Overhead projectors
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 is. 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). Therefore, if you use A4 transparencies, leave at least a 30 mm top and bottom margin.
Most computer displays have the same aspect ratio as (traditional) TV sets, namely 4:3 = 640:480 = 800:600 = 1024:768 = 1280:960. If you prepare presentation slides, I recommend that you arrange your layout inside a 280 × 210 mm field and make sure that you leave at least 20 mm margin on the left and right side. This way, you plan for the aspect ratio of a TV/VGA projector and ensure at the same time that you can print on A4 transparencies such that every standard overhead projector will show all parts of your slides.
Identification cards
ISO 7810 specifies three formats for identification cards:
- ID-1 = 85.60 × 53.98 mm (= 3.370 × 2.125 in)
- ID-2 = 105 × 74 mm (= A7)
- 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 driver’s licences. Some people prefer A8 (74 × 52 mm) for business cards. The standard passport format is B7 (= ID-3), the German ID card has A7 (= ID-2) format and the European Union driver’s licence is an ID-1 card.
History of the ISO paper formats
One of the oldest written records regarding the sqrt(2) aspect ratio for paper sizes is a letter that the physics professor Georg Christoph Lichtenberg (University of Göttingen, Germany, 1742-1799) wrote 1786-10-25 to Johann Beckmann. In it, Lichtenberg explains the practical and aesthetic advantages of the sqrt(2) aspect ratio, and of his discovery that paper with that aspect ratio was commonly available at the time. (There are also suggestions that the task to find a paper format that is similar to itself after being cut in half appeared as a question in mathematics exams as early as 1755.)
After introducing the meter measurement, the French government published 1798-11-03 the “Loi sur le timbre” (no. 2136), a law on the taxation of paper that defined several formats that already correspond exactly to the modern ISO paper sizes: “Grand registre” = ISO A2, “grand papier” = ISO B3, “moyen papier” = ISO A3, “petit papier” = ISO B4, “demi feuille” = ISO B5, “effets de commerce” = ISO 1/2 B5.
The French format series never became widely known and was quickly forgotten again. The A, B, and C series paper formats, which are based on the exact same design principles, were completely independently reinvented over a hundred years after the “Loi sur le timbre” in Germany by Dr. Walter Porstmann. They were adopted as the German standard DIN 476 in 1922 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. (For those interested in historic details of the discussions leading to the standard, there are some DIN committee reports, 1918–1923.)
Porstmann’s DIN paper-format concept was convincing, and soon introduced as a national standard in many other countries, for example, Belgium (1924), Netherlands (1925), Norway (1926), Switzerland (1929), Sweden (1930), Soviet Union (1934), Hungary (1938), Italy (1939), Uruguay (1942), Argentina (1943), Brazil (1943), Spain (1947), Austria (1948), Romania (1949), Japan (1951), Denmark (1953), Czechoslovakia (1953), Israel (1954), Portugal (1954), Yugoslavia (1956), India (1957), Poland (1957), United Kingdom (1959), Venezuela (1962), New Zealand (1963), Iceland (1964), Mexico (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) as well as the official United Nations document format in 1975 and it is today used in almost all countries on this planet, leaving North America as the only remaining exception. In 1977, a large German car manufacturer performed a study of the paper formats found in their incoming mail and concluded that out of 148 examined countries, 88 already used the A series formats then. [Source: Helbig/Hennig 1988]
Note: The Lichtenberg Ratio – used by the standard paper 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(2), whereas the Golden Ratio is defined by a/b = (a+b)/a = b/(a−b) = (1 + sqrt(5))/2. While aesthetically pleasing properties have been attributed to both, the Lichtenberg Ratio has the advantage of preserving the aspect ratio when cutting a page into two. The Golden Ratio, on the other hand, preserves the aspect ratio when cutting a maximal square from the paper, a property that seems not particularly useful for office applications. The Golden Ratio was for a while a more fashionable topic in the antique and renaissance arts literature and it has a close connection to the Fibonacci sequence in mathematics.
[A more divine origin of the A4 format has been suggested by Mr. Vernon Jenkins in an effort to reduce unicity distance.]
Hints for North American paper users
The United States, Canada, and in part Mexico, are today the only industrialized nations in which the ISO standard paper sizes are not yet widely used. In U.S. office applications, the paper formats “Letter” (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 Y14.1 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.
While all ISO paper formats have consistently the same aspect ratio of sqrt(2) = 1.414, the U.S. format series has two different alternating aspect ratios 17/11 = 1.545 and 22/17 = 1.294. Therefore, you cannot reduce or magnify from one U.S. format to the next higher or lower without leaving an empty margin, which is rather inconvenient.
The new 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 usually have a fixed drawing scale (e.g., 1:100 means that one meter is drawn as one centimeter), therefore it is not easily possible to resize technical drawings between U.S. and standard paper formats. As a result, internationally operating U.S. corporations increasingly find it more convenient to abandon the old ANSI Y14.1 formats and prepare technical drawings for ISO paper sizes, like the rest of the world does.
The historic origins of the 216 × 279 mm U.S. Letter format, and in particular its rationale, seem rather obscure. The earliest documented attempts to standardize U.S. paper format used a completely different 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, first director of the Bureau of the Budget) as the general U.S. 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 first of these basic sizes halved. One hypothesis for the origin of this format series is that it was derived from a then typical mold size used then in the production of hand-made paper. “It does not appear, even in the selection of 8 1/2 × 11 inch size paper, that any 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 force until the government declared in 1980-01 the 216 × 279 mm format to be the new official paper format for U.S. government offices.
The Canadian standard CAN 2-9.60M “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 just the U.S. sizes rounded to the nearest half centimeter (P4 ~ U.S. Letter, P3 ~ U.S. Ledger). This Canadian standard was introduced in 1976, even though the Ontario Government already had introduced the ISO A series formats before in 1972. Even though these Canadian paper sizes look somewhat like a pseudo-metric standard, they still suffer from the two major inconveniences of the U.S. formats, namely they have no common 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) as an interim measure for countries that use 215 × 280 mm paper and have not yet adopted the ISO A series. Some magazines and other print products that have to be printed economically on both A4 and U.S. Letter presses use the PA4 format today. Incidentally, this PA4 format has a width/height ratio of 3:4, the same as traditional TV screens and most computer monitors and video modes.
Both the “Letter” and “Legal” 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 hoped and 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. Conversion to A4 as the common business letter and document format in North America would not be too difficult, as practically all modern software, copying machines, and laser printers sold today in the U.S. already support A4 paper as a standard feature.
Users of photocopiers outside the U.S. and Canada usually take it for granted that the machine is able to enlarge A4 → A3 or reduce A3 → A4, the two paper formats usually kept in machines with two paper trays. When they use a copier in North America, it often comes as a disappointing surprise when they find out that magnifying an entire page is not a function available there. The absence of this useful capability is a direct result of the unfortunate design of the U.S. paper formats. North American copiers usually also have two or more paper trays, but these are mostly used for the two very similar “Letter” and “Legal” formats, wasting the opportunity of offering a highly useful magnifying capability. Any enlarging of a “Letter” page onto “Legal” paper will always chop off margins and is therefore of little use. The Legal format itself is quite rarely used, the notion that it is for “legal” work is a popular myth; the vast majority of U.S. legal documents are actually using the “Letter” format. Some copiers also offer in addition or instead the next larger “Ledger” format, but that again has a different aspect ratio and will therefore change the margins of a document during magnification or reduction.
