2 displaystyle sqrt 2 , within rounding to millimetres. This ratio has the unique property that when cut or folded in half width-wise, the halves also have the same aspect ratio. Each ISO paper size is one half of the area of the next larger size in the same series. Contents 1 Dimensions of A, B and C Series 2 History 3 A series 4 B series 5 C series 6 Tolerances 7 Application 8 Matching technical pen widths 9 See also 10 References 11 External links Dimensions of A, B and C Series[edit] ISO/DIN paper sizes in millimetres and in inches Size A series formats B series formats C series formats (mm) (in) (mm) (in) (mm) (in) 0 841 × 1189 33.1 × 46.8 1000 × 1414 39.4 × 55.7 917 × 1297 36.1 × 51.1 1 594 × 841 23.4 × 33.1 707 × 1000 27.8 × 39.4 648 × 917 25.5 × 36.1 2 420 × 594 16.5 × 23.4 500 × 707 19.7 × 27.8 458 × 648 18.0 × 25.5 3 297 × 420 11.7 × 16.5 353 × 500 13.9 × 19.7 324 × 458 12.8 × 18.0 4 210 × 297 8.3 × 11.7 250 × 353 9.8 × 13.9 229 × 324 9.0 × 12.8 5 148 × 210 5.8 × 8.3 176 × 250 6.9 × 9.8 162 × 229 6.4 × 9.0 6 105 × 148 4.1 × 5.8 125 × 176 4.9 × 6.9 114 × 162 4.5 × 6.4 7 74 × 105 2.9 × 4.1 88 × 125 3.5 × 4.9 81 × 114 3.2 × 4.5 8 52 × 74 2.0 × 2.9 62 × 88 2.4 × 3.5 57 × 81 2.2 × 3.2 9 37 × 52 1.5 × 2.0 44 × 62 1.7 × 2.4 40 × 57 1.6 × 2.2 10 26 × 37 1.0 × 1.5 31 × 44 1.2 × 1.7 28 × 40 1.1 × 1.6 Comparison of
History[edit] "Lichtenberg ratio" redirects here. For 2 displaystyle sqrt 2 , see Square root of 2.
In 1786, the German scientist
2 displaystyle sqrt 2 in a letter to Johann Beckmann.[1] The formats that became ISO paper sizes A2, A3, B3, B4, and B5 were developed in France. They were listed in a 1798 law on taxation of publications that was based in part on page sizes.[2] Comparison of A4 (shaded grey) and C4 sizes with some similar paper and photographic paper sizes. The main advantage of this system is its scaling. Rectangular paper with an aspect ratio of 2 displaystyle sqrt 2 has the unique property that, when cut or folded in half midway between its shorter sides, each half has the same 2 displaystyle sqrt 2 aspect ratio and half the area of the whole sheet before it was divided. Equivalently, if one lays two same-sized sheets paper with an aspect ratio of 2 displaystyle sqrt 2 side-by-side along their longer side, they form a larger rectangle with the aspect ratio of 2 displaystyle sqrt 2 and double the area of each individual sheet. The ISO system of paper sizes exploit these properties of the 2 displaystyle sqrt 2 aspect ratio. In each series of sizes (for example, series A), the largest size is numbered 0 (for example, A0), and each successive size (for example, A1, A2, etc.) has half the area of the preceding sheet and can be cut by halving the length of the preceding size sheet. The new measurement is rounded down to the nearest millimetre. A folded brochure can be made by using a sheet of the next larger size (for example, an A4 sheet is folded in half to make a brochure with size A5 pages. An office photocopier or printer can be designed to reduce a page from A4 to A5 or to enlarge a page from A4 to A3. Similarly, two sheets of A4 can be scaled down to fit one A4 sheet without excess empty paper. This system also simplifies calculating the weight of paper. Under ISO 536, paper's grammage is defined as a sheet's weight in grams (g) per area in square metres (abbreviated g/m2 or gsm).[3] Since an A0 sheet has an area of 1 m2, its weight in grams is the same as its grammage. One can derive the grammage of other sizes by arithmetic division in g/m2. A standard A4 sheet made from 80 g/m2 paper weighs 5 g, as it is 1 16 textstyle frac 1 16 (four halvings, ignoring rounding) of an A0 page. Thus the weight,
and the associated postage rate, can be easily approximated by
counting the number of sheets used.
