ISO 216 and US paper sizes, with aspect ratio and area calculated
A4 is 210 by 297 mm, which is 8.27 by 11.69 inches; US Letter is 8.5 by 11 inches, or 215.9 by 279.4 mm. A4 is narrower, taller and 3.4 percent larger in area. Every ISO size shares the ratio 1.4142, which is what lets each one fold into the next.
ISO 216 A series and the common US sizes
Each size is quoted in the unit its own standard defines it in: the A series in whole millimetres from ISO 216, the US sizes in inches. The other unit column is calculated through the exact inch of 25.4 mm, and the aspect ratio and area are calculated from the millimetre figures. 10 sizes in total.
| Size | Standard | Millimetres | Inches | Aspect ratio (long over short) | Area (m2) |
|---|---|---|---|---|---|
| A0 | ISO 216 | 841 x 1,189 | 33.11 x 46.81 | 1.4138 | 0.9999 |
| A1 | ISO 216 | 594 x 841 | 23.39 x 33.11 | 1.4158 | 0.4996 |
| A2 | ISO 216 | 420 x 594 | 16.54 x 23.39 | 1.4143 | 0.2495 |
| A3 | ISO 216 | 297 x 420 | 11.69 x 16.54 | 1.4141 | 0.1247 |
| A4 | ISO 216 | 210 x 297 | 8.27 x 11.69 | 1.4143 | 0.0624 |
| A5 | ISO 216 | 148 x 210 | 5.83 x 8.27 | 1.4189 | 0.0311 |
| A6 | ISO 216 | 105 x 148 | 4.13 x 5.83 | 1.4095 | 0.0155 |
| US Letter | ANSI A | 215.9 x 279.4 | 8.5 x 11 | 1.2941 | 0.0603 |
| US Legal | US traditional | 215.9 x 355.6 | 8.5 x 14 | 1.6471 | 0.0768 |
| US Tabloid | ANSI B | 279.4 x 431.8 | 11 x 17 | 1.5455 | 0.1206 |
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The ratio that makes the A series work
Every ISO 216 size has the same shape: the long side divided by the short side is the square root of two, 1.4142. That is the only ratio that survives being folded in half, because halving the long side of a sheet with that proportion produces a sheet with the same proportion again.
The consequence is the property everybody uses without thinking about it. A3 folds to A4, A4 folds to A5, and a document scaled from one to the next needs a single scale factor of about 0.7071 with no cropping and no changed margins. Photocopier buttons marked 71 percent and 141 percent are that ratio rounded.
The series is anchored by area rather than by a side length. A0 is defined as one square metre at that ratio, which is why the table computes 0.9999 m2 for it: 841 by 1189 mm is the nearest whole-millimetre pair to the exact answer. Every step down halves the area, so A4 is a sixteenth of A0 at 0.0624 m2.
Why this matters when a document crosses the Atlantic
US Letter is neither the same shape nor the same size. Its ratio is 1.2941 against the A series 1.4142, so it is relatively wider and shorter, and A4 carries 3.4 percent more area. A layout that fits one will not sit correctly on the other without either scaling or a margin change.
In practice A4 is 17.6 mm taller and 5.9 mm narrower than Letter. That is enough to push the last line of a full page onto a second sheet, or to clip a design that assumed the wider format, which is the usual reason a PDF prints wrongly in the other market.
The safe habit for anything that will be printed in both places is to keep the content inside the overlap: the width of A4 and the height of Letter. A document laid out that way prints correctly on either sheet without scaling.
Legal, Tabloid and the sizes around them
US Legal keeps the Letter width and stretches to 14 inches, so its ratio drifts further from the A series again at 1.6471. Tabloid, also called Ledger, is exactly two Letter sheets side by side at 11 by 17 inches, which mirrors what A3 is to A4.
The ANSI series continues upward from Letter as ANSI A through ANSI E, alternating shape at each step rather than holding one ratio, which is precisely the property the ISO series was designed to avoid. That alternation is why enlarging an ANSI drawing to the next size does not preserve its proportions.
Below A6 the ISO series carries on to A10, and the B and C series exist alongside it for posters and envelopes. C4 envelopes take an unfolded A4 sheet, C5 takes an A4 folded once, and that relationship is the whole reason the C series has its own ratio anchor.
Frequently asked questions
What size is A4 in inches?
8.27 by 11.69 inches, converted from the ISO 216 definition of 210 by 297 mm through the exact inch of 25.4 mm. The commonly seen 8.3 by 11.7 is that figure rounded to one decimal.
Is A4 bigger than US Letter?
In area, yes, by 3.4 percent. In shape they differ both ways: A4 is 17.6 mm taller and 5.9 mm narrower. That combination is why a Letter-sized layout can overflow on A4 and an A4 layout can be clipped on Letter.
Why is A4 210 by 297 mm rather than a round number?
Because the series is defined by area and ratio, not by side lengths. A0 is one square metre with sides in the ratio 1.4142, each step halves the area, and the results are rounded down to whole millimetres. 210 by 297 mm is what falls out of that at the fourth halving.
How do I scale A4 to A3 without distortion?
Enlarge by 141.4 percent, or reduce A3 to A4 by 70.7 percent. Because every A size shares one ratio, that single factor moves a document up or down the series with no cropping and no change to the proportion of the margins.
What is the area of an A4 sheet?
0.0624 square metres, calculated from 210 by 297 mm. That is one sixteenth of A0, which is one square metre by definition, and it is the figure paper weight in grams per square metre is applied to when you work out what a ream weighs.
Can I republish this table?
Yes, under Creative Commons Attribution 4.0 International (CC BY 4.0). Credit UnitGlide, https://unitglide.net and link back. The dimensions are facts from published standards; the calculated ratio and area columns and the compilation are what this licence covers.
Sources
- ISO 216, writing paper and certain classes of printed matter, trimmed sizes, for the A series trimmed sizes in millimetres and the square root of two ratio.
- NIST Special Publication 811, for the exact inch of 25.4 mm used to convert between the millimetre and inch columns.
- ANSI/ASME Y14.1, decimal inch drawing sheet size and format, for the ANSI A and ANSI B sheet sizes that US Letter and Tabloid correspond to.