# Paper Sizes

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## What are the Different Paper Sizes?

The size of sheets of paper used as writing paper, stationery, cards, and for certain printed documents are governed by paper size standards. The international standard for paper size is the ISO 216 standard, which includes the widely used A4 page size. It is used worldwide, except in North America and parts of Central and South America, where we have North American paper sizes such as "Letter" and "Legal" is used.

The best way to describe the aspect ratio of A sizes is to compare two of a single scale with one of the next sizes. For example, 2 x side-by-side A4 page size (portrait) will be equal to 1 x page A3 and 2 x side-by-side A3 page size (portrait) will be equal to 1 x page A2 size dimensions. The bigger the paper size, the smaller the volume - the smallest is A10, and the largest is A0.

## Paper Size Dimensions:

 Size Metric Imperial A0 1189 × 841 mm 46.8 × 33.1 in A1 841 × 594 mm 33.1 × 23.4 in A2 594 × 420 mm 23.4 × 16.5 in A3 420 × 297 mm 16.5 × 11.7 in A4 297 × 210 mm 11.7 × 8.3 in A5 210 × 148 mm 8.3 × 5.8 in A6 148 × 105 mm 5.8 × 4.1 in A7 105 × 74 mm 4.1 × 2.9 in A8 74 × 52 mm 2.9 × 2.0 in A9 52 × 37 mm 2.0 × 1.5 in A10 37 × 26 mm 1.5 × 1.0 in

In a letter written on 25 October 1786 by the German scientist Georg Christoph Lichtenberg to Johann Beckmann, the oldest recorded mention of the advantages of basing a paper size on an aspect ratio of $\sqrt{2}$ can be found. The formats that became ISO paper sizes A2, A3, B3, B4, and B5 were developed in France. They were mentioned in a law of 1798 on publication taxation that was partly based on page sizes.

### Types

• A2 Size Dimensions: 420 × 594 mm or 16.5 × 23.4 inches measures an A2 sheet of paper. Two A3 page size will be formed by splitting these in half. In a C2 envelope, an A2 piece of paper would fit in. It will fit into a C3 envelope when folded in half. A2 is part of the A-series and is specified by the international standard for paper size, ISO 216.

• A3 Size Dimensions: An A3 page size piece measures 297 × 420 mm or 11.7 × 16.5 inches in height. Two A4 sheets of paper will be formed by cutting them in half. In a C3 envelope, an A3 piece of paper would fit in. It will fit into a C4 envelope when folded in half. A3 is part of the A-series and is specified by the international standard for paper size, ISO 216.

• A4 Size Dimensions: 210 × 297 mm or 8.3 × 11.7 inches measures an A4 piece of paper. Two A5 sheets of paper would be formed by cutting it in half. In a C4 envelope, an A4 piece of paper would fit in. It will fit into a C5 envelope when folded in half. A4 is part of the A-series and is specified by the international standard for paper size, ISO 216.

### Properties

The aspect ratio of paper in the A series format is $\sqrt{2}$ (approximately 1,414, when rounded). Before rounding to the nearest millimetre, A0 is specified so that it has an area of 1 m2. Successive paper sizes in the series (A1, A2, A3, etc.) are described by halving and rounding down the area of the previous paper size so that A(n + 1)'s long side is the same length as An's short side.

Scaling is the key benefit of this method. The special property of rectangular paper with an aspect ratio of $\sqrt{2}$ is that when cut or folded halfway between its longer sides, each half has the same aspect ratio of $\sqrt{2}$ as the whole sheet before it was broken.

### Application

The ISO 216 formats are arranged around the 1: $\sqrt{2}$ ratio; two sheets have the same ratio together, horizontally, next to each other. Two A4 sheets reduced to A5 size fit exactly on one A4 sheet in scaled photocopying, for example, A4 page size in magnified size fits on an A3 page size; there is neither waste nor want in each case.