ISO 216:2007, defining the A and B series of paper sizes ISO 269:1985, defining the C series for envelopes ISO 217:2013, defining the RA and SRA series of raw ("untrimmed") paper sizes A series[edit] Paper in the A series format has an aspect ratio of 2 displaystyle sqrt 2 (≈ 1.414) when ignoring rounding. A0 is defined so that it has an area of 1 square metre before rounding to the nearest millimeter. Successive paper sizes in the series (A1, A2, A3, etc.) are defined by halving the length of the preceding paper size and rounding down, so that the long side of A(n+1) is the same length as the short side of An. The most used of this series is the size A4 which is 210 mm × 297 mm (8.27 in × 11.7 in) and thus almost 1 16 textstyle frac 1 16 square metres in area. For comparison, the letter paper size commonly used in North America (8.5 in × 11 in, 216 mm × 279 mm) is about 6 mm (0.24 in) wider and 18 mm (0.71 in) shorter than A4. The geometric rationale behind the square root of 2 is to maintain the aspect ratio of each subsequent rectangle after cutting or folding an A series sheet in half, perpendicular to the larger side. Given a rectangle with a longer side, x, and a shorter side, y, ensuring that its aspect ratio, x y textstyle frac x y , will be the same as that of a rectangle half its size, y x / 2 textstyle frac y x/2 , means that x y = y x / 2 textstyle frac x y = frac y x/2 , which reduces to x y = 2 textstyle frac x y = sqrt 2 ; in other words, an aspect ratio of 1: 2 displaystyle sqrt 2 . The formula that gives the larger border of the paper size An in metres and without rounding off is the geometric sequence: a n = 2 1 4 − n 2 displaystyle a_ n =2^ frac 1 4 - frac n 2 . The paper size An thus has the dimension a n × a n + 1 displaystyle a_ n times a_ n+1 and area (before rounding) 2 − n m 2 textstyle 2^ -n mathrm m ^ 2 . The measurement in millimetres of the long side of An can be calculated as ⌊ 1000 / ( 2 2 n − 1 4 ) + 0.2 ⌋ textstyle leftlfloor 1000/left(2^ frac 2n-1 4 right)+0.2rightrfloor (brackets represent the floor function). B series[edit] The B series is defined in the standard as follows: "A subsidiary series of sizes is obtained by placing the geometrical means between adjacent sizes of the A series in sequence." The use of the geometric mean makes each step in size: B0, A0, B1, A1, B2 … smaller than the previous one by the same factor. As with the A series, the lengths of the B series have the ratio 2 displaystyle sqrt 2 , and folding one in half (and rounding down to the nearest millimeter) gives the next in the series. The shorter side of B0 is exactly 1 metre. The measurement in millimetres of the long side of Bn can be calculated as ⌊ 1000 / ( 2 n − 1 2 ) + 0.2 ⌋ textstyle leftlfloor 1000/left(2^ frac n-1 2 right)+0.2rightrfloor . There is also an incompatible Japanese B series which the JIS defines to have 1.5 times the area of the corresponding JIS A series (which is identical to the ISO A series).[4] Thus, the lengths of JIS B series paper are 1.5 ≈ 1.22 displaystyle sqrt 1.5 approx 1.22 times those of A-series paper. By comparison, the lengths of ISO B series paper are 2 4 ≈ 1.19 textstyle sqrt[ 4 ] 2 approx 1.19 times those of A-series paper. C series[edit] The C series formats are geometric means between the B series and A series formats with the same number (e.g., C2 is the geometric mean between B2 and A2). The width to height ratio is 2 displaystyle sqrt 2 as in the A and B series. The C series formats are used mainly for envelopes. An A4 page will fit into a C4 envelope. C series envelopes follow the same ratio principle as the A series