Paper sizes
Every ISO and North American paper size, and the percentage to scale between any two — derived from three seed sizes and one rule rather than copied from another table. Nothing you type here leaves your browser — it is worked out on your own device, so there is nothing to send and nothing to log.
How the sizes are actually derived
Almost every explanation says: halve the area of the unrounded preceding size and round down. That rule does not produce the standard. It gives A0 as 840 × 1189 where ISO 216 says 841, and C0 as 917 × 1296 where the standard says 1297.
The rule that reproduces all thirty-three sizes is simpler: take the previous size as printed, halve its long edge, round down — and that is the new short edge. The old short edge becomes the new long one, unchanged. Three seed sizes (A0, B0, C0) and that one step give every size in the standard exactly, which is how this page produces its table rather than carrying thirty-three numbers somebody could mistype.
A0 is not one square metre
It is 841 × 1189 mm = 999,949 mm², or 0.999949 m². The definition asks for a square metre with sides in the ratio 1:√2, which comes to 840.896 × 1189.207 mm, and rounding to whole millimetres takes 51 mm² away. Nobody minds. It is still true, and it is the reason for the next section.
A5 is not half of A4
Because the rounding happens at every step and does not always land cleanly:
| A3 → A4 | Exactly half. 124,740 to 62,370 mm². |
|---|---|
| A4 → A5 | 0.34% short. Half of A4 is 31,185 mm²; A5 is 31,080. |
| A7 → A8 | 0.95% short — the worst in the series. |
Six of the ten halvings are exact and four are not. It has never mattered to anybody and it is not what the textbooks say.
Why 141% is on every photocopier
The ratio 1:√2 is the only one that survives being halved — cut a √2 rectangle across its long edge and you get two √2 rectangles. So every A size is the same shape, and scaling from any of them to the next is one number: 141.4% up, 70.7% down. Two steps is 200%. Nothing else on the page needs to be remembered.
North American sizes have no common ratio at all — Letter is 1:1.294 and Tabloid is 1:1.545 — which is why American copiers have a row of odd buttons and European ones have two.
Letter and A4 are not interchangeable
A4 is 6 mm narrower and 18 mm taller than Letter. There is no single percentage that converts between them, so printing one on the other either crops it or leaves a margin. Fitting Letter onto A4 is 97.3% and leaves 25 mm of A4 unused down the page; fitting A4 onto Letter is 94.1%. The tool above gives both, and says which edge the waste lands on.
What B and C are for
The B series is the geometric mean between consecutive A sizes, so B4 sits between A4 and A3. It is used for posters, for books, and in Japan for office paper. The C series is the geometric mean between A and B, which is exactly what makes a C4 envelope take an A4 sheet unfolded and a C5 take it folded once. That is not a coincidence; it is the reason the C series exists.
What it will not do
- It will not know your printer's unprintable margin. Almost no printer reaches the edge of the sheet, and the margin is a property of the machine rather than of the paper.
- It will not do Japanese B sizes (JIS B), which are a different series from ISO B and about 1.5% larger.
- It will not tell you about paper weight. Grammage is measured in grams per square metre, which is a separate question and a genuinely useful property of A0 being a square metre: an A4 sheet of 80 gsm paper weighs 80/16 = 5 grams.