The Metric Paper Tiger

By The Metric Maven

I had the privilege to work with a number of television engineers who developed HDTV. Early on there was much discussion about the aspect ratio chosen for HDTV. The idea was to chose an aspect ratio that would fit as many different film formats as optimally as possible. The aspect ratio finally chosen was 16:9. I naively asked why on earth they didn’t just make it 2:1 (18:9). This choice was apparently some manner of committee decision I was told. A detailed discussion of the choice of 16:9 for the HDTV aspect ratio is offered here. The original television aspect ratio in the US was 4:3, but now there was an opportunity to choose an aspect ratio that fit as many film formats as possible. The aspect ratio used for HDTV would be increased and would enhance a viewers experience.

When an image has an aspect ratio that is 4:3 it cannot be stretched (i.e. mapped) onto a 16:9 aspect ratio rectangle without distortion. Early HDTVs were set so that the 4:3 images were expanded, cropped and distorted. I very much disliked this, and I’m most pleased that for the most part the aspect ratio of the old 4:3 television shows are shown with black (sometimes grey) side panels. This leaves the image undistorted. There is no way to stretch an image into a different aspect ratio without distortion.

I attempted to explain this to a number of people in the early days of HDTV, but it clearly was not intuitive to them, and in some cases they found it hard to believe “there wasn’t a way to do it.” There is not, it is as mathematically impossible as squaring a circle. Here are a number of common aspect ratios of films and the side panels they generate when projected on an HDTV screen:

I introduced this discussion of HDTV aspect ratios in an attempt to better explain why the world uses A4 paper rather than 8 1/2″ x 11″.  A-series (ISO 216) paper is used by all countries with the exception of the United States and Canada. This is why quite often a photocopier or printer will request that one “load A4 paper” when its paper cassette is empty. A4 is the international default paper size. At first glance, the size of A4 paper seems odd. It is 210 mm x 297 mm. Despite the random appearance of these numerical values, they have, in fact, been chosen very carefully. Unfortunately, it is  not immediately obvious that this is the case to most people in the US.

I worked as a printer for a number of years, and I can assure you that during that time I never heard of A4 paper. I could tell you right off what the “standard” American paper sizes are:  8.5″ x 11″, 11″ x 17″, 17″ x 22″, 22″ x 34.”   The “approximately equivalent” A-series “metric paper” sizes are:  210 mm x 297 mm, 297 mm x 420 mm, 420 mm x 594 mm and 594 mm x 841 mm.

So why would the rest of the world choose these strange paper sizes over the nice monotonic values of American paper? It all comes down to what happens as one doubles each paper size in one direction only, as both of these paper sizes do. Below I have taken American paper sizes and “Metric Paper” sizes, placed them side by side, and formed a triangle from each of the paper sizes. This is equivalent to cutting a sheet along its diagonal and producing a triangle with exactly half the original area. If one mirrors a copy of the triangle from top to bottom and left to right, and then joins the edges, it produces the original rectangular paper from which it was derived.

Do you notice any difference so far? I thought I did, but then I knew for what I was looking, which can affect my perception. The way to clearly see a difference, is to overlay all the colored triangles for each paper size with a common shared point at the vertex of their right angle:

It should be immediately obvious that the hypotenuses of the A-Series “metric paper” are all parallel and the American sizes are not. But what does this mean? It means that the aspect ratios of the “metric paper” are all identical. They are all equal to the square root of two. If you take 297 mm divided by 210 mm you will obtain 1.414 which is the square root of two. The American paper aspect ratios oscillate back-and-forth between 1.2941 and 1.5455. Why is the aspect ratio important? Well, if the paper aspect ratio is the same, then one can enlarge A4 paper to A3 exactly, and from A3 to A2 exactly. The lengths of the two legs of the “metric paper” triangles can both be altered by the same amount to fit into the next sized triangle without distortion. This is not the case for American paper. One cannot exactly fit an 8.5″ x 11″ image onto 11″ x 17″. One can fit every other size however, so 8.5″ x 11″ will fit onto 17″ x 22″ or 34″ x 44″ and 11″ x 17″ will fit onto 22″ x 34″ but they will not map onto each other without distortion or “letterbox” waste–just like HDTV.

