About A4 paper

ISO 216 defines three groups of paper sizes: A, B, and C. Group C paper sizes are primarily used for envelopes.

The commonly used paper size is A4, which measures 21cm×29.7cm (210mm×297mm).

How big is an A4 paper?

Group A paper

The aspect ratio of the dimensions is √2:1.

The foundation for developing the A series begins with obtaining a sheet of paper with an aspect ratio of √2 and an area of 1 square meter (m2). Therefore, the width and length of this sheet of paper are 841 millimeters and 1189 millimeters respectively (aspect ratio of √2:1), and it is numbered A0. If the long edge of the A0 paper is cut in half, two sheets of A1 paper are obtained, both with a width of 594 millimeters and a length of 841 millimeters. By continuing to cut the A1 paper in half in this manner, one can sequentially obtain A2, A3, A4, and so on. When establishing standards, dimensions are based on whole numbers, so if the cut paper dimensions have decimals (less than 1 millimeter), they are rounded off for calculation.

Group B paper

The size is the geometric mean of Group A paper with the same number and the paper with one less number.
The B series is based on the concept of obtaining a sheet of paper with a width of 1 meter and an area of √2 square meters (m2). 

Therefore, the width and length of this sheet of paper are 1000 millimeters and 1414 millimeters respectively (with a length-to-width ratio of √2:1), and it is numbered B0. If the long edge of B0 paper is cut in half, two sheets of B1 paper are obtained, with a width and length of 707 millimeters and 1000 millimeters respectively. By continuing to cut the B1 paper in half in this manner, one can obtain B2, B3, B4, and so on in sequence. Compared to the A series, the area of B series paper is √2 times that of the corresponding A series paper. For example, the area of B4 paper is √2 times that of A4 paper. (Additionally, there is an incompatible B group paper size in Japan, which is defined using arithmetic mean rather than geometric mean.). ）

Group C paper

The size is the geometric mean of Group A and Group B papers with the same number.

The basis for formulating the C series is to obtain the geometric mean of the dimensions of the A series and B series. For example, the paper size of C4 is the geometric mean of A4 and B4 sizes, and the aspect ratio of the paper remains √2:1. In this way, the size of C4 falls between A4 and B4. A4 paper can be placed into an envelope bag of C4 size, and C4 paper can be placed into an envelope bag of B4 size.

Other formats

Before the widespread adoption of ISO 216, there were many different paper formats internationally. These formats were not a coherent system, and many were not defined using metric units. The format of ISO 216 follows a 1:√2 ratio; two sheets placed together have the same aspect ratio and side margins. This characteristic simplifies many things, such as: reducing two 

A4 sheets and photocopying them onto one A4 sheet; enlarging an A4 sheet and photocopying it onto an A3 sheet; photocopying and enlarging half of an A4 sheet onto an A4 sheet, and so on. The main obstacle to this standard is the United States and Canada, which still use the Letter, Legal, and Executive paper size systems. (Canada uses a P group paper size, but it is actually the paper size used in the United States, rounded to the nearest metric size.)