(210mm by 297mm)
A4 Paper (ISO 216)
Abstract
This page is written to base an understanding of the signifiance of A4 paper. This inclues the origin, reasoning, and other uses of A4.
Origin
A4 was standarized by
Markus Kuhn who suggested in correspondence we call the ratio the Lichtenberg Ratio, after
Professor Georg Christoph Lichtenberg, a physics professor at University of Göttingen (Germany, 1742-1799), who first proposed the ratio as a basis for paper formats in 1786. [1]
Here is a paper for those interested in the
historic details.
Significance
In the ISO paper size system, the height-to-width ratio of all pages is the square root of two (1.4142 : 1). In other words, the width and the height of a page relate to each other like the side and the diagonal of a square. This aspect ratio is especially convenient for a paper size. If you put two such pages next to each other, or equivalently cut one parallel to its shorter side into two equal pieces, then the resulting page will have again the same width/height ratio. [2]
ISO 216 defines the A series of paper sizes based on these
simple principles:
- The height divided by the width of all formats is
the square root of two (1.4142).
- Format A0 has an area of one square meter.
- Format A1 is A0 cut into two equal pieces. In other words, the
height of A1 is the width of A0 and the width of A1 is half the height
of A0.
- All smaller A series formats are defined in the same way. If you
cut format An parallel to its shorter side into two equal
pieces of paper, these will have format A(n+1).
- The standardized height and width of the paper formats is a
rounded number of millimeters.
For applications where the ISO A series does not provide an adequate
format, the B series has been introduced to cover a wider range of
paper sizes. The C series of formats has been defined for envelopes. [2]
Geometry
| A Series Formats | B Series Formats | C Series Formats
|
|---|
| 4A0 | 1682 × 2378 | - | - | - | -
|
| 2A0 | 1189 × 1682 | - | - | - | -
|
| A0 | 841 × 1189 | B0 | 1000 × 1414 | C0 | 917 × 1297
|
| A1 | 594 × 841 | B1 | 707 × 1000 | C1 | 648 × 917
|
| A2 | 420 × 594 | B2 | 500 × 707 | C2 | 458 × 648
|
| A3 | 297 × 420 | B3 | 353 × 500 | C3 | 324 × 458
|
| A4 | 210 × 297 | B4 | 250 × 353 | C4 | 229 × 324
|
| A5 | 148 × 210 | B5 | 176 × 250 | C5 | 162 × 229
|
| A6 | 105 × 148 | B6 | 125 × 176 | C6 | 114 × 162
|
| A7 | 74 × 105 | B7 | 88 × 125 | C7 | 81 × 114
|
| A8 | 52 × 74 | B8 | 62 × 88 | C8 | 57 × 81
|
| A9 | 37 × 52 | B9 | 44 × 62 | C9 | 40 × 57
|
| A10 | 26 × 37 | B10 | 31 × 44 | C10 | 28 × 40
|
Fun:
A fun look at how A4 uses its beautiful basis for its ratio is looking at the
pentagon.
Sources:
Compiled together by Paul Schou on 5 Feb 2005.