pages. For example, if an A4 page is folded in half so that it is A5 in size, it will fit into a C5 envelope (which will be the same size as a C4 envelope folded in half). The lengths of ISO C series paper are therefore 2 8 textstyle sqrt[ 8 ] 2 times those of A-series paper – i.e., about 9% larger. A, B, and C paper fit together as part of a geometric progression, with ratio of successive side lengths of 2 8 textstyle sqrt[ 8 ] 2 , though there is no size half-way between Bn and A(n − 1): A4, C4, B4, "D4", A3, …; there is such a D-series in the Swedish extensions to the system. The measurement in millimetres of the long side of Cn can be as ⌊ 1000 / ( 2 4 n − 3 8 ) + 0.2 ⌋ displaystyle leftlfloor 1000/left(2^ frac 4n-3 8 right)+0.2rightrfloor . Tolerances[edit] The tolerances specified in the standard are: ±1.5 mm for dimensions up to 150 mm, ±2.0 mm for dimensions in the range 150 to 600 mm, and ±3.0 mm for dimensions above 600 mm. These are related to comparison between series A, B and C.
Application[edit]
The
2 displaystyle sqrt 2 ; two sheets next to each other together have the same ratio, sideways. In scaled photocopying, for example, two A4 sheets reduced to A5 size fit exactly onto one A4 sheet, and an A4 sheet in magnified size onto an A3 sheet; in each case, there is neither waste nor want. The principal countries not generally using the ISO paper sizes are the United States and Canada, which use the Letter, Legal and Executive system. Although they have also officially adopted the ISO 216 paper format, Mexico, Panama, Venezuela, Colombia, the Philippines, and Chile also use mostly U.S. paper sizes. Rectangular sheets of paper with the ratio 1: 2 displaystyle sqrt 2 are popular in paper folding, such as origami, where they are sometimes called "A4 rectangles" or "silver rectangles".[5] In other contexts, the term "silver rectangle" can also refer to a rectangle in the proportion 1:(1 + 2 displaystyle sqrt 2 ), known as the silver ratio. Matching technical pen widths[edit] An important adjunct to the ISO paper sizes, particularly the A series, are the technical drawing line widths specified in ISO 128, and the matching technical pen widths of 0.13, 0.18, 0.25, 0.35, 0.5, 0.7, 1.0, 1.40, and 2.0 mm, as specified in de:ISO 9175-1. Color codes are assigned to each size to facilitate easy recognition by the drafter. These sizes increase by a factor of 2 displaystyle sqrt 2 , so that particular pens can be used on particular sizes of paper, and then the next smaller or larger size can be used to continue the drawing after it has been reduced or enlarged, respectively. For example, a continuous thick line on A0 size paper shall be drawn with a 0.7 mm pen, the same line on A1 paper shall be drawn with a 0.5 mm pen, and finally on A2, A3, or A4 paper it shall be drawn with a 0.35 mm pen.[6][7][8] Linewidth in mm 0.13 0.18 0.25 0.35 0.50 0.70 1.0 1.4 2.0 color Violet Red White Yellow Brown Blue Orange Green Gray The earlier DIN 6775 standard upon which ISO 9175-1 is based also specified a term and symbol for easy identification of pens and drawing templates compatible with the standard, called fr:micronorm, which may still be found on some technical drafting equipment. See also[edit] ANSI/ASME Y14.1
International standard envelope sizes
References[edit] ^ Lichtenberg, Georg Christoph (February 7, 2006) [Written October 25,
1786]. "Lichtenberg's letter to Johann Beckmann" (in German with
English translation). Translated by Kuhn, Markus. University of
Cambridge. Retrieved May 10, 2016. CS1 maint: Unrecognized
language (link) Published in Lichtenberg, Georg Christoph (1990).
