How ISO 216 sizes are derived
A0 measures 841×1189 mm and B0 measures 1000×1414 mm — both defined so the long side is √2 times the short side, with the published millimeter figures rounded to the nearest mm. Each higher number is the previous sheet folded in half along its long side, with the new short side cut down to a whole millimeter — so every published size stays close to √2 without sitting exactly on it (A4 is 297/210 = 1.4143, A5 is 210/148 = 1.4189).
- n — paper number, 0–10
- shortₙ / longₙ — short/long side of size n, in mm
- √2 — long-to-short side ratio (≈1.414); rounded to whole mm, every published size lands within ±0.7% of it
More detail
Why the √2 ratio matters
In the ideal geometry long/short = √2, so halving the long side gives a new sheet with the same aspect ratio and half the area. Whole-millimeter rounding means the published sizes only approximate that: A9 (37×52) is the flattest at 1.4054 and A8 (52×74) the tallest at 1.4231, both within ±0.7% of √2. Where the halving divides evenly the numbers are exact — A3 (124,740 mm²) is precisely twice A4 (62,370 mm²) — which is why an A4 sheet scaled to A3 looks identical, just bigger, with no stretching or letterboxing.
A series vs. B series
The A series (A0–A10) covers everyday printing — A4 for documents, A5 for notebooks. The B series starts from a larger base (1000×1414 mm vs. 841×1189 mm) and sits between two A sizes, used for posters, passports, and books where A sizes feel like an awkward fit.
Quick reference. A4 (210×297 mm) is the everyday document size; A3 is exactly double its area for posters and spreads. If you need a size between two A numbers, check the matching B number instead.
Frequently asked questions
What are the exact dimensions of A4 paper?
A4 is 210×297 mm. Select series A and number 4 above to see it computed directly from the A0 base size (841×1189 mm) via the halving rule.
Why is every ISO paper size in a ratio of √2?
Folding a sheet in half along its long side exactly preserves the long-to-short ratio only when that ratio is √2 (≈1.414). That's why A0 through A10 — and B0 through B10 — all look like scaled copies of each other.
What's the difference between the A series and B series?
A series starts at A0 (841×1189 mm, defined as 1 m²) and is used for documents; B series starts at B0 (1000×1414 mm, larger) and fills the gap between two A sizes — common for passports, posters, and books.
Is A0 exactly 1 square meter?
In theory yes — A0 is defined to have an area of exactly 1 m². The published 841×1189 mm dimensions are that theoretical size rounded to the nearest millimeter, so the actual printed area is 999,949 mm² (≈0.9999 m²), not perfectly 1 m².