Based on the experience from the introduction of ISO paper formats in other industrialized countries at various points during the 20th century, it becomes clear that this process needs to be initiated by a political decision to move all government operation to the new paper format system. History shows that the commercial world then gradually and smoothly adopts the new government standard for office paper within about 10–15 years. It would not be a major operation to do this in the U.S. and Canada as well, especially considering that most standard software and office machines are already prepared for A4. However, such a project can succeed only if the national executive has the political will to accomplish this. The transition period of about a decade is necessary to avoid expensive equipment replacement costs for printers, especially those with older large rotary presses that were not yet designed to be easily retooled for ISO paper sizes.
If you purchase new office or printing equipment in North America, it might be wise to pay attention whether the equipment is suitable for use with A4 paper. When you make inquiries, best indicate to vendors that ISO 216 compatibility of equipment is of concern to you.
If you live in the U.S. and have never been abroad, you might not be aware that paper and accessories in the North-American sizes are not commonly available outside the U.S. or Canada. They are very difficult to obtain in any other country and the only practical way to get U.S. “Letter” there is to cut one of the next larger available sizes (usually B4, A3 or RA4). Therefore, do not expect anyone to send you documents in “Letter” format from abroad. If you send documents to any other country, your use of A4 will greatly ease the handling and filing of your documents for the recipient. If you design software that might be used globally, please keep in mind that the vast majority of laser printer users will print onto A4 paper. Therefore, always make A4 the default setting and the first selection choice in your printing user interface. Remember that it is the paper format used by about 95% of the people on this planet.
Due to popular demand, I have prepared an unofficial table with the ISO sizes in inch fractions. Each listed inch fraction has the smallest denominator that keeps the value within the ISO 216 tolerance limits. Product designers should use the official millimeter values instead. There is also a table in PostScript points.
| A Series Formats | B Series Formats | C Series Formats | |||
|---|---|---|---|---|---|
| 4A0 | 66 1/4 × 93 5/8 | – | – | – | – |
| 2A0 | 46 3/4 × 66 1/4 | – | – | – | – |
| A0 | 33 × 46 3/4 | B0 | 39 3/8 × 55 3/4 | C0 | 36 × 51 |
| A1 | 23 3/8 × 33 | B1 | 27 3/4 × 39 3/8 | C1 | 25 1/2 × 36 |
| A2 | 16 1/2 × 23 3/8 | B2 | 19 3/4 × 27 3/4 | C2 | 18 × 25 1/2 |
| A3 | 11 3/4 × 16 1/2 | B3 | 13 7/8 × 19 3/4 | C3 | 12 3/4 × 18 |
| A4 | 8 1/4 × 11 3/4 | B4 | 9 7/8 × 13 7/8 | C4 | 9 × 12 3/4 |
| A5 | 5 7/8 × 8 1/4 | B5 | 7 × 9 7/8 | C5 | 6 3/8 × 9 |
| A6 | 4 1/8 × 5 7/8 | B6 | 4 7/8 × 7 | C6 | 4 1/2 × 6 3/8 |
| A7 | 2 7/8 × 4 1/8 | B7 | 3 1/2 × 4 7/8 | C7 | 3 3/16 × 4 1/2 |
| A8 | 2 × 2 7/8 | B8 | 2 1/2 × 3 1/2 | C8 | 2 1/4 × 3 3/16 |
| A9 | 1 1/2 × 2 | B9 | 1 3/4 × 2 1/2 | C9 | 1 5/8 × 2 1/4 |
| A10 | 1 × 1 1/2 | B10 | 1 1/4 × 1 3/4 | C10 | 1 1/8 × 1 5/8 |
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 size 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.
Universities in the U.S. increasingly use A4 size paper in laser printers and library copying machines, because most 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 108-mm filing system widely used in the U.S. is not compatible with the two-hole 80-mm 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. Another disadvantage of the three-hole system is that it is not suitable for storing formats smaller than U.S. “Letter”.
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. The U.S. currently use quite a large number of envelope formats.
The U.S. paper industry has managed to come up with a truly bizarre way of specifying the density of paper. Instead of providing you with the obvious quotient of mass per area (e.g., 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 means, you have to know four (!) values in order to understand how to calculate the (scalar) density of the paper. For example “20 lb paper” can mean that a ream of 500 pages in format 24×36 in has a total mass of 20 pounds. These ream sizes of 500 × 24 in × 36 in = 278.70912 m² are somewhat typical in newsprint applications but not universal, as 17×22 in, 25×38 in and other reference sheet sizes are used as well! With 453.59237 g/lb and 278.70912 m²/ream, we get roughly 1 lb/ream = 1.63 g/m² for this particular ream size. It is a big pain if you have to do these conversions yourself and you really should complain to paper suppliers who still do not manage to communicate the proper g/m² values (commonly called “grammage” in both English and French) for their products.
And before I forget it, readers fascinated by the idea of Central Europeans using A6 as a toilet paper size might also be interested to hear that the U.S. have for the same application field a standard square format of 4.5×4.5 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 will help you to enter the ISO paper format world.
- The Guide to International Paper Sizes by EDS Inc. describes ISO, JIS, and non-metric paper formats
- Brian Forté: A4 & US Letter
- 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
- Imperial Paper and Book Sizes
- Paper sizes for screenplay presentation
- Some very nice A4 paper artwork by Peter Callesen
Although it is still rarely advertised, ISO A4 laser printer and copying paper, as well as suitable files and folders, are available today from many U.S. office supply companies. A4 paper and supplies have been regularly ordered in the U.S. for many years, especially by companies and organizations with a lot of international correspondence, including patent lawyers, diplomats, universities, and some government agencies.
Many of the larger stationery chains do offer at least one type of A4 paper in their catalogues. Often the only type of A4 paper available is a higher-quality brand; the type of paper one might prefer for important documents, such as international patent applications.
The U.S.-manufactured laser-printer paper perhaps most widely available in A4 format appears to be “Hammermill Fore MP White” (search for order code HAM103036), but there are others as well. If the shop assistant is unfamiliar with “A4 paper”, try asking for “210 mm × 297 mm”, “8 1/4 in × 11 3/4 in”, “international size”, or “European size” paper.
When I first wrote this page in 1996 while I lived in the U.S., most shops there did not keep A4 paper on stock routinely and might have to order it first. Many were only able to order entire boxes of 10 reams (5000 sheets) and many shop assistants were unfamiliar with the ISO paper-size system. I am being told that the situation has improved quite a bit during the last decade and that A4 paper and accessories are now a lot easier to obtain, but are still considered specialty items.
If you still cannot find any supply for A4 paper in your area, then try for example the following vendors, who have confirmed to have A4 paper or related articles on stock for fast delivery:
- Empire Imports Inc., custsvc@empireimports.com, 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 Way, Mississauga, Ontario L5V 1A1, Canada, phone 1-877-929-9713, sells A4 copier paper and many accessories.
- Office Depot sells Hammermill Fore DP Paper, 8 1/4" x 11 3/4", 20 Lb., 96 Brightness, Ream Of 500 Sheets, Item #: 261782, .29
- 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.
