ISO Paper Sizes Explained: A0 to A6, the Square-Root-of-Two Ratio, and US Letter
October 21, 2026
Most of the world uses the ISO 216 paper sizes, in which every sheet has the same aspect ratio of 1 to √2, about 1:1.4142. This ratio has a neat property: cut a sheet in half across its longer side, and each half has the same proportions as the original. Therefore A3 halves into two A4 sheets, A4 into two A5 sheets, and so on, and you can scale documents from one size to another without changing their shape.
The series is anchored on A0, which has an area of exactly one square meter: 841 × 1189 mm. A4, the common office size, is 210 × 297 mm. The United States and Canada use Letter (8.5 × 11 inches, or 216 × 279 mm), which has a ratio of 1.294.
Skip the math and get your answer instantly:
Open the Aspect Ratio Calculator →Dimensions of the A-Series
Each step down halves the area. A1 is 594 × 841 mm, A2 is 420 × 594, A3 is 297 × 420, A4 is 210 × 297, A5 is 148 × 210, A6 is 105 × 148. The dimensions are rounded to whole millimeters. The area of A4 is 210 × 297 = 62,370 mm², about 1/16 of a square meter (since A0 is 16 times A4).
The B-series, used for posters and books, sits between the A sizes in geometric progression, and the C-series is used for envelopes that fit A-series paper.
| Size | Millimetres | Inches | Typical use |
|---|---|---|---|
| A0 | 841 x 1189 | 33.1 x 46.8 | Technical drawings, posters |
| A3 | 297 x 420 | 11.7 x 16.5 | Drawings, small posters |
| A4 | 210 x 297 | 8.27 x 11.69 | Letters, documents |
| A5 | 148 x 210 | 5.83 x 8.27 | Notebooks, flyers |
| A6 | 105 x 148 | 4.13 x 5.83 | Postcards |
| US Letter | 216 x 279 | 8.5 x 11 | Documents in North America |
| US Legal | 216 x 356 | 8.5 x 14 | Legal documents |
Why the Square Root of Two?
If a sheet has sides in the ratio x:1 and you cut it in half, the new sheet has sides 1 and x/2. For these to have the same ratio, x/1 = 1/(x/2), so x² = 2, and x = √2. This is the only ratio with this self-similar halving property. The idea was proposed by Georg Lichtenberg in 1786, and the standard was formalized in Germany in 1922 (DIN 476), later becoming ISO 216.
Photocopiers use this property: enlarging A4 to A3 is a 141% scaling, and reducing A3 to A4 is 71%, simple, regular factors.
Converting Between A4 and Letter
A4 is slightly narrower and taller than Letter: 8.27 by 11.69 inches versus 8.5 by 11. Printing an A4 document on Letter paper without scaling can cut off the top or bottom margins, and printing Letter on A4 can cut off the sides. Print dialogs offer 'fit to page' or scale options. The scale needed to fit Letter content onto A4 is about 97% (210 ÷ 216), and to fit A4 content onto Letter about 94% (279 ÷ 297). Set margins of at least 0.5 inch (13 mm) to reduce problems, especially in templates that must work in both regions.
Practical Tips
Check the paper size setting in your word processor before sending documents abroad, and use margins that work for both sizes. For printing posters, choose the size by viewing distance. For envelopes, use DL (110 × 220 mm), which fits an A4 sheet folded in thirds, or C5 for A5 sheets. In design software, set artboards to the target size from the start, because converting later changes the proportions.
Frequently Asked Questions
What are the dimensions of A4 paper?
210 by 297 millimetres, or 8.27 by 11.69 inches.
Why do A-series sheets have a ratio of 1.414?
Because that ratio keeps the same proportions when a sheet is halved.
How big is A0?
841 by 1189 mm, an area of one square meter.
Is US Letter bigger than A4?
Letter is wider (216 vs. 210 mm) but shorter (279 vs. 297 mm).
How do I print an A4 document on Letter paper?
Use the 'fit to page' scaling option to avoid cutting off content.