The first evidence of standard paper sizes being discussed was in a letter dated October 1786 written by physics Professor Georg Christoph Lichtenberg to his friend Johann Beckmann. In his letter, Lichtenberg outlined the benefits of a height to width ratio of 1 to the square root of 2.

And indeed, that's where we've arrived. ISO 216 paper sizes are all based on a single aspect ratio of the square root of 2, or approximately 1:1.41421; and each ISO paper size is one half of the area of the next larger size in the same series.

There are 11 sizes in the A series, designated A0 to A10. The A0 base size is defined as having an area of 1m² with dimensions, rounded to the nearest millimetre, of 1,189mm × 841mm. As metric paper weights are usually measured in grams per square metre (gsm), this doubling/halving relationship between each size makes mass calculations very easy when dealing with large volumes of paper in the print and publishing industries. An A0 sheet of 80gsm paper weighs 80g. So, an A5 sheet of that same paper would weigh 1/16 of that 80g, i.e. 5g. This gives the A series of paper another great trick up its sleeve that saves printers and designers time when estimating weights for printed things.

The shared aspect ratio across all sizes also means that (say) an A4 page can be scaled up by 41% and all the artwork and text is the perfect width and height to fill an A3 page. Similarly, scaling A4 artwork down to 71% of its original size will see it fit perfectly on an A5 page with no unpleasant stretching, squashing, or redesigning of artwork required. Thank you Lichtenberg!

Series C, the basis for many envelope formats, is based on C0 with width of 917mm, and Series B is a bit bigger again, based on B0 with width of 1m.

This is all very soothing. However, the United States will have none of it. Over there, the US “Letter” (8.5 x 11 inches) and “Legal” (8.5 x 14 inches) sizes are almost exclusively used.

And why those particular sizes? The answer is historical and somewhat pragmatic. Early paper makers dipped wooden framed screens of various sizes into vats of water and pulp. These “vat men” would then heave them back out — all by hand — and once they’d left them to dry, they’d end up with large sheets of paper. One of the common frame sizes was a size that was about 44 inches x 17 inches. Cutting those paper sheets into quarters would result in “letter” sized sheets that were 8.5 x 11 inches.

And last but not least there is “foolscap” at 8.5 x 14 inches.

Foolscap was named after the fool's cap and bells watermark commonly used from the 15th century onwards on paper of these dimensions. This was a traditional paper size used in some parts of Europe, and the British Commonwealth, before the adoption of the ISO 216 standards.

According to Mark Pitts, an executive director at the American Forest and Paper Association, restaurants are still big buyers of foolscap paper. The extra length works well for a daily menu. Folded in half, they makes a perfect cocktail menu, and in half again, it’s just right for daily specials.

Story Idea: Jane Campbell
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References

wikipedia.org/wiki/Paper_size
wikipedia.org/wiki/Foolscap_folio
news.gatech.edu/archive/features/hidden-georgia-tech-robert-c-williams-museum-papermaking.shtml
Lichtenberg’s letter to Johann Beckmann

Images

1. A Series sizes with US Letter and Legal
2. Georg Christoph Lichtenberg (1 July 1742 – 24 February 1799)
3. The Lichtenberg ratio of 1:√2
4. ISO 216 paper sizes: A, C and B series
5. Map of the world showing adoption of paper sizes. ISO is blue.
6. Foolscap paper watermark: Fool's hat with bells
7. An early paper frame with watermark mould. Courtesy Georgia Tech Institute Communications.
8. Paper sizes A0 to A8, life-size installation "The invasion of the square root" at the CosmoCaixa Barcelona science museum