- OfficeMax also sells Hammermill Fore Multipurpose Paper, A4 (11-3/4" x 8-1/4"). Item # 20120174, Style # HPG103036.
- Xpedx operate a chain of paper stores in the U.S. (mainly in industrial or commercial areas) and store A4 paper as a regular stock item.
- IKEA has been reported to sell in its U.S. stores not only filing cabinets that are designed for both A4 and U.S. Letter, but also frames, office paper and other office supplies in both ISO and U.S. format.
- Hammermill Fore MP White Office Paper, 20-lb.Sub., 210mm x 297mm, Internat’l A4
- Xerox, phone 1-800-822-2200, sells A4 paper (e.g., "Premium Multipurpose 4024, a-4 size", order no. 3R2594) for laser printers and copying machines.
- Southworth Company, 265 Main Street, Agawam, MA 01001, phone 1-800-225-1839 is a producer of fine cotton and inkjet A4 paper and matching DL envelopes in various colors and textures. These are now also distributed in the U.S. to resellers, for example via S.P. Richards.
- Carstens carstens@carstens.com, phone 1-800-782-1524, sells A4 ringbinders.
- Keysan, sales@keysan.com, PO Box 5146 Pittsburgh, PA 15206, phone 1-800-969-5397, sell A4 ringbinders.
- Metro Paper, sales@metropaper.com, phone 1-800-607-2737.
- Boise Cascade now also sells A4 paper in the U.S. (catalog number P110303-6)
- GRAYTEX PAPERS, phone 1-800-813-5828, are another US supplier of A3, A4, and A5 papers.
- Sunrise Paper Inc., phone +86 13917368073, are an American owned wholesale export broker of A4, offset, and coated paper grades from China.
- 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, envelopes, filing material, office furniture, etc.) to contact me so that I can collect pointers to these companies here.
If you want to purchase cheap A4 paper and accessories in the U.S. but still have difficulties finding any locally, please do take the time to inform the purchasing department of your usual office supply company about your needs. Point them to this web page if they are not familiar with the paper size system used by >90% of the people on this planet.
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
The following standards contain 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 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: +41 22 749 01 11
fax: +41 22 733 34 30
web: www.iso.org
The most comprehensive source of information about the ISO and North American paper formats and many related standards, as well as their respective histories, is the book
- Max Helbig, Winfried Hennig: DIN-Format A4 – Ein Erfolgssystem in Gefahr. Beuth-Kommentare, Deutsches Institut für Normung, Beuth Verlag, 1988, 144 pages, ISBN 3-410-11878-0, ~17 EUR.
Here are a few more references for those interested in the introduction of ISO paper sizes in North 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 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 in 1992 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.
Some related media coverage:
- The logic behind metric paper sizes. Slashdot, 2004-05-14.
If you have any questions or 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 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 also to the German-American Fulbright Commission for the scholarship that allowed me to spend a year at Purdue University, Indiana, where this text was born, along with my interest in U.S. metrication.
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, or in the discussions on the USENET group misc.metric-system.
ISO 216
Mau 发表于 2007-12-24 09:59:44
ISO 216
国际标准化组织的ISO 216定义了今日世界上大多数国家所使用
这个标准最初是被德意志帝国在1922年纳入DIN（编号是DIN 476），虽然其中一些格式
ISO 216定义了A、B、C三组纸张尺寸。C组纸张尺寸主要使用于
A组纸张尺寸的长宽比都是1:√2，然后舍去到最接近的毫米值。A0定义成面积为一平方米，长宽比为1:√2的纸张。接下来的A1、A2、A3……等纸张尺寸，都是定义成将编号少一号的纸张沿著长边对折，然后舍去到最接近的毫米值。最常用到的纸张尺寸是A4，它的大小是210乘以297毫米。
B组纸张尺寸是编号相同与编号少一号的A组纸张的几何平均。举例来说，B1是A1和A0的几何平均。同样地，C组纸张尺寸是编号相同的A、B组纸张的几何平均。举例来说，
C组纸张尺寸主要使用于信封。一张A4大小的纸张可以刚好放进一个C4大小的信封。如果你把A4纸张对折变成
在ISO 216被广泛采用之前，国际间有著许多不同的纸张格式。这些格式并不是一个连贯的系统，而且很多都不是用公制的单位来定义的。ISO 216的格式遵循著的1:√2比率；放在一起的两张纸有著相同的长宽比和侧边。这个特性简化了很多事，例如：把两张A4纸张缩小影印成一张A4纸张；把一张A4纸张放大影印到一张A3纸张；影印并放大A4纸张的一半到一张A4纸张等等。这个标准最主要的障碍是美国和加拿大，它们仍然使用信度（Letter），Legal，Executive纸张尺寸系统。（加拿大用的是一种P组纸张尺寸，不过它其实是美国用的纸张尺寸，然后取最接近的公制尺寸。）
中华人民共和国国家标准GB/T 148-1997《印刷、书写和绘图纸幅面尺寸》，与ISO 216:1975非等效采用。
中华民国《中国国家标准》CNS 5《纸张尺度（裁切后）》，与ISO 216类似。
International standard paper sizes
by Markus Kuhn
Standard paper sizes like ISO A4 are widely used all over the world today. 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, the height-to-width ratio of all pages is the square root of two (1.4142 : 1). In other words, the width and the height of a page relate to each other like the side and the diagonal of a square. This aspect ratio is especially convenient for a paper size. If you put two such pages 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 does not permit both the height and width of the pages to be nicely rounded metric lengths. Therefore, the area of the pages has been defined to have round metric values. As 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 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. In other words, the height of A1 is the width of A0 and the width of A1 is half the height of A0.
- All smaller A series formats are defined 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(n+1).
- 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 Bn format are the geometric mean between those of the An and the next larger A(n−1) format. For instance, B1 is the geometric mean between A1 and A0, that means the same 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 series formats with the same number. For example, 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 letter once to A5 format, then it will fit nicely into a C5 envelope.
- B and C formats naturally are also square-root-of-two formats.
Note: The geometric mean of two numbers x and y is the square root of their product, (xy)1/2, whereas their arithmetic mean is half their sum, (x+y)/2. For example, the geometric mean of the numbers 2 and 8 is 4 (because 4/2 = 8/4), whereas their arithmetic mean is 5 (because 5−2 = 8−5). The arithmetic mean is half-way 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 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. Using the JIS B series should be avoided. It introduces additional magnification factors and is not an international standard.
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 equivalents of ISO 216 specify tighter tolerances, for instance DIN 476 requires ±1 mm, ±1.5 mm, and ±2 mm respectively for the same ranges of dimensions.
