Paper sizes (A4)

Why every A-paper folded in half makes the next size — and why the magic ratio is √2.

International paper sizes (A0, A1, A2…) all share one neat property: fold any of them in half along the long edge and you get the next size down with the same proportions.

Why √2 is the magic ratio

If a rectangle has sides 1 and √2, folding it in half gives one of size √2 / 2 by 1 — which is the same shape, just smaller. So the long-to-short ratio of 1 : √2 ≈ 1 : 1.414 is the only ratio that survives folding.

The A series

A0 — 841 × 1189 mm. Area = 1 m². Anchor of the whole series.
A1 — half of A0 → 594 × 841 mm.
A2 — half of A1 → 420 × 594 mm.
A3 — 297 × 420 mm.
A4 — 210 × 297 mm. The standard letter/printer size.
A5 — 148 × 210 mm. Half-page handouts.