Editing ISO 216 (section)

==Advantages==
The main advantage of this system is its scaling. [[Rectangle|Rectangular]] paper with an aspect ratio of <math display="inline">\sqrt{2}</math> has the unique property that, when cut in two across the midpoints of the longer sides, each half has the same <math display="inline">\sqrt{2}</math> aspect ratio as the whole sheet before it was divided. Equivalently, if one lays two same-sized sheets of paper with an aspect ratio of <math display="inline">\sqrt{2}</math> side by side along their longer side, they form a larger rectangle with the aspect ratio of <math display="inline">\sqrt{2}</math> and double the area of each individual sheet.

The ISO system of paper sizes exploits these properties of the <math display="inline">\sqrt{2}</math> aspect ratio. In each series of sizes (for example, series A), the largest size is numbered 0 (so in this case A0), and each successive size (A1, A2, etc.) has half the area of the preceding sheet and can be cut by halving the length of the preceding size sheet. The new measurement is rounded down{{dubious|Contradictory?|date=April 2025}} to the nearest millimetre. A folded [[brochure]] can be made by using a sheet of the next larger size (for example, an A4 sheet is folded in half to make a brochure with size A5 pages). An office [[photocopier]] or printer can be designed to reduce a page from A4 to A5 or to enlarge a page from A4 to A3. Similarly, two sheets of A4 can be scaled down to fit one A4 sheet without excess empty paper.

This system also simplifies calculating the weight of paper. Under [[ISO 536]], paper's [[grammage]] is defined as a sheet's mass in [[gram]]s (g) per area in [[square metre]]s (unit symbol g/m<sup>2</sup>; the nonstandard abbreviation "gsm" is also used).<ref name="ISO 536">{{Cite web
|url=https://www.iso.org/obp/ui/#iso:std:iso:536:ed-4:v1:en
|access-date=8 June 2021
|author=International Organization for Standardization |author-link=International Organization for Standardization
|title=ISO 536:2019(en): Paper and board — Determination of grammage
|edition=4 |at=§&nbsp;3.1 note 1.
|work=ISO Browsing Platform
|date=November 2019}}</ref>  One can derive the grammage of other sizes by [[Division (mathematics)|arithmetic division]]. A standard A4 sheet made from {{Nowrap|80 g/m<sup>2</sup>}} paper weighs {{convert|5|g}}, as it is {{frac|1|16}} (four halvings, ignoring rounding) of an A0 page. Thus the weight, and the associated [[mail#postage|postage rate]], can be approximated easily by counting the number of sheets used.

ISO 216 and its related standards were first published between 1975 and 1995:
* ISO 216:2007, defining the A and B series of paper sizes
* ISO 269:1985, defining the C series for envelopes
* ISO 217:2013, defining the RA and SRA series of raw ("untrimmed") paper sizes