A4
In the A-series paper size, the ratio between length and width is √2 : 1.
Explanation
When a sheet of A4 paper is cut into two equal pieces (i.e. the surface halved), two sheets of A5 paper with exactly the same ratio in terms of dimensions are created.
√2 1
So it must apply
Note
If you turn a corner of a sheet of A4 paper, you get a bevel with length √2. So that is exactly the length of the sheet.
√2 1
Other sizes
An A4 paper measures 297 mm by 210 mm. In the United States, the US letter format 279.4 mm by 215.8 mm is often used, which is 6 mm wider and 18 mm shorter.