Joost, Ulrich; Schöne, Albrecht, eds. Briefwechsel [Correspondence]
(in German). Volume III (1785-1792). Munich: Beck. pp. 274–75.
ISBN 3-406-30958-5. Retrieved May 10, 2016.
^ Kuhn, Markus (October 8, 2005). "Loi sur le timbre (No. 2136)" [Law
of Taxation (No. 2136)]. Retrieved May 11, 2016. Kuhn includes
copies of pages from the journal article that announced the law:
Republic of France (November 3, 1798). "Loi sur le timbre (Nº 2136)".
Bulletin des lois de la République (in French). Paris (237):
1–2.
^
External links[edit] Wikimedia Commons has media related to DIN EN ISO 216. International standard paper sizes:
v t e ISO standards by standard number List of ISO standards / ISO romanizations / IEC standards 1–9999 1 2 3 4 5 6 7 9 16 31 -0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 128 216 217 226 228 233 259 269 302 306 428 518 519 639 -1 -2 -3 -5 -6 646 690 732 764 843 898 965 1000 1004 1007 1073-1 1413 1538 1745 1989 2014 2015 2022 2047 2108 2145 2146 2240 2281 2709 2711 2788 2848 2852 3029 3103 3166 -1 -2 -3 3297 3307 3602 3864 3901 3977 4031 4157 4217 4909 5218 5428 5775 5776 5800 5964 6166 6344 6346 6385 6425 6429 6438 6523 6709 7001 7002 7098 7185 7200 7498 7736 7810 7811 7812 7813 7816 8000 8178 8217 8571 8583 8601 8632 8652 8691 8807 8820-5 8859 -1 -2 -3 -4 -5 -6 -7 -8 -8-I -9 -10 -11 -12 -13 -14 -15 -16 8879 9000/9001 9075 9126 9293 9241 9362 9407 9506 9529 9564 9594 9660 9897 9899 9945 9984 9985 9995 10000–19999 10005 10006 10007 10116 10118-3 10160 10161 10165 10179 10206 10218 10303 -11 -21 -22 -28 -238 10383 10487 10585 10589 10646 10664 10746 10861 10957 10962 10967 11073 11170 11179 11404 11544 11783 11784 11785 11801 11898 11940 (-2) 11941 11941 (TR) 11992 12006 12182 12207 12234-2 13211 -1 -2 13216 13250 13399 13406-2 13450 13485 13490 13567 13568 13584 13616 14000 14031 14224 14289 14396 14443 14496 -2 -3 -6 -10 -11 -12 -14 -17 -20 14644 14649 14651 14698 14750 14764 14882 14971 15022 15189 15288 15291 15292 15398 15408 15444 -3 15445 15438 15504 15511 15686 15693 15706 -2 15707 15897 15919 15924 15926 15926 WIP 15930 16023 16262 16612-2 16750 16949 (TS) 17024 17025 17100 17203 17369 17442 17799 18000 18004 18014 18245 18629 18916 19005 19011 19092 (-1 -2) 19114 19115 19125 19136 19439 19500 19501 19502 19503 19505 19506 19507 19508 19509 19510 19600 19752 19757 19770 19775-1 19794-5 19831 20000+ 20000 20022 20121 20400 21000 21047 21500 21827:2002 22000 23270 23271 23360 24517 24613 24617 24707 25178 25964 26000 26300 26324 27000 series 27000 27001 27002 27006 27729 28000 29110 29148 29199-2 29500 30170 31000 32000 38500 40500 42010 55000 80000 -1 -2 -3 Category v t e Deutsches Institut für Normung DIN standards DIN 1025 DIN 1451 DIN 1530 DIN 5008 DIN 31635 DIN 41612 DIN 43700 DIN 4420 DIN 47100 DIN 62056 DIN 72552 Engschrift ISO 216 Committees Municipal Services Standards Committee Connectors DIN connector Mini-DIN connector Multimedia extension connector Ra |