How big is a sheet of paper?

When I was a kid, the size of a piece of paper was described by a name, some of which were almost poetic. A “standard” working pad would be “Foolscap”, which was 13″ x 8″ – somewhat similar to the current US “Legal” size which is 14″ x 8.5″. A full Foolscap sheet was actually 17″ x 13.5″ and this was halved and trimmed for everyday use. Other sizes include “Emperor” [72" × 48"], “Antiquarian” [53" × 31"], “Grand Eagle” [42" × 28.75"], “Double Elephant” [40" × 27"], “Colombier” [34.5" × 23.5"] and “Atlas” [34" × 26"] and a whole load of smaller sizes. There seems to be a certain amount of fuzziness in the definitions of these archaic dimensions.

Nowadays, most countries outside of the US talk in terms of “A4″ and its cousins …

The [almost] worldwide paper size standard is ISO 216. This is based on A0, which is a sheet that has an area of exactly 1 square meter, with sides on a ratio of 1 to the square root of 2 – i.e. approximately 1:1.4142. This yields dimension of approximately 841mm × 1189mm.

The system has the big advantage of scaling. If you divide an A0 sheet in two, parallel to the shortest side, you get two sheets with exactly the same aspect ratio – their size is A1. As you keep dividing, you get A2, A3, A4, A5 and so on. This also works for folding, of course. You can fold an A4 sheet to make an A5 brochure. Photocopying with enlargement/reduction is similarly straightforward.

In addition to the A series, the standard defines the B and C series of sizes. The B series are intermediate sizes based on similar mathematical relationships; B0 is 1000mm × 1414mm. The C series are for envelopes, which are designed to accommodate the A series of paper; a C4 envelope, for example, will comfortably take an A4 document without folding.

If you want all the details of the ISO standard and more on paper sizes, take a look here.

Something is a mystery to me. Given that paper size is more or less standardized, why do digital cameras have sensor sizes based on archaic ratios [i.e. that of 35mm and APS film]? Sure the 1:1.4142 ratio would make more sense?

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Posted April 11th, 2013, by

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This blog is a discussion of embedded software matters - news, comment, technical issues and ideas, along with other passing thoughts about anything that happens to be on my mind. The Colin Walls Blog


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Commented on 11 April 2013 at 18:30
By Peter Bushell

“why do digital cameras have sensor sizes based on archaic ratios [i.e. that of 35mm and APS film]?”

A similar question would be why do monitors keep getting wider and relatively shorter? Is this really advantageous in some field of activity or is it done so that the marketeers can quote ever-increasing diagonal “sizes” without incurring the cost of increasing the actual area?

If the trend carries on, we’ll have to find some way of coping with a very long line of light, one pixel wide, viewed through a diffraction slit.

Commented on 12 April 2013 at 09:42
By Colin Walls

Good point Peter. My screen nicely accommodates 2 A4 pages side by side, which suits my way of working. So they do get it right sometimes.
I like your final extrapolation.

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