If I have an engineering drawing which is A4 I can double it to A3 perfectly on a printer or plotter. I could double its size again from A3 to A2 and still it would fit perfectly without distorting the dimensions, or producing “letterbox” waste. I have many times thought about using A4 paper so I could do just that, but try finding A4 paper at your local Office Max or other office supply store. You might as well go on a snipe hunt. Try finding A4 notebook binders at the same location. Because we’ve never had coordinated weights and measures in the United States we waste lots of paper and continue along the path of least resistance, and least intellectual effort, as always. It’s what makes us the “Greatest Country in the World.” I feel so free.

Secretary of Commerce Herbert Hoover (1874-1964) chose 8.0″ x 10.5″ for government use on March 28, 1921. Why he chose this size appears to be unknown. There is conjecture, but no established scholarship. A January, 12, 1979 newspaper article, entitled: Government, After 58 Years, Standardizes Paper Size, printed in the Lawrence Journal-World states it was Senator Clayborne Pell (1918-2009) who wrote a memo implementing 8.5″ x 11.0″ for government use. This was the recommendation of the Joint Committee on Printing (JCP). Clayborne Pell is seen by some as a pro-metric Senator, but he would only support voluntary (i.e. no real) change in 1975. I have written about his testimony in the 1975 Metric Hearings. The newspaper article indicates that government archivists could not find any information about why 8.0″ x 10.5″ paper had been chosen by Hoover in 1921, but there apparently was a government Bureau of Efficiency which appears to have had a hand in the choice. In 1923 the printing and paper industries were consulted and recommended 8.5″ x 11.0″ but government and industry simply continued to disagree on paper size.

Is it possible?—that in 1979, Clayborne Pell, and the members of the JCP could not have known about A4 paper?—had the issue of paper size been researched exhaustively? The simple answer is no. The Germans first created the initial standard in 1922, it was next adopted by Belgium in 1924 and by 1977 A4 was the standard letter format in 88 of 148 countries. Today “metric paper” is used by all countries with the exception of the United States and Canada. Was Pell’s mandate to use 8.5″ x 11.0″ paper in government simply the implementation of what the paper industry wanted in 1923?—and they finally had their way?—I don’t know. What I do know is that Pell did not recommend A4 metric paper—and it was clearly in wide international use.

Some might take exception with my calling A4 “metric paper” but it seems very appropriate to me. The base size is A0 which has a 1 square meter area. The paper sizes exactly halve the area of each sheet:

A0   1,000,000 mm2
A1     500,000  mm2
A2     250,000  mm2
A3     125,000  mm2
A4      62,500   mm2

The weight (paper density) of “metric paper” is given as grammage or grams per square meter, and often called GSM.  So if the grammage of typical office paper is 80 grams/square meter, one can immediately compute the mass in one’s head for all the paper sizes:

A0    80 grams
A1    40 grams
A2    20 grams
A3    10 grams
A4     5 grams

So how is this done with American Paper? Well a common value is 50 lb offset. So, is this the weight of one square yard?—one square rod?—-one square mile?—or one square Ye Olde something? No. The paper weight designation depends on the “basis size” and the “basis weight” of 500 sheets of that basis size. Which is a known as a long ream, which is of course 20 quires of 25 sheets.  Here is a list of the basis sizes for some common papers:

Australian A10 Postage Stamp 26 mm x 37 mm

Yes, they are all random. This table succinctly explains why my father would shake his head with annoyance when he would try to discuss computation using the basis weight of American paper. The baroque nature of this non-system is almost beyond comprehension and is so anachronistic as to be almost beyond description. Some basis sizes are not even manufactured anymore, but exist as “virtual standards.”  This situation is nothing short of an embarrassment. We need a comprehensive set of mandatory weights and measurement reforms throughout what is left of our industries. If every industry in this country cannot be bothered, resists, or waits so they are not the first to change, and continue to subvert governmental reform, as they have for over 150 years, all the worse for “The Greatest Country in the World.”

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page and contribute. Also purchase his books about the metric system:

The first book is titled: Our Crumbling Invisible Infrastructure. It is a succinct set of essays  that explain why the absence of the metric system in the US is detrimental to our personal heath and our economy. These essays are separately available for free on my website,  but the book has them all in one place in print. The book may be purchased from Amazon here.