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:
| A0, A1 | technical drawings, posters |
| A1, A2 | flip charts |
| 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 |
| B8, A8 | playing cards |
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 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) |
The magnification factors between all A sizes:
| fromto | A0 | A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 | A10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| A0 | 100% | 71% | 50% | 35% | 25% | 18% | 12.5% | 8.8% | 6.2% | 4.4% | 3.1% |
| A1 | 141% | 100% | 71% | 50% | 35% | 25% | 18% | 12.5% | 8.8% | 6.2% | 4.4% |
| A2 | 200% | 141% | 100% | 71% | 50% | 35% | 25% | 18% | 12.5% | 8.8% | 6.2% |
| A3 | 283% | 200% | 141% | 100% | 71% | 50% | 35% | 25% | 18% | 12.5% | 8.8% |
| A4 | 400% | 283% | 200% | 141% | 100% | 71% | 50% | 35% | 25% | 18% | 12.5% |
| A5 | 566% | 400% | 283% | 200% | 141% | 100% | 71% | 50% | 35% | 25% | 18% |
| A6 | 800% | 566% | 400% | 283% | 200% | 141% | 100% | 71% | 50% | 35% | 25% |
| A7 | 1131% | 800% | 566% | 400% | 283% | 200% | 141% | 100% | 71% | 50% | 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% |
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:
| Format | Width [m] | Height [m] |
|---|---|---|
| An | 2−1/4−n/2 | 21/4−n/2 |
| Bn | 2−n/2 | 21/2−n/2 |
| Cn | 2−1/8−n/2 | 23/8−n/2 |
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:
| 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 |
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.
Envelope formats
For postal purposes, ISO 269 and DIN 678 define the following 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 letter format. DL probably originally stood for “DIN lang”, but ISO 269 now explains this abbreviation instead more diplomatically as “Dimension Lengthwise”. 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.
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 example:
- Germany: DIN 680 specifies that a transparent address window is 90 × 45 mm large and its left edge 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 edge of the envelope. The letterhead standard DIN 676 does not specify the actual content or form 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 large address field visible through the window, in which the top 5 mm are reserved for printing in a small font the sender’s address and the bottom 40 mm are for writing the recipient’s address. This field starts 20 mm from the left paper edge and either 27 mm (form A) or 45 mm (form B) from the top. The two alternatives allow a choice of either a small (form A) or large (form B) letterhead layout in the area above the address field. Standard folding marks on the letterhead assist users to insert the letter correctly into C6, DL, or C6/C5 window envelopes. There is one folding mark (for C6) on the top edge of the page, 148 mm from the left edge. There are also two folding marks on the left edge of the page, either 105 and 210 mm from the bottom edge (form A) or 105 and 210 mm from the top edge (form B).
- United Kingdom: BS 4264 specifies that the transparent window on a DL envelope should be 93 × 39 mm large. Its top-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 80 × 30 mm large address panel on the letterhead. Its top-left corner is located 20 mm from the left margin and 51 mm from the top margin of the page. The address panel is embedded inside a 91 × 48 mm large exclusion zone whose top left corner is located 20 mm from the left margin and 42 mm from the top margin of the page. In other words, the area 9 mm above and below and 11 mm right of the address 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 top and 8 mm from the right edge of the A4 page. [from: H.R. Bosshard, 1980, ISBN 3-85584-010-5]
- 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 top margin 40 mm. SFS 2487:2000 (“Layout of document text area”) and SFS 2486:1999 (“Forms Layout”) specify that the area for the recipient’s address is 76.2 × 25.4 mm, located 20 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).
According to ISO 11180 and Universal Postal Union standards, an international postal address should be not longer than 6 lines with up to 30 characters each. This requires a maximum area of 76.2 × 38.1 mm with the commonly used typewriter character width of 2.54 mm (1/10") and a baseline distance of 6.35 mm (1/4").
The Universal Postal Union Letter 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 address text.
A widely used international standard A4 document format is the United Nations Layout Key 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 page can be unfolded and folded again without being removed from the file, and that the label field at the bottom-left corner of technical drawings ends up in correct orientation on top of the folded page 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 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 helps to optimize shelf designs and provides a uniform look and handling even if folders from various manufacturers are used.
Filing holes
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. Any format that is at least as large as A7 can be filed using this system.
Not specified in ISO 838, but also widely used, is an upwards compatible 4-hole system. Its two middle holes correspond to ISO 838, plus there are two additional holes located 80 mm above and below these to provide for more stability. This way, sheets with four punched holes can also be filed in ISO 838 2-hole binders. This system is also known under the nickname "888", presumably because the three gaps between the holes are all 8 cm wide. Some hole punches have on their paper guide not only markings for "A4", "A5", and "A6", but also for "888". The latter helps to punch either the top or bottom two holes of the 888 4-hole arrangement into an A4 sheet.
Technical drawing pen sizes
Technical drawing pens follow the same size-ratio principle. The standard sizes differ by a factor sqrt(2): 2.00 mm, 1.40 mm, 1.00 mm, 0.70 mm, 0.50 mm, 0.35 mm, 0.25 mm, 0.18 mm, 0.13 mm. So after drawing with a 0.35 mm pen on A3 paper and reducing it to A4, you can continue with the 0.25 mm pen. (ISO 9175-1)
Ruled writing paper
There seems to be no international standard yet for ruled writing paper. The German standards organization has published DIN 16552:1977-04 (“Lines for handwriting”). That system is widely used, at least in Germany, by primary school teachers to specify which school exercise books pupils should use at which stage of learning how to write. Writing paper with fine gray 5 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.e. these are the dimensions of the paper 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 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
| 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 as roll widths in rotating printing presses.
Overhead projectors
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 is. 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). Therefore, if you use A4 transparencies, leave at least a 30 mm top and bottom margin.
Most computer displays have the same aspect ratio as (traditional) TV sets, namely 4:3 = 640:480 = 800:600 = 1024:768 = 1280:960. If you prepare presentation slides, I recommend that you arrange your layout inside a 280 × 210 mm field and make sure that you leave at least 20 mm margin on the left and right side. This way, you plan for the aspect ratio of a TV/VGA projector and ensure at the same time that you can print on A4 transparencies such that every standard overhead projector will show all parts of your slides.
Identification cards
ISO 7810 specifies three formats for identification cards:
- ID-1 = 85.60 × 53.98 mm (= 3.370 × 2.125 in)
- ID-2 = 105 × 74 mm (= A7)
- 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 driver’s licences. Some people prefer A8 (74 × 52 mm) for business cards. The standard passport format is B7 (= ID-3), the German ID card has A7 (= ID-2) format and the European Union driver’s licence is an ID-1 card.
History of the ISO paper formats
One of the oldest written records regarding the sqrt(2) aspect ratio for paper sizes is a letter that the physics professor Georg Christoph Lichtenberg (University of Göttingen, Germany, 1742-1799) wrote 1786-10-25 to Johann Beckmann. In it, Lichtenberg explains the practical and aesthetic advantages of the sqrt(2) aspect ratio, and of his discovery that paper with that aspect ratio was commonly available at the time. (There are also suggestions that the task to find a paper format that is similar to itself after being cut in half appeared as a question in mathematics exams as early as 1755.)
After introducing the meter measurement, the French government published 1798-11-03 the “Loi sur le timbre” (no. 2136), a law on the taxation of paper that defined several formats that already correspond exactly to the modern ISO paper sizes: “Grand registre” = ISO A2, “grand papier” = ISO B3, “moyen papier” = ISO A3, “petit papier” = ISO B4, “demi feuille” = ISO B5, “effets de commerce” = ISO 1/2 B5.
The French format series never became widely known and was quickly forgotten again. The A, B, and C series paper formats, which are based on the exact same design principles, were completely independently reinvented over a hundred years after the “Loi sur le timbre” in Germany by Dr. Walter Porstmann. They were adopted as the German standard DIN 476 in 1922 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. (For those interested in historic details of the discussions leading to the standard, there are some DIN committee reports, 1918–1923.)
