The encyclopedia · Product & Design · Product decision · 1786–1975
A4 paper won because its √2 ratio keeps every folded or copied half the same shape.
ISO 216's A series uses a 1:√2 ratio, so halving keeps proportions and wastes nothing, which made A4 the world's office-paper standard.
ISO · DIN · Georg Christoph Lichtenberg
the move
Before a common rule, paper came in many unrelated sizes. Copying needed trimming, filling cabinets needed odd folders, and a page-scale step changed the proportions, so print shops had to guess and cut.
The fix came from geometry. In a letter dated 25 October 1786, the German scientist Georg Christoph Lichtenberg pointed out the benefit of a paper ratio of the square root of two: cut a sheet in half and the half keeps the same ratio. Early A-family sizes appeared in a 1798 French tax law.
In 1921 the German standards body DIN published DIN 476, four series built on that ratio, with the A series preferred; A0 has an area of one square metre and A4 was recommended for business, administrative and government correspondence. The idea spread to dozens of national standards in the following decades.
In 1975 the system became international standard ISO 216 and the official United Nations document format, and it is used in almost all the world except a handful of countries in the Americas that keep North American sizes.
why it works
- A 1:√2 ratio means halving or folding keeps the exact proportions
- Area halves with each size, so weight and postage can be derived by arithmetic
- A single ratio makes A3-to-A4 copying a fixed 71% scale with no waste
- One standard let printers, copiers and envelopes all reference the same page
what transfers
When every downstream step must scale or fold, pick a shape that is invariant under that operation: the single geometric choice removes waste and makes the whole family interchangeable.
what came after
ISO 216 became the global default for business and administrative paper. The only significant holdouts, the United States and Canada, kept North American letter and legal sizes, which is why a supply of A4 still meets a different standard across the border. The ratio-based logic also carried into related standards, such as the B and C series for posters and envelopes.
references
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