A4 paper

A Japanese diagram showing the size of an A4 sheet of paper

I love conferences (okay IWMW 2006 wasn’t a conference it was a workshop!) where you come away with little facts like the ratio of the long side of a sheet of A4 paper to the short side is 1:1.4142, which is 1:√2 (one to the square root of two).

A4 paper is genius! It’s an international standard (if someone could please tell the Americans, with their Letter size nonsense!) defined by ISO 216.

Here is what the lovely Wikipedia has to say on the matter of ISO A4:

A4 is a standard paper size, defined by the international standard ISO 216 as 210—297 mm (roughly 8.27—11.69 in). It is the normal size of paper for both domestic and business purposes in all countries except the United States, Canada, Mexico, the Philippines, Chile and other American countries. See paper size standards in North America.

An A4 sheet cut in half along the long side produces two A5 sheets. An A3 sheet is double the area of an A4. All the A paper sizes are similar to each other. The ratio between the long side and short side is the square root of 2 (i.e. the short side * √2 (which is approximately 1.414)). This ratio remains the same when the sheet is cut in half along the long side.

But does it stop there? No siree. Look, there’s a whole page about other paper sizes, like A0, A1, A2, A3, A5, A6, A7 and A8. And it’s not just A4 that has that groovy 1:1.4142 ratio, they all do! Wikipedia again:

ISO paper sizes are all based on a single aspect ratio of the square root of two, or approximately 1:1.4142. Basing paper upon this ratio was conceived by the German scientist Georg Lichtenberg in 1786

Just thought I’d share that with you…

Published by

Gareth Saunders

I’m Gareth J M Saunders, 52 years old, 6′ 4″, father of 3 boys (including twins). Enneagram type FOUR and introvert (INFP), I am a non-stipendiary priest in the Scottish Episcopal Church, I sing with the NYCGB alumni choir, play guitar, play mahjong, write, draw and laugh… Scrum master at Safeguard Global; latterly at Sky and Vision/Cegedim. Former web architect and agile project manager at the University of St Andrews and previously warden at Agnes Blackadder Hall.

8 thoughts on “A4 paper”

  1. Just found your blog on the 1st page of Google results of a search for “a4 paper” while trying to find a supplier for A4 paper in the US. Anyway, just wanted to say that this is one American who thinks that a4 rocks and we’re stupid not to have converted to it already.

    Along with metric measurements, the euro, etc…

  2. The ISO paper sizes are based on the metric system. The square-root-of-two ratio does not permit both the height and width of the pages to be nicely rounded metric lengths. Therefore, the area of the pages has been defined to have round metric values.

  3. Clarification on the Wikipedia article: A4 (and the rest of the A series sizes) have been officially adopted in The Philippines (and readily available at shops and office suppliers albeit at a slightly higher price than letter/legal), however everyone is so used to the American letter/legal sizes that they’re still the dominant paper sizes in The Philippines

  4. I found a reference to “American A4” which was extremely puzzling because (as you know) A4 is well-defined and NOT American!
    Happy to see that at least some Americans have seen the light.
    A4 is extremely elegant and (surprisingly) also practical.
    I am a South African, and proud that we have “gone metric” about 40 years ago – while the USA have not managed much of that, to their detriment. Aren’t there some Americans who want to start a “Let’s join the rest of the word” movement?

  5. A document formatted for A4 paper must be reformatted (possibly causing page numbering and referencing errors) to print on Letter size — otherwise information at the bottom of the longer A4 page may be lost.

  6. It is always interesting to learn something new about ordinary things. We use A4 paper all our lives and I never thought of such ratio. Your post has become useful for my erudition 🙂

  7. US letter isn’t a nice format, it’s almost illogical! I love the A series of paper sizes, it makes total sense. Well as far as I’m concerned US can keep their letter format whilst the rest of us use the lovely A4!

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