It is known to all that paper plays an important role of human. In the past different sizes and names were used in different parts of the world, which caused the inconvenience among different countries. So people needed a new standard of paper size which can be used all over the world.
The new standard is based on the square root of 2 (1.414…). The advantages of basing a paper size upon an aspect ratio of 1.414 were already noted in 1786 by the German scientist Georg Christoph Lichtenberg, in a letter to Johann Beckmann. The formats that became A2, A3, B3, B4 and B5 were developed in France, and published in 1798 during the French Revolution.
Early in the twentieth century, Dr Walter Porstmann turned Lichtenberg's idea into a proper system of different paper sizes. Porstmann's system was introduced as a DIN standard (DIN 476) in Germany in 1922, replacing a vast variety of other paper formats. Even today the paper sizes are called "DIN Ax" in everyday use in Germany, Austria, Spain and Portugal.
The main advantage of this system is its scaling: if a sheet with an aspect ratio of 1.414 is divided into two equal halves parallel to its shortest sides, then the halves will again have an aspect ratio of 1.414. Folded brochures of any size can be made by using sheets of the next larger size, e.g. A4 sheets are folded to make A5 brochures. The system allows scaling without compromising the aspect ratio from one size to another – as provided by office photocopiers, e.g. enlarging A4 to A3 or reducing A3 to A4. Similarly, two sheets of A4 can be scaled down to fit exactly one A4 sheet without any cutoff or margins.
The weight of each sheet is also easy to calculate given the basis weight in grams per square metre (g/m² or "gsm"). Since an A0 sheet has an area of 1 m², its weight in grams is the same as its basis weight in g/m2. A standard A4 sheet made from 80 g/m² paper weighs 5 g, as it is one 16th (four halvings) of an A0 page. Thus the weight, and the associated postage rate, can be easily calculated by counting the number of sheets used.
ISO 216 and its related standards were first published between 1975 and 1995:
- 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
- Now we use 3 series of paper size: A, B and C.
A series:
Paper in the A series format has a 1:1.414 aspect ratio, although this is rounded to the nearest millimetre. A0 is defined so that it has an area of 1 m², prior to the rounding. So the A0 paper size is 841 mm × 1189 mm. Successive paper sizes in the series (A1, A2, A3, etc.) are defined by halving the preceding paper size, cutting parallel to its shorter side so that the long side of A(n+1) is the same length as the short side of An prior to rounding. The most frequently used of this series is the size A4 which is 210 mm × 297 mm.
The significant advantage of this system is its scaling: if a sheet with an aspect ratio of 1.414 is divided into two equal halves parallel to its shortest sides, then the halves will again have an aspect ratio of 1.414. Folded brochures of any size can be made by using sheets of the next larger size, e.g. A4 sheets are folded to make A5 brochures. The system allows scaling without compromising the aspect ratio from one size to another—as provided by office photocopiers, e.g. enlarging A4 to A3 or reducing A3 to A4. Similarly, two sheets of A4 can be scaled down and fit exactly 1 sheet without any cutoff or margins.
The behaviour of the aspect ratio is easily proven: on a sheet of paper, let a be the long side and b be the short side; thus, a/b=1.414. When the sheet of paper is folded in half widthwise, let c be the length of the new short side: c=a/2. If we take the ratio of the newly folded paper we have:
b/c=b/(a/2)=2/(a/b)=1.414
Therefore, the aspect ratio is preserved for the new dimensions of the folded paper.
B series:
In addition to the A series, there is a less common B series. The area of B series sheets is the geometric mean of successive A series sheets. So, B1 is between A0 and A1 in size, with an area of 0.707 m². As a result, B0 is 1 m wide, and other sizes in the B series are a half, a quarter or further fractions of a metre wide. While less common in office use, it is used for a variety of special situations. Many posters use B-series paper or a close approximation, such as 50 cm × 70 cm; B5 is a relatively common choice for books. The B series is also used for envelopes and passports. The B-series is widely used in the printing industry to describe both paper sizes and printing press sizes, including digital presses. B3 paper is used to print two A4 pages side by side using imposition; four pages would be printed on B2, eight on B1, etc.
C series:
The C series is used only for envelopes and is defined in ISO 269. The area of C series sheets is the geometric mean of the areas of the A and B series sheets of the same number; for instance, the area of a C4 sheet is the geometric mean of the areas of an A4 sheet and a B4 sheet. This means that C4 is slightly larger than A4, and slightly smaller than B4. The practical usage of this is that a letter written on A4 paper fits inside a C4 envelope, and C4 paper fits inside a B4 envelope.
Here is all the ISO/DIN paper sizes in SI units:
The tolerances specified in the standard are
- ±1.5 mm for dimensions up to 150 mm,
- ±2 mm for lengths in the range 150 to 600 mm and
- ±3 mm for any dimension above 600 mm.
By 1975 so many countries were using the German system that it was established as an ISO standard, as well as the official United Nations document format. By 1977, A4 was the standard letter format in 88 of 148 countries. Today the standard has been adopted by all countries in the world. ISO paper sizes affect writing paper, stationery, cards, and some printed documents all over the world.
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