Paper Sizes

What are the ISO paper sizes?

ISO 216 defines three families. The A series is the one you use daily: A0 is a sheet of one square metre, and every size after it is the previous one folded in half. The B series sits between the A steps, with B0 exactly one metre wide. The C series is for envelopes, sized between A and B of the same number so that a C4 envelope swallows an A4 sheet without folding it.

The tables here are generated from the standard's construction rather than copied from somewhere, and every one of the 33 sizes is checked against the published figures. You can read them in millimetres, inches, PostScript points or pixels at whatever resolution you pick.

The interesting part is not the numbers, though. It is why A4 is 210 by 297 rather than something rounder.

How to use this page

1. Pick a series and a resolution. A for ordinary paper, B for posters and books, C for envelopes. The pixel column recomputes for whichever DPI you choose — 300 for print, 96 for the web, or type your own.
2. Use the comparison box to check a scale. Type any two sizes, ISO or North American. It gives the scale factor and, more usefully, says whether one factor fits both edges. Within a series it always does; across the Atlantic it never does.
3. Look at the ratio column. Every ISO size sits near 1.414 and every North American one does not, which is the whole difference between the two systems in a single column of numbers.

Why √2, and why it could not be anything else

Fold a sheet of width w and height h in half across its long side and you get a sheet measuring h/2 by w. For the new sheet to be the same shape as the old one, h/w must equal w divided by h/2. Rearranged, that is h² = 2w², so h/w = √2. There is no other answer: √2 is the only number that is unchanged when you map it to 2 divided by itself.

That is the entire design. Because the ratio survives folding, every A size is a scaled copy of every other A size, so enlarging A4 artwork to A3 is a single scale factor with nothing cropped and nothing left blank — and the factor is exactly √2, about 141 per cent, which is the number on every photocopier in Europe.

US Letter is 8.5 by 11 inches, a ratio of 1.292. Fold it and you get 1.548, a different shape. Legal is 1.648, and Tabloid 1.548, and no two of them match. There is no size in that system you can halve to get another one, which is why enlarging Letter to Legal is not an enlargement at all: Legal is the same width as Letter and simply longer. The closest any North American size comes to √2 is Executive at 1.451, still 0.037 away.

The sizes are generated, not tabulated — and that matters

It is tempting to assume each size comes straight from the formula, and building this page that way produces a table that is subtly wrong. Take A0: one square metre at ratio √2 works out to 840.896 by 1189.207 millimetres. Floor that and you get 840, but the published A0 is 841. Round instead and A0 comes out right while six other sizes go wrong — A5 becomes 149 where the standard says 148.

The actual rule is sequential. Round the base size once, then produce every later size by halving the previous one and rounding down. Only that order reproduces all 33 published A, B and C sizes, and it is why A5 is 148: it comes from halving 297, not from rounding 148.651 on its own.

The rounding has a visible cost, and it is worth stating rather than hiding. Because real sheets are whole millimetres, no ISO size is exactly √2. A4 is 1.41429. The worst case across all three series is C10 at 1.4286, which is 1.02 per cent off the ideal; within the A series alone the worst is 0.63 per cent. In practice that is invisible, but it does mean folding a real A8 sheet does not land exactly on A9.

Honest limits

The pixel column is a conversion, not a promise about your printer. It rounds, because a canvas cannot be 2480.3 pixels wide — which is exactly why A4 at 300 DPI is 2480 by 3508. One consequence surprises people: doubling the resolution does not quite double the pixel count, since 4960.63 rounds to 4961 rather than 4960. Both figures are correct; they are rounded independently.

Nor do these dimensions account for printer margins. Almost no desktop printer can put ink on the full sheet, so the printable area is smaller than every number here by a few millimetres on each edge, and how much varies by machine. If you are laying out a full-bleed design, the sheet size is the starting point rather than the answer.

The North American sizes are given in millimetres rounded from their inch definitions, which is why they look untidy. Letter is exactly 8.5 by 11 inches; 216 by 279 millimetres is that value rounded, and converting back gives 8.504 by 10.984. If you need exactness in a US workflow, work in inches and let this table be the approximation it is.

Why is it free?

Because it is arithmetic on a public standard. The whole page is generated in your browser from the construction ISO 216 describes — nothing is uploaded, nothing is stored, and no server is involved in reading a table.

So there is no account, no sign-up and nothing held back. The script that generates the sizes and checks all 33 of them against the published figures sits in the repository alongside the page.