A format is based on homothetic, that is to say, the proportions must be maintained when a sheet is folded in its longest side. This feature allows you to reproduce every size A(x) in the size A(x+1) or A(x-1) maintaining the proportions of all what is on the page.

All A size are based on an aspect ratio which gives a proportion of 1.4142 (a / b = 2 b / a = √2). The square root of 2 is therefore the basis of size A. This is what Professor of Physics Georg Christoph Lichtenberg explained to his friend Johann Beckmann in a letter dated October 25, 1786, written on a sheet that just used this ratio. This is the oldest record of a homothetic format with √2 ratio.

We can therefore say that Lichtenberg is the father of A format as we know it today, and as it is worldwide used, that is to say, in all industrialized countries except the North America.

Lichtenberg ratio was taken in 1918 by Walter Portsmann, who proposed to the DIN (*Deutches Institut für Normung, german norms Institute*) to optimize storage, save space and especially harmonize once and for all formats used in Germany. DIN accepted it in 1922 (DIN 476), followed by 42 countries around the world. ISO 216 took over in 1975, making this format A ratio an international standard.

**All A formats are based on a number that determines the size of the paper. The A0, which is 1 square meter, can be declined above and below, to size A10. The length of the smaller size is always equal to width of the larger size. The smaller size is obtained by folding in half the larger size in its longest side. Whenever a format is divided into two, there is always the ratio √2 between length and width.**

- X
- A0
- A1
- A2
- A3
- A4
- A5
- A6
- A7
- A8
- A9
- A10
- A0
- 100
- 71
- 50
- 35
- 25
- 18
- 12.5
- 8.8
- 6.2
- 4.4
- 3.1
- A1
- 141
- 100
- 71
- 50
- 35
- 25
- 18
- 12.5
- 8.8
- 6.2
- 4.4
- A2
- 200
- 141
- 100
- 71
- 50
- 35
- 25
- 18
- 12.5
- 8.8
- 6.2
- A3
- 283
- 200
- 141
- 100
- 71
- 50
- 35
- 25
- 18
- 12.5
- 8.8
- A4
- 400
- 283
- 200
- 141
- 100
- 71
- 50
- 35
- 25
- 18
- 12.5
- A5
- 566
- 400
- 283
- 200
- 141
- 100
- 71
- 50
- 35
- 25
- 18
- A6
- 800
- 566
- 400
- 283
- 200
- 141
- 100
- 71
- 50
- 35
- 25
- A7
- 1131
- 800
- 566
- 400
- 283
- 200
- 141
- 100
- 71
- 50
- 35
- A8
- 1600
- 1131
- 800
- 566
- 400
- 283
- 200
- 141
- 100
- 71
- 50
- A9
- 2263
- 1600
- 1131
- 800
- 566
- 400
- 283
- 200
- 141
- 100
- 71
- A10
- 3200
- 2263
- 1600
- 1131
- 800
- 566
- 400
- 283
- 200
- 141
- 100

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