Paper Size Converter
One Ratio Behind Every A-Series Sheet
The ISO 216 A-series paper sizes — A0 down through A10 — aren't arbitrary; every size in the series shares the same width-to-height ratio, and folding any sheet in half along its long side produces the next size down at exactly the same aspect ratio. That elegant property is why A4 fits proportionally inside A3, which fits inside A2, and so on. This calculator looks up any standard A-series size, or derives a matching height or width from that same ratio for non-standard dimensions.
The Formula
Width = Height / √2
The √2 ≈ 1.41421 ratio is what makes the series self-similar: cutting an A-series sheet in half across its long dimension yields two sheets, each with the same aspect ratio as the original, one size smaller.
Where This Calculation Matters
- International print jobs — most of the world outside North America uses A-series sizes as the default for documents, letterhead, and envelopes.
- Design software setup — setting up a custom document size that still preserves the standard A-series proportions.
- Scaling and imposition — understanding how many A5 flyers fit on an A3 sheet relies on this same halving relationship.
- Envelope and folder sizing — matching envelope dimensions to a folded A-series sheet requires knowing the exact ratio, not just a rounded approximation.
Standard ISO 216 A-Series Sizes
| Size | Millimeters | Inches |
|---|---|---|
| A0 | 841 × 1189 mm | 33.11 × 46.81 in |
| A1 | 594 × 841 mm | 23.39 × 33.11 in |
| A2 | 420 × 594 mm | 16.54 × 23.39 in |
| A3 | 297 × 420 mm | 11.69 × 16.54 in |
| A4 | 210 × 297 mm | 8.27 × 11.69 in |
| A5 | 148 × 210 mm | 5.83 × 8.27 in |
| A6 | 105 × 148 mm | 4.13 × 5.83 in |
These are the exact standard ISO 216 dimensions in millimeters; the inch figures are direct conversions (1 mm = 1/25.4 in) rounded to two decimal places.
How to Use This Calculator
- Choose a mode: A-Series Size Lookup, Known Width → Height, or Known Height → Width.
- In lookup mode, select the A-series size (A0 through A10) from the dropdown.
- In the ratio modes, enter the known width or height.
- Select Calculate to get the standard size or the matching dimension.
Related Calculations
Once you know the sheet size in the units you need, check the resulting paper weight in that region's units with the Paper Weight Calculator, or plan a layout with the Business Card Layout Calculator.