Porstmann’s DIN paper-format concept was convincing, and soon introduced as a national standard in many other countries, for example, Belgium (1924), Netherlands (1925), Norway (1926), Switzerland (1929), Sweden (1930), Soviet Union (1934), Hungary (1938), Italy (1939), Uruguay (1942), Argentina (1943), Brazil (1943), Spain (1947), Austria (1948), Romania (1949), Japan (1951), Denmark (1953), Czechoslovakia (1953), Israel (1954), Portugal (1954), Yugoslavia (1956), India (1957), Poland (1957), United Kingdom (1959), Venezuela (1962), New Zealand (1963), Iceland (1964), Mexico (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) as well as the official United Nations document format in 1975 and it is today used in almost all countries on this planet, leaving North America as the only remaining exception. In 1977, a large German car manufacturer performed a study of the paper formats found in their incoming mail and concluded that out of 148 examined countries, 88 already used the A series formats then. [Source: Helbig/Hennig 1988]
Note: The Lichtenberg Ratio – used by the standard paper 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(2), whereas the Golden Ratio is defined by a/b = (a+b)/a = b/(a−b) = (1 + sqrt(5))/2. While aesthetically pleasing properties have been attributed to both, the Lichtenberg Ratio has the advantage of preserving the aspect ratio when cutting a page into two. The Golden Ratio, on the other hand, preserves the aspect ratio when cutting a maximal square from the paper, a property that seems not particularly useful for office applications. The Golden Ratio was for a while a more fashionable topic in the antique and renaissance arts literature and it has a close connection to the Fibonacci sequence in mathematics.
[A more divine origin of the A4 format has been suggested by Mr. Vernon Jenkins in an effort to reduce unicity distance.]
Hints for North American paper users
The United States, Canada, and in part Mexico, are today the only industrialized nations in which the ISO standard paper sizes are not yet widely used. In U.S. office applications, the paper formats “Letter” (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 Y14.1 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.
While all ISO paper formats have consistently the same aspect ratio of sqrt(2) = 1.414, the U.S. format series has two different alternating aspect ratios 17/11 = 1.545 and 22/17 = 1.294. Therefore, you cannot reduce or magnify from one U.S. format to the next higher or lower without leaving an empty margin, which is rather inconvenient.
The new 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 usually have a fixed drawing scale (e.g., 1:100 means that one meter is drawn as one centimeter), therefore it is not easily possible to resize technical drawings between U.S. and standard paper formats. As a result, internationally operating U.S. corporations increasingly find it more convenient to abandon the old ANSI Y14.1 formats and prepare technical drawings for ISO paper sizes, like the rest of the world does.
The historic origins of the 216 × 279 mm U.S. Letter format, and in particular its rationale, seem rather obscure. The earliest documented attempts to standardize U.S. paper format used a completely different 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, first director of the Bureau of the Budget) as the general U.S. 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 first of these basic sizes halved. One hypothesis for the origin of this format series is that it was derived from a then typical mold size used then in the production of hand-made paper. “It does not appear, even in the selection of 8 1/2 × 11 inch size paper, that any 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 force until the government declared in 1980-01 the 216 × 279 mm format to be the new official paper format for U.S. government offices.
The Canadian standard CAN 2-9.60M “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 just the U.S. sizes rounded to the nearest half centimeter (P4 ~ U.S. Letter, P3 ~ U.S. Ledger). This Canadian standard was introduced in 1976, even though the Ontario Government already had introduced the ISO A series formats before in 1972. Even though these Canadian paper sizes look somewhat like a pseudo-metric standard, they still suffer from the two major inconveniences of the U.S. formats, namely they have no common 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) as an interim measure for countries that use 215 × 280 mm paper and have not yet adopted the ISO A series. Some magazines and other print products that have to be printed economically on both A4 and U.S. Letter presses use the PA4 format today. Incidentally, this PA4 format has a width/height ratio of 3:4, the same as traditional TV screens and most computer monitors and video modes.
Both the “Letter” and “Legal” 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 hoped and 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. Conversion to A4 as the common business letter and document format in North America would not be too difficult, as practically all modern software, copying machines, and laser printers sold today in the U.S. already support A4 paper as a standard feature.
Users of photocopiers outside the U.S. and Canada usually take it for granted that the machine is able to enlarge A4 → A3 or reduce A3 → A4, the two paper formats usually kept in machines with two paper trays. When they use a copier in North America, it often comes as a disappointing surprise when they find out that magnifying an entire page is not a function available there. The absence of this useful capability is a direct result of the unfortunate design of the U.S. paper formats. North American copiers usually also have two or more paper trays, but these are mostly used for the two very similar “Letter” and “Legal” formats, wasting the opportunity of offering a highly useful magnifying capability. Any enlarging of a “Letter” page onto “Legal” paper will always chop off margins and is therefore of little use. The Legal format itself is quite rarely used, the notion that it is for “legal” work is a popular myth; the vast majority of U.S. legal documents are actually using the “Letter” format. Some copiers also offer in addition or instead the next larger “Ledger” format, but that again has a different aspect ratio and will therefore change the margins of a document during magnification or reduction.
Based on the experience from the introduction of ISO paper formats in other industrialized countries at various points during the 20th century, it becomes clear that this process needs to be initiated by a political decision to move all government operation to the new paper format system. History shows that the commercial world then gradually and smoothly adopts the new government standard for office paper within about 10–15 years. It would not be a major operation to do this in the U.S. and Canada as well, especially considering that most standard software and office machines are already prepared for A4. However, such a project can succeed only if the national executive has the political will to accomplish this. The transition period of about a decade is necessary to avoid expensive equipment replacement costs for printers, especially those with older large rotary presses that were not yet designed to be easily retooled for ISO paper sizes.
If you purchase new office or printing equipment in North America, it might be wise to pay attention whether the equipment is suitable for use with A4 paper. When you make inquiries, best indicate to vendors that ISO 216 compatibility of equipment is of concern to you.
If you live in the U.S. and have never been abroad, you might not be aware that paper and accessories in the North-American sizes are not commonly available outside the U.S. or Canada. They are very difficult to obtain in any other country and the only practical way to get U.S. “Letter” there is to cut one of the next larger available sizes (usually B4, A3 or RA4). Therefore, do not expect anyone to send you documents in “Letter” format from abroad. If you send documents to any other country, your use of A4 will greatly ease the handling and filing of your documents for the recipient. If you design software that might be used globally, please keep in mind that the vast majority of laser printer users will print onto A4 paper. Therefore, always make A4 the default setting and the first selection choice in your printing user interface. Remember that it is the paper format used by about 95% of the people on this planet.