The second book is titled The Dimensions of the Cosmos. It takes the metric prefixes from yotta to Yocto and uses each metric prefix to describe a metric world. The book has a considerable number of color images to compliment the prose. It has been receiving good reviews. I think would be a great reference for US science teachers. It has a considerable number of scientific factoids and anecdotes that I believe would be of considerable educational use. It is available from Amazon here.

The third book is called Death By A Thousand Cuts, A Secret History of the Metric System in The United States. This monograph explains how we have been unable to legally deal with weights and measures in the United States from George Washington, to our current day. This book is also available on Amazon here.

20 thoughts on “The Metric Paper Tiger

  1. ‘Murica! If you don’t like our arbitrary paper sizes, then git out!

    Another great example of why the greatest country on Earth is really just the most stubborn. I’ve dealt with a lot of printing too and trying to scale on US paper standards is a nightmare. It’s practically not worth it, whereas the standard in the rest of the world makes it all very easy. Aside from laziness, stubbornness, and an inability to admit we are wrong (none of which are of little significance), what do you think is the biggest block from the US coming around? Is it corporate? Thanks!

    • If it can make you feel better, also the SI (or, rather, its “bureaucracy”) is stubborn, for example in still not having changed the name of the kilogram, a base unit with a prefix, which is neither elegant nor acceptable, for a worldwide universal measurement system of the future.

      Sadly, “customary” habits strike again – even among the best (the “oi aristoi” of the SI), not only among the the “ye olde” stubborns (or the “oi barbaroi”, to say it à la ancient Greeks).

      If the SI were more projected towards the future, maybe its adoption could be easier, in the US…? Or maybe not -who knows…

      Anyway, if good old Isaac Asimov eventually converted to the word processor, there should be hope also for an eventually metric US.

  2. @Kimberly

    I think it is paper “accessories.” A4 paper is relatively available if you order online in case or larger lots. Multinational companies generally have to deal with some A4 paper. My company probably used 20% A4, 60% US letter, and the balance, assorted sizes, legal, ledger, et al.

    The biggest problem is that paper is a system. File cabinets designed for letter are a little narrow for A4, binders, Pendeflex folders, etc don’t work. If you can find A4 accessories in the US, they don’t work for letter.

    Multinationals are stuck dealing with a mix. I think a line of file cabinets, binders, file folders that could handle the length of A4 and width of letter would make “some A4” easier to deal with and reduce resistance.

    I really wonder if the scaling argument is the most important. For a fully dimensioned drawing it doesn’t matter, but a scaled drawing scaled up or down by the sqrt(2) really isn’t very usable because the scale is then an irrational number. If I had to print such a drawing on another size sheet, I would use a magnification factor that gave me a more usable scale, and figure out how to manage the margins. Having a scale of 1:50 become 1:35.355 339 or 1:70.710 678 is just a PITA.

    • So, three more rationalizations for inertia, and the well-known American “Can’t Do” Spirit? I actually don’t want to be snarky, but I see a pattern here. Let’s take these in order:

      First, the “you can buy it online” argument: it’s no different in form, and no more impressive here, than in reference to any other metric item. Metric drill bits, to name just one, are readily available over the counter in all countries — except this one. In effect, yes, you can get them, but you have none of the usual societal infrastructure (in these cases, office supply and hardware stores) which we expect for archaic choices. What you seem to regard as an acceptable state of affairs is what we call the Invisible Metric Embargo.

      Second, filing cabinets. I became momentarily obsessed with the utterly fascinating question of whether or not it’s possible to get A4 paper into hanging folders intended for US paper, and therefore into US filing cabinets. The odd thing was that I couldn’t find dimensions for hanging folders online. Manufacturers list the weight of the material (“11-point stock” — whatever that means) but apparently don’t bother with dimensions, perhaps because they’re all so wonderfully “standard.” So I took an empirical approach, went to my local office store, and asked to see a selection of hanging folders. Result: by an astounding coincidence, the long dimension of such folders seems to be almost exactly 298 mm, or just one mm longer than A4 paper. This is the length of the folder proper, excluding the hanger bar at the top, which is longer by at least 10 mm on each end. So with careful joggling, a sheaf of A4 should fit within a US letter folder, if only just. Even with some carelessness, it should still work, depending on the precise design of the drawer rails.

      If some enterprising American entrepreneur wanted to bring his company into the 20th century, the number of new filing cabinets needed might well be — zero. That some sort of new “hybrid” sized cabinet be designed to support the paper change seems pointless. In fact, if said entