ISO 216 Standard
ISO 216 sets the A and B paper series used in each country except the United States and Canada. Two rules define it: the sides sit in the ratio 1 : √2, and each size is half the area of the size above.
At a Glance
| Full name | Writing paper and certain classes of printed matter |
|---|---|
| First published | 1975 (from DIN 476, 1921) |
| A0 definition | 2^(-1/4) m × 2^(1/4) m = 841 × 1189 mm, area 0.999949 m² |
| Covers | A series and B series trimmed sizes |
| Does not cover | Envelopes (ISO 269), untrimmed RA/SRA stock (ISO 217), US sizes, JIS B |
| Current edition | ISO 216:2007 |
The √2 Rule
The ratio 1 : √2, about 1 : 1.414, is the only proportion that survives being halved. Cut a 1 : √2 rectangle across its long side and the two halves keep the same proportion. That is why an A3 sheet folds to two A4s, and why each photocopier has 71% and 141% zoom buttons, reducing one A size to the next is ×0.707, enlarging is ×1.414, with no distortion.
The A Series
A0 is defined as 2−1/4 metres wide by 21/4 metres tall, which works out to 841 × 1189 mm and an area of 0.999949 m², one square metre bar a rounding error. Each smaller size halves the longer side of the one above and rounds down to the nearest millimetre: A1 is 594 × 841, A2 is 420 × 594, down to A10 at 26 × 37 mm. Full A series table.
The B and C Series
B sizes are the geometric mean of two consecutive A sizes, so B4 sits between A3 and A4; B0’s short side is exactly one metre. C sizes are the geometric mean of the A and B size with the same number (C4 is between A4 and B4) and are used for envelopes, a C4 envelope holds an A4 sheet unfolded.
Tolerances
ISO 216 permits a manufacturing deviation of ±1.5 mm for dimensions up to 150 mm, ±2 mm between 150 and 600 mm, and ±3 mm above 600 mm. This is why two sheets both sold as A4 rarely align exactly.
RA and SRA: Untrimmed Sizes
Commercial printing starts from larger sheets so the press has room for gripper margin and bleed. ISO 217 defines RA (raw format A) at 860 × 1220 mm for RA0 and SRA (supplementary raw format A) at 900 × 1280 mm for SRA0. The printed job is trimmed down to its ISO 216 size afterwards.
Where It Came From
Georg Christoph Lichtenberg described the √2 sheet in a letter dated 25 October 1786. Early √2 formats appeared in an 1798 French law on the taxation of publications. Walter Porstmann tied the idea to the metric system in 1918, and it was published as German standard DIN 476 in 1921. In 1975 it became ISO 216 and the official document format of the United Nations.
Where It Is Not Used
The United States and Canada use Letter, Legal and Tabloid, fixed by custom before ISO 216 existed. The Philippines and parts of Latin America, Mexico, Colombia, Chile, Peru and Panama among them, also use mostly US sizes. Everywhere else uses ISO 216. See how A4 compares with Letter.
Frequently Asked Questions
Which countries use ISO 216 paper?
Each country except the United States, Canada, the Philippines and parts of Latin America, where US sizes are still common.
What are the 71% and 141% buttons on a photocopier?
They scale between ISO paper sizes. 141% (√2) enlarges one A size to the next up, such as A4 to A3; 71% (1/√2) reduces it one size down. The √2 ratio means nothing is cropped.
Is US Letter part of ISO 216?
No. Letter is 216 × 279 mm and follows no geometric rule; ISO 216 sizes all follow the 1 : √2 rule.
Why is A4 not exactly 210 × 297 by calculation?
It is. A0 is set so its area is one square metre; each smaller size halves the long side and rounds down to the nearest millimetre, so A4 lands on 210 × 297.
✓ Details per the cited standards and the ISO catalogue. Last verified . Editorial Process →