08 January 2015

Guest Post - Metric Paper Sizes - Alan

The typical North American has very little appreciation of the wonders and logic of metric paper sizes.  Rather, when confronted with something produced on A4, the metric equivalent to Letter sized, they are likely to grumble about the extra 7/10ths of an inch of length that inevitably results in some sticking out of binders, file folders, etc.

In fact, it is this extra 7/10ths of an inch, and the fact that it doesn’t fit into standard North American filing systems that have been a major impediment to metrification of paper in North America.


So, what is the logic of metric paper sizing?

First, when metric sizing was being devised, it was decided that scalability among the various sizes would be part of the implementation.  This means that ASPECT RATIO, the ratio of the length to the width, would always be the same.  (Aspect ratio can be either Length over Width or Width over Length; I’ll use Length over Width in this post.) North Americans trying to scale something formatted for letter (11x8.5”) up tabloid (17x11”) or down the opposite way, have been vexed by the fact that there will either be some wasted white space or elongation or compression in one dimension due to the different aspect ratios.  Letter sized has an aspect ratio of 11/8.5 = 1.294 whereas tabloid has an aspect ratio of 17/11 = 1.545.  

A few years before the French Revolution, over 200 years ago, Georg Christoph Lichtenberg, a German scientist, noted that paper with an aspect ratio of √2 (=1.4142…) would allow any page to be folded in half and the resulting folded sheet would have the same aspect ratio of 1.4142.  (In fact, √2 is sometimes referred to as the Lichtenberg Ratio.)  

Shortly after the First War, another German scientist, Dr. Walter Porstmann, developed a formal system of metric based paper sizes.  The starting point was a sheet of paper with an area of one square meter with an aspect ratio of √2 or 1189x841mm, rounded to the nearest millimetre.  This was designated A0, read as “A-zero”.  Folding this in half once results in a sheet half the size but retaining the same aspect ratio of √2, called A1.  Folding an A1 in half once results in a sheet half the size (1/4 m2) but retaining the same aspect ratio of √2, called A2.  Here is a table of the A-series paper sizes:




So where does B5, used in the Deskfax, fit in?  Every B-sized page has an area that is √2 times larger than the A-sized bearing the same number.  Thus, Area(B5) = Area(A5) x √2 and Area(A4) = Area(B5) x √2.  This puts the B-series papers half-way between adjacent A-sized paper sizes.

In the “Files” section of the blog, there is a new file called “Paper Size Diagrams” that illustrates the various paper sizes, including the different planner page sizes. Download the docx version or the pdf version

Thank you Alan for your excellent explanations. 

19 comments:

  1. Good morning :-) excellent post, Alan! I did enjoy reading it. Thank you.

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  2. Alan, thanks for a very well-written piece, it made it easy to understand. The diagram of the diagonal line was especially enlightening. It always vexed me when I went to the US and had to make notes on Letter paper, which then didn't fit in my file when I got back. The ability to take an A4 document, and easily reduce to A5, then punch and file in a Filofax was one of the biggest benefits for me, when I was involved in project and programme management. I just couldn't have done it with Personal size, due to the massive overhead of cutting to size and printing. I have always wondered if the US would ever be able to make the switch as it seems so deeply entrenched in business and government. Do you think this is widely known and hankered for, by the majority of the American public, or is it just invisible to them?

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    1. Based on my experience (German but I worked in the US for a few months) it's unknown to most Americans. The company I worked for had bought an US subsidiary and they were really vexed with and confused by the DIN/EN standards, even the engineers. They all didn't know about them.

      It was not only the actual paper which didn't fint into US binders but also all the documents created in Word/Excell/Powerpoint. They were of course in A5 and not letter-size which made printing them an issue and they had to be reformatted. Same of course with documents send from the US to Germany/Switzerland.

      I still have my letter of recommendation from that time and filing it is always a problem because it doesn't fit into the standard punched pockets we have in Germany.

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    2. Paul: It IS virtually unknown or invisible to the American public, who are extremely resistant to change. My guess is that 98% would question why they need to change something that works perfectly well. In addition, millions of letter sized filing cabinets and unadjustable three hole punches would become obsolete.

      Also, from a planner perspective, Franklin Covey sizes are not consistent with metric. The full-page Monarch - often a zipped binder - might not have enough room top and bottom for A4; the Classic uses half-sheet, which is quite close to A5 and "Plannerds" do use A5 in half-sheet and half-sheet in A5. However, the half-sheet binders made here are either 7-ring (Franklin Covey) or 3-ring (Coach, Martha Stewart, Hilroy, etc.) with the ring spacings different than A5.

