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A4 paper sizing: Why is A4 sized the way it is?

In the US, there is little understanding of the A4 paper size used everywhere except in North America.

It is a great system – elegant and rational – and worth looking at.  There is also a reason that your 3-ring binder won’t work with A4 paper as it is taller.

The A series of paper sizes are designed so that when you cut one in half, you get two pieces of the next-smallest-size, and every size has height and width in the same proportion. A little math reveals that one can achieve this by having the height and width in the ratio sqrt(2):1, or approximately 1.414:1.

So once you’ve decided that this is the ratio you want for your page, how do you decide the absolute size?

In the case of the A series of paper sizes, an A0 piece of paper is exactly 1 square metre, requiring width x width x 1.414 = 1, which gives a width of 84.1cm and height of 118.9cm (to the nearest mm).

An A1 piece of paper has a length that’s the same as the width of A0, or 84.1cm, and a width of 84.1cm / sqrt (2) = 59.5cm. Which you’ll notice is half the height of the A0 size (118.9cm).

These relationships hold true going all the way down to A10:

It happens that of the A series, A4 is the one that’s closest to the traditional size used for correspondence, and this has therefore become the de facto standard paper size in the metric world (i.e. pretty much globally except the United States).

One fairly obvious consequence of this is that one can make a booklet of a particular size, from a sheet of the next-largest-size folded in half. So A3 sheets of paper can be folded to create A4-size booklets.

Another interesting consequence is that it becomes easy to calculate the weight of single sheets. Standard photocopy paper is usually 80gsm (grams per square metre), thus an A0 sheet, being 1 square metre, weighs 80g. An A1 weighs 40g, A2 is 20g, A3 is 10g, and A4 is 5g. (And so on.)

Stumbled on at Quora


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