A Series
Paper in the A series format has a aspect ratio, although this is rounded to the nearest millimetre. A0 is defined so that it has an area of 1 square metre, prior to the aforementioned rounding. 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, again prior to rounding).
The most frequently used of this series is the size A4 which is 210 mm × 297 mm (8.3 in × 11.7 in). For comparison, the letter paper size commonly used in North America (8.5 in × 11 in (220 mm × 280 mm)) is approximately 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, will be the same as that of a rectangle half its size, means that, which reduces to ; in other words, an aspect ratio of .
The formula that gives the larger border of the paper size A in metres and without rounding off is the geometric sequence: . The paper size A thus has the dimension × .
The exact millimetre measurement of the long side of A is given by .
Read more about this topic: ISO 216
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