Due to popular demand, I have prepared an unofficial table with the ISO sizes in inch fractions. Each listed inch fraction has the smallest denominator that keeps the value within the ISO 216 tolerance limits. Product designers should use the official millimeter values instead. There is also a table in PostScript points.
| A Series Formats | B Series Formats | C Series Formats | |||
|---|---|---|---|---|---|
| 4A0 | 66 1/4 × 93 5/8 | – | – | – | – |
| 2A0 | 46 3/4 × 66 1/4 | – | – | – | – |
| A0 | 33 × 46 3/4 | B0 | 39 3/8 × 55 3/4 | C0 | 36 × 51 |
| A1 | 23 3/8 × 33 | B1 | 27 3/4 × 39 3/8 | C1 | 25 1/2 × 36 |
| A2 | 16 1/2 × 23 3/8 | B2 | 19 3/4 × 27 3/4 | C2 | 18 × 25 1/2 |
| A3 | 11 3/4 × 16 1/2 | B3 | 13 7/8 × 19 3/4 | C3 | 12 3/4 × 18 |
| A4 | 8 1/4 × 11 3/4 | B4 | 9 7/8 × 13 7/8 | C4 | 9 × 12 3/4 |
| A5 | 5 7/8 × 8 1/4 | B5 | 7 × 9 7/8 | C5 | 6 3/8 × 9 |
| A6 | 4 1/8 × 5 7/8 | B6 | 4 7/8 × 7 | C6 | 4 1/2 × 6 3/8 |
| A7 | 2 7/8 × 4 1/8 | B7 | 3 1/2 × 4 7/8 | C7 | 3 3/16 × 4 1/2 |
| A8 | 2 × 2 7/8 | B8 | 2 1/2 × 3 1/2 | C8 | 2 1/4 × 3 3/16 |
| A9 | 1 1/2 × 2 | B9 | 1 3/4 × 2 1/2 | C9 | 1 5/8 × 2 1/4 |
| A10 | 1 × 1 1/2 | B10 | 1 1/4 × 1 3/4 | C10 | 1 1/8 × 1 5/8 |
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 size 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.
Universities in the U.S. increasingly use A4 size paper in laser printers and library copying machines, because most 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 108-mm filing system widely used in the U.S. is not compatible with the two-hole 80-mm 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. Another disadvantage of the three-hole system is that it is not suitable for storing formats smaller than U.S. “Letter”.
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. The U.S. currently use quite a large number of envelope formats.
The U.S. paper industry has managed to come up with a truly bizarre way of specifying the density of paper. Instead of providing you with the obvious quotient of mass per area (e.g., 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 means, you have to know four (!) values in order to understand how to calculate the (scalar) density of the paper. For example “20 lb paper” can mean that a ream of 500 pages in format 24×36 in has a total mass of 20 pounds. These ream sizes of 500 × 24 in × 36 in = 278.70912 m² are somewhat typical in newsprint applications but not universal, as 17×22 in, 25×38 in and other reference sheet sizes are used as well! With 453.59237 g/lb and 278.70912 m²/ream, we get roughly 1 lb/ream = 1.63 g/m² for this particular ream size. It is a big pain if you have to do these conversions yourself and you really should complain to paper suppliers who still do not manage to communicate the proper g/m² values (commonly called “grammage” in both English and French) for their products.
And before I forget it, readers fascinated by the idea of Central Europeans using A6 as a toilet paper size might also be interested to hear that the U.S. have for the same application field a standard square format of 4.5×4.5 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 will help you to enter the ISO paper format world.
- The Guide to International Paper Sizes by EDS Inc. describes ISO, JIS, and non-metric paper formats
- Brian Forté: A4 & US Letter
- 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
- Imperial Paper and Book Sizes
- Paper sizes for screenplay presentation
- Some very nice A4 paper artwork by Peter Callesen
Although it is still rarely advertised, ISO A4 laser printer and copying paper, as well as suitable files and folders, are available today from many U.S. office supply companies. A4 paper and supplies have been regularly ordered in the U.S. for many years, especially by companies and organizations with a lot of international correspondence, including patent lawyers, diplomats, universities, and some government agencies.
Many of the larger stationery chains do offer at least one type of A4 paper in their catalogues. Often the only type of A4 paper available is a higher-quality brand; the type of paper one might prefer for important documents, such as international patent applications.
The U.S.-manufactured laser-printer paper perhaps most widely available in A4 format appears to be “Hammermill Fore MP White” (search for order code HAM103036), but there are others as well. If the shop assistant is unfamiliar with “A4 paper”, try asking for “210 mm × 297 mm”, “8 1/4 in × 11 3/4 in”, “international size”, or “European size” paper.
When I first wrote this page in 1996 while I lived in the U.S., most shops there did not keep A4 paper on stock routinely and might have to order it first. Many were only able to order entire boxes of 10 reams (5000 sheets) and many shop assistants were unfamiliar with the ISO paper-size system. I am being told that the situation has improved quite a bit during the last decade and that A4 paper and accessories are now a lot easier to obtain, but are still considered specialty items.
If you still cannot find any supply for A4 paper in your area, then try for example the following vendors, who have confirmed to have A4 paper or related articles on stock for fast delivery:
- Empire Imports Inc., custsvc@empireimports.com, 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 Way, Mississauga, Ontario L5V 1A1, Canada, phone 1-877-929-9713, sells A4 copier paper and many accessories.
- Office Depot sells Hammermill Fore DP Paper, 8 1/4" x 11 3/4", 20 Lb., 96 Brightness, Ream Of 500 Sheets, Item #: 261782, .29
- 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.
- OfficeMax also sells Hammermill Fore Multipurpose Paper, A4 (11-3/4" x 8-1/4"). Item # 20120174, Style # HPG103036.
- Xpedx operate a chain of paper stores in the U.S. (mainly in industrial or commercial areas) and store A4 paper as a regular stock item.
- IKEA has been reported to sell in its U.S. stores not only filing cabinets that are designed for both A4 and U.S. Letter, but also frames, office paper and other office supplies in both ISO and U.S. format.
- Hammermill Fore MP White Office Paper, 20-lb.Sub., 210mm x 297mm, Internat’l A4
- Xerox, phone 1-800-822-2200, sells A4 paper (e.g., "Premium Multipurpose 4024, a-4 size", order no. 3R2594) for laser printers and copying machines.
- Southworth Company, 265 Main Street, Agawam, MA 01001, phone 1-800-225-1839 is a producer of fine cotton and inkjet A4 paper and matching DL envelopes in various colors and textures. These are now also distributed in the U.S. to resellers, for example via S.P. Richards.
- Carstens carstens@carstens.com, phone 1-800-782-1524, sells A4 ringbinders.
- Keysan, sales@keysan.com, PO Box 5146 Pittsburgh, PA 15206, phone 1-800-969-5397, sell A4 ringbinders.
- Metro Paper, sales@metropaper.com, phone 1-800-607-2737.
- Boise Cascade now also sells A4 paper in the U.S. (catalog number P110303-6)
- GRAYTEX PAPERS, phone 1-800-813-5828, are another US supplier of A3, A4, and A5 papers.
- Sunrise Paper Inc., phone +86 13917368073, are an American owned wholesale export broker of A4, offset, and coated paper grades from China.
- 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, envelopes, filing material, office furniture, etc.) to contact me so that I can collect pointers to these companies here.
If you want to purchase cheap A4 paper and accessories in the U.S. but still have difficulties finding any locally, please do take the time to inform the purchasing department of your usual office supply company about your needs. Point them to this web page if they are not familiar with the paper size system used by >90% of the people on this planet.
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
The following standards contain 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 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: +41 22 749 01 11
fax: +41 22 733 34 30
web: www.iso.org
The most comprehensive source of information about the ISO and North American paper formats and many related standards, as well as their respective histories, is the book
- Max Helbig, Winfried Hennig: DIN-Format A4 – Ein Erfolgssystem in Gefahr. Beuth-Kommentare, Deutsches Institut für Normung, Beuth Verlag, 1988, 144 pages, ISBN 3-410-11878-0, ~17 EUR.
