International standard paper sizes
by Markus Kuhn (page from www.cl.cam.ac.uk)
Standard paper sizes like ISO A4 are widely used all over the world today. This text explains the ISO 216 paper size system and the ideas behind its design.
The ISO paper size concept
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.
The ISO paper sizes are based on the metric system. The square-root-of-two ratio does not permit both the height and width of the pages to be nicely rounded metric lengths. Therefore, the area of the pages has been defined to have round metric values. As paper is usually specified in g/m², this simplifies calculation of the mass of a document if the format and number of pages are known.
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.
The following table shows the width and height of all ISO A and B paper formats, as well as the ISO C envelope formats. The dimensions are in millimeters:
| 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 |
The ISO standard paper size system covers a wide range of formats, but not all of them are widely used in practice. Among all formats, A4 is clearly the most important one for daily office use. Some main applications of the most popular formats can be summarized as:
| A0, A1 | technical drawings, posters |
| A1, A2 | flip charts |
| A2, A3 | drawings, diagrams, large tables |
| A4 | letters, magazines, forms, catalogs, laser printer and copying machine output |
| A5 | note pads |
| A6 | postcards |
| B5, A5, B6, A6 | books |
| C4, C5, C6 | envelopes for A4 letters: unfolded (C4), folded once (C5), folded twice (C6) |
| B4, A3 | newspapers, supported by most copying machines in addition to A4 |
| B8, A8 | playing cards |
The main advantage of the ISO standard paper sizes becomes obvious for users of copying machines:
| fromto | 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% |