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    3. I wonder if Personal sized paper originates from the US from the LeFax days? Perhaps the dimensions are cut from a US paper size? Possibly from book publishing which seems to have its own unique paper sizing? ISO 216 (and foolscap/folio) was designed in ratio to be halved, quartered etc to save on paper wastage (costs) when printing and to estimate the cost of postage by calculating the weight per sheet. It seems extraordinarily wasteful (costly) to get only 3 sheets of Personal out of a sheet of A4, so I wonder if at some point there was a paper size four times the size of Personal? Of course back then it would have been measured in inches!

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    4. The Imperial sizing of Personal (6.75"x3.75") has been around for decades and was supported by North American Companies like Oxford and Hilroy, in addition to being used by Lefax and Filofax. You can get 3 Personal sheet out of a letter sized page with a moderate amount of waste. The Franklin Covey "Compact" size reduces that waste to the minimum possible by adding 1/2" of width. If you cut 6.75" off an 11" page, you are get and piece 6.75"x8.5" and a piece 4.25"x8.5". Cit the 6.75"x8.5" in half to make 2 6.75"x4.25" and trim 1.75" off the 4.25"x8.5" and you have 3 FC Compact pages with only 1.75"x4.25" wasted.

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  3. Grreat explanation, Alan :-). If you want to confuse Americans even further you can also mention C which is the standard for envelops, although some envelops are also sized using B.

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  4. Thank you for taking the time to explain that, Alan. My coffee-time learning for today. :)

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  5. What a fascinating article/history lesson! Thank you.

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  6. Thank you so much for taking the time and trouble to do this. As an American, I can tell you that converting back and forth is really irksome and I wish the US would be sensible and adopt metric. I will print your guide out and put it in my Filo right now. Again---thanks!

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  7. Thanks, Alan, for such a clear explanation. I love the logic and practicality of it all, and I wish the US would adopt the metric sizing system for paper. It's well-nigh impossible to purchase A4--and to some extent, A5--paper here. I think it's an invisible matter to most Americans; most wouldn't even know what A4 or A5 paper is, so I doubt that there would be a change anytime soon.

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  8. Thank you all. For the record, I an North American (Toronto, Canada) and I agree with Cathleen, I'd be quite surprised if North Americans adopted metric paper sizing in my lifetime.

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  9. I notice that the PDF is truncated. I have sent Steve a new version that works.

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  10. Although you refer at it as "metric sizing", the proper name is "International Standard (ISO) 216". The American sizing is known as a "local standard". The UK had its own standard until 1959 and in my childhood, paper was always "foolscap" or "quarto". Only the USA and Canada has yet to adopt ISO 216, although it is still not in widespread use in several South American countries.

    I sometimes ponder as to the benefits of organiser companies getting together and agreeing to adopt ISO 216 for paper planners and agree a standard for ring spacing at the same time! Companies are too entrenched now but Filofax could drastically simplify its range and costs if it replaced Personal and Pocket with A6 and abandoned Flex Slim and other odd sizes. Not just binders but the inserts (A4, A5, A6) could all be produced from one set of artwork in the same layout, with simple scaling between the sizes.

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    1. Point taken, but I suspect that 95% of people refer to A4, A5, etc, generically as either metric or A-sized paper.

      As for standardization across all companies, there are costs to the firms as well as that allows customers to buy their inserts from any firm. It would be like Schick and Gillette agreeing to a standard for razor blades - not happening.

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    2. If you want to be really pendantic you should say that the was originally called DIN 476 (Deutsche Industrienorm = German Industrial norm), which it's still called in Germany. We usually say Din A4, Din A5, etc.

      Then there's EN (European Nom). And now ISO. The official titel now it's ISO 261. Though in some European paperwork it's referred to as EN ISO 216. And some in some German papers you can even find DIN EN ISO 216.

      The German Industrial Norm was originally companies getting together (in 1917) and agreeing that an industrial norm would make everything easier. Production, ordering, etc. The main catalyst was the military and companies producing for the military. By agreeing on standard sizes, production could be streamlined and weapons produced much faster.

      Instead of producing all kinds of special formats for each and every company, companies now simply produce the standard sizes that everyone knows and expects to get when they order paper Din A4 or screws DIN XY.

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  11. The biggest impediment to the US adopting ISO 216 is the federal government, which adopted Letter size formally, displacing the more common size of 8x10, which is still frequently used in educational materials and of course, photography.

    Like Cloudberry, I strongly suspect the Personal size Filofax adopted from LeFax was based on something common here first - it measures too perfectly at 3.75 x 6.75", but why?

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    1. Bree, I replied to Cloudberry, just today, which addresses you question, albeit not authoritatively!

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  12. Thank you, this is a wonderful post.

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