Here are a few more references for those interested in the introduction of ISO paper sizes in North 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 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 in 1992 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.
Some related media coverage:
- The logic behind metric paper sizes. Slashdot, 2004-05-14.
If you have any questions or 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 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 also to the German-American Fulbright Commission for the scholarship that allowed me to spend a year at Purdue University, Indiana, where this text was born, along with my interest in U.S. metrication.
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, or in the discussions on the USENET group misc.metric-system.
吉他学习
Mau 发表于 2007-09-28 11:40:16
1.把吉他当成一种乐器来学习（就跟二胡笛子啊什么的一样，没什么特别的）。
2.多学习乐理知识，不要因为很难而自己是初学者就不看。
3.不要被gibson,epiphone,fender,ibanze,prs等品牌所迷惑---他们只是工具，而我们要学习的是一门如何演奏吉他的艺术。
4.不要放过任何一个看上去很简单的基本功练习，他们往王并不简单，或者可以引申出许多高级的技巧。
5.家里一堆gibson，fender，并不代表你会弹琴，别再现了好吗？
6.学琴并不难，难的是长期坚持练习和保持谦虚。
7.如果不是天才的话，想学好吉他就不要去琢磨如何泡mm，传奇又升级了之类的事情，每天请至少花2个小时来练习，要不你别指望你能真正的演奏，骗个把无知的mm的那种除外。
8.光看各种教材，是学不了吉他的。
9.浮躁的人说：XXX人弹得不行，应该跟XXX人学。----是你自己不行了吧。
10.浮躁的人说：我到底该练什么？----别问了，练就对了。
11.浮躁的人说：弹琴有前途吗？---建议你去抢银行。
12. 浮躁的人说：我要最好最漂亮的琴，国产的squier没法弹，音色出不来。---我看你永远都没机会出来了。
13.浮躁的人说：XX大师和YY大师哪个好？---告诉你吧，都好，都有你值得学习的地方。
14.浮躁的人分两种：1）只灌水拍砖而不练琴的人；2）只练而不能坚持的人。
15.把高难的技术挂在嘴边，还不如把基本的练在手上。
16.吉他只是一种乐器是一个工具，你心里面有没有音乐？
17.学习吉他的方法之一：一开始就正确的弹奏。
18.学习吉他的方法之二：找一位好的老师。
19.学习吉他的方法之三：多与别人交流。
20.让别人快去吧，你得慢慢来。
21.任何时候都不要以为手里有把好琴就够了。
22.请爱惜手上的琴，不管她有多便宜。
23.看得懂的乐理请仔细看，看不懂的，请硬着头皮看。
24.别指望看一遍就能记住什么，请看第二遍，第三遍，并在琴上练习。
25.别老问一些弱智的问题，问之前自己先查查书，翻翻以前的帖子，你不至于那么懒吧？
26.和别人讨论有意义的吉他方面的知识吧，而不是争吵XX不行或者YY哪个好。
27.别以为翻弹的很像就把自己当大个了，远着呢，学无止境。
28.请不要认为学过古典或者民谣再改学电声会有什么问题----你只不过又在学习一种全新的乐器而已。
29.多听多看高手的演奏和音乐，再来认定自己是不是已经学会吉他了。
30.学好吉他的秘诀是：练习，练习，再练习。
31.你觉得弹吉他很酷很眩是吗？那我建议你不如去跳街舞。
32.记住：不止有吉他能表现音乐。
33.既然决定了学吉他，请坚持学下去。
34.让各种品牌的琴争去吧，我们要以学习吉他学习音乐本身为主。
35.没有什么比亲自去写一首去扒一首去编一首进步更快的了。
36.别心急，把一首乐曲完美的弹下来是不容易，你只需要不断的练习就可以完善了。
37.不要因为乐曲很简单就不去遵循那些基本的技巧和指法，甚至不开节拍器，好习惯是平时培养出来的，不是演出的时候掉到你头上的。
38.如果有可能，请保存你写过的歌录过的曲子---那是你最好的积累和美好回忆。
39.请不要做浮躁的人。
40.请热爱吉他，热爱音乐，爱你的亲人。
EU-Paris-巴黎景点中文对照
Mau 发表于 2007-06-16 16:09:27
Palais de Chaillot 夏约宫
Ecole Militaire 军校
l'Hotel des Invalides 荣军院
Statue de la Liberte 自由女神像
Maison de Balzac 巴尔扎克故居
pont Alexandre III 亚历山大三世桥
Grand Palais et Petit Palais 大宫 小宫
les Champs Elysees 香榭丽舍
l'Arc de Triomple 凯旋门
l'Opera 歌剧院
la Colonne Vendome 旺多姆圆柱
l'Eglise de la Madeleine 玛德莲那教堂
Palais de l'Elysee 爱丽舍宫
la Place de la Concorde 协和广场
Musee du Louvre 卢浮宫
pont des Arts 艺术桥
Institut de France 法兰西学院
Musee d'Orsay 奥赛美术馆
Montmartre: 蒙玛特
Sacre-Coeur 圣心教堂
Moulin Rouge 红磨坊
Marais: 玛莱区
la Place des Vosges 孚日广场
Maison de Victro Hugo 雨果故居
la Bastille 巴士底
Hotel de ville 市政厅
Centre Pompidou 蓬皮杜中心
Cite: 西岱
pont Neuf 新桥
la Conciergerie 监狱 （这个词音译意译都比较麻烦，监狱算是说明吧）
Notre Dame 圣母院
Tour de Notre Dame 圣母院钟楼
Latin: 拉丁区
Sorbonne 索邦（大学）
le Pantheon 先贤祠
Jardin du Luxembourg 卢森堡公园
Cimetiere du Pere Lachaise 拉雪兹神父公墓
Tour Montparnasse 蒙帕纳斯
Verseilles 凡尔赛
Fontaine bleau 枫丹白露
la Seine 塞纳河
EU-Paris-博物馆列表
Mau 发表于 2007-06-16 15:40:50
Aquarium tropical de la Porte Dorée
Arc de Triomphe
Musée de l’Armée - Tombeau de Napoléon 1er
Centre Pompidou - Musée national d’Art moderne
Musée national des Arts asiatiques - Guimet
Musée des Arts décoratifs
Musée de la Mode et du textile
Musée de la Publicité
Musée Nissim de Camondo
Musée des Arts et métiers
Musée de l’Assistance Publique - Hôpitaux de Paris
Musée du quai Branly
Chapelle expiatoire
La Cinémathèque française - Musée du Cinéma
Cité des Sciences et de l’Industrie - La Villette
Conciergerie
Musée national Eugène Delacroix
Musée des Égouts de Paris
Musée d’Ennery*
Musée Galliera - Musée de la Mode de la Ville de Paris
Musée Hébert*
Musée Jean-Jacques Henner*
Musée de l’Institut du Monde arabe
Musée du Louvre
Musée national de la Marine
Musée de la Monnaie
Cité de l’Architecture et du Patrimoine - Musée national des Monuments français
Musée Gustave Moreau
Musée national du Moyen Âge - Thermes et hôtel de Cluny
Cité de la Musique - Musée de la Musique
Crypte archéologique de Notre-Dame
Tours de Notre-Dame
Musée national de l’Orangerie
Musée de l’Ordre de la Libération
Musée d’Orsay
Panthéon
Musée national Picasso
Musée des Plans-reliefs
Musée de la Poste
Musée Rodin
Sainte-Chapelle
Musée de l’Air et de l’Espace
Musée d’Archéologie nationale de Saint-Germain-en-Laye
Musée national de Céramique de Sèvres
Abbaye royale de Chaalis
Château de Champs*
Musée et domaine nationaux du Château de Compiègne
Musée Condé - Château de Chantilly
Musée national de la Coopération franco-américaine - Château de Blérancourt*
Musée départemental Maurice Denis - Le Prieuré
Château de Fontainebleau
Château de Maisons-Laffitte
Musée national des Châteaux de Malmaison et Bois-Préau
Château de Pierrefonds
Musée national de Port-Royal des Champs
Château de Rambouillet
Musée national de la Renaissance - Château d’Ecouen
Maison d’Auguste Rodin à Meudon
Basilique cathédrale de Saint-Denis
Villa Savoye
Musée national des Châteaux de Versailles et de Trianon
Château de Vincennes
EU-Paris-公共交通优惠票
Mau 发表于 2007-06-16 15:08:15
巴黎有着相当发达的公共交通，如同蜘蛛网一般密密分布。其中包括公车、市区地铁(meter)和近郊地铁（rer），而且票是通用的。我想M去了那里，绝对不会像在天苍苍野茫茫的德州农场那样举目四望全无人影，靠两条腿完全不能做任何事。
巴黎的地铁是最便捷最快速的交通工具，每两站之间只需要2分钟，只要再给转线留下5分钟的预算，那么出行时间基本可以预测。单张票的价格是1.40欧，紫色票面。一下子买十张票有优惠，这个被叫做“carnet”，是10.90欧。这种票只能在两圈内活动，不过也基本够了，因为市区和大部分景点都在两圈内。出圈的话，另外购买票。如果一直在地铁里转车不出地面，还是使用同一张票的，当然也是要在两圈内。
公车的话，可以用同样的那种地铁票， 但是换车的话，需要用得第二张票。
除了老年人、儿童和学生用的优惠年卡，游客适用的优惠通票包括如下这些，适合不同的停留时间和不同的活动区域。
1）日票（Mobilis）
当天可用的不限次票，根据活动区域不同而票价不同，从1－2圈一直到1－8圈都有。不需要照片。
2）巴黎观光票 （Paris Visite）
巴黎观光票可以在一定时间段内（1天、2天、3天、5天）无限制乘坐市区和近郊的任何公车和地铁（1－3圈、1－5圈、1－8圈三种）。并随送一本小册子，里面有一些打折票，据说这些票没太大的用处。不需要照片。可以提前买，因为是从使用之时开始算天数。所有地铁以及机场有卖。
1－3圈价格如下（分成人和儿童），一般就够用了（2006年12月1日后的价格）：
Price Adult 1 day (12 and over) : 8,50 € TTC
3）伟大的橙子卡！（Carte Orange）——分周卡和月卡
需要一张护照上的那种照片贴在上面。从1－2圈到1－8圈都有。
对游客来说最有用的周票，只能在周一～周日的时间段内有效，而非连续七天。比如周三买的话，只能用周三、四、五、六、日这五天。另外，只有在周三之前才能买到本周的周票。周五开始卖下周的周票。像我这种周四才到的人就很头大了，买不到周票：（
最后但不是最不重要的！
很多人都搞不清巴黎地铁的“圈”怎么算，在英文里用的单词是“zone”。
我终于在人家地铁交通的官网上找到这幅图，可以看到圈和地铁线的关系了。
EU-Paris-博物馆通票
Mau 发表于 2007-06-16 15:05:28
在巴黎观光的几件必做之事，一定包括逛博物馆。我是博物馆狂人，不管博物馆美术馆是大是小，是公是私，总觉得开卷有益，看到心弛神往。巴黎有相当为游客考虑的博物馆通票，并有单独的博物馆通票网站，浏览了一遍，做点笔记——
1）博物馆通票的好处：
价格实惠除外，还可以在数日内多次进入60余家博物馆和纪念碑（虽然很少有人能做到），并且可以免去缴款买票排队之苦，尤其是卢浮宫，越过队伍大摇大摆进馆的感觉一定很爽。
2）三种博物馆通票及其价格：
2日通票－30欧
4日通票－45欧
6日通票－60欧
买通票附送一个小册子，介绍可以参观的地点。
与此对比，通票所包含的一些博物馆的单次票价：
蓬皮杜－10欧，卢浮宫－8.5欧，毕加索博物馆－6.5欧，凡尔赛宫－13.5欧，巴黎圣母院7.5欧。（这几个加起来，就基本上是4日通票的价格了。）另外还包含：pantheon，奥赛艺术馆，电影博物馆之类。全部名单在此。
3）使用方法：
所谓2日并不代表48小时有效，而是指两天，比如周二与周三，不可能跨越到第三天去。
所以最好在决定开始参观博物馆的那一天的早晨开卡，充分利用它的时限。 所谓开卡，也就是在卡背面写上自己的姓与名和开卡日期，不许涂改。然后在检票口出示一下，怎么个一弄，就好了。千万不要一买到卡就兴高采烈签名哦。
4）购买地点：
可以直接在链接里面的官网在线购买，然后在巴黎观光局那里取。
可以在戴高乐机场买，具体地点：
Roissy Charles-de-Gaulle
Tourist Information Area
Roissy Charles de Gaulles Airport, Terminal 2F
“Arrivals” level, between gate 0.10 and gate 0.11
Opening Hours From 9am to 8pm every day
以及巴黎市内各大博物馆和其他地点。
5）注意事项：
通票不包含一些临时性的特别展出。 如果遇到特定情形和节假日，某些博物馆临时免票，也不会对通票进行部分退款。18岁以下的人无需考虑买通票，因为大部分博物馆对这个年龄段的人免票（暗暗下决心让我的小孩在18岁前用一个暑假环游欧洲）。19－25岁的人也常常能获得优惠票价，是否买通票可以根据情况决定。像我这样的大龄女青，只能暗叹而内伤了。
“美好时光” 陈墙个展
Mau 发表于 2007-05-10 11:41:53
开幕时间：2007年4月21日（周六）18:30
展览时间：2007年4月21日-5月20日(11:00-19:00)
展览地址：上海市光复路423号后面 苏河艺术（近大统路）
艺 术 家：陈 墙
艺术总监：Lise Kolstad Yuen
展览策划：李消非
展览主办：苏河艺术 | http://www.creekart.cn/
陈墙的艺术自律起于偶然发现的一对器官配合。当感受与联想的信息占据中枢神经，视网膜和手却在纸或布的平面达成默契。……
陈墙的作品不仅将起点和目标划定在视网膜，他采用的装饰方案原本就有“非艺术”的性格。
……
陈墙的作品在作品层面是安静的，其动，是被有意放弃的强势部分对视网膜引导的视皮层的联系冲动。他们必然地按捺不住。……
肖开愚
T恤图案-for a girl who's about to be abroad
Mau 发表于 2007-05-08 22:55:46
这个是第二步
第3次
