# How A4 paper and Japanese architecture share the same geometric logic

By [Brandon Donnelly](https://brandondonnelly.com) · 2026-05-15

architecture, japanese-architecture, a4-paper, letter-paper, geometry, design, modular

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This post is ultimately going to be about architecture, but bear with me while I get there. The international standard for paper sizes has three series: [A, B, and C](https://www.adobe.com/uk/creativecloud/design/discover/guide-paper-sizes.html). From this standard comes A4 paper, which many of you might recognize as the most common paper size in the world, serving as the standard for most business documents. However, not all countries use this sizing. Canada and the US, for instance, use Letter-sized paper instead of A4, which is simply a result of a historical norm. Canada tried to switch to the international standard (ISO 216) when we started adopting the metric system in the 1970s, but our deep economic integration with the US made it simply too cumbersome to juggle different sizes of paper.

The beauty of A4 paper is that it follows something known as the Silver Ratio (which equals 1 : √2 or 1 : 1.414). Its exact dimensions are 210 x 297 mm. What's important about this ratio is that it allows for a perfectly recursive system. It works like this: A0 paper is 841 x 1189 mm (the same Silver Ratio) or exactly one square metre. If you fold this paper in half along its long side, you get two pieces of A1 paper with the exact same ratio. If you repeat the same fold, you will then get A2 paper, and so on, all the way down to A10 paper. The Silver Ratio is the only rectangle where, when you fold or cut it in half, the proportions stay exactly the same. This is a neat feature because it means there's no waste when manufacturing different paper sizes.

So, what does this have to do with architecture?

Well, the Silver Ratio is heavily embedded in Japanese architecture and heritage. In fact, it's also known as the "Japanese proportion." It has long been appreciated for the scale it creates — it's more square and humble, as opposed to rectangular and grand — and for the modularity that it affords. Indeed, the recursive nature of the ratio makes it practical for construction and perfectly suited to the Japanese concept of _mottainai_, which is a term that describes a deep sense of regret when things are wasted. A good example of this concept in practice is the recently completed [_Circularity Cabin_](https://www.nevertoosmall.com/post/small-home-circularity-cabin) by architect Takaaki Fuji. A simple family home made from standard store-bought timber, the 60 m2 structure follows a strict modular system to minimize waste and improve efficiency.

_Mottainai_ might be my new favourite Japanese concept.

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_Cover photo by_ [_Takuya Seki_](https://takuyaseki.com) _via_ [_Never Too Small_](https://www.nevertoosmall.com/post/small-home-circularity-cabin)

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*Originally published on [Brandon Donnelly](https://brandondonnelly.com/how-a4-paper-and-japanese-architecture-share-the-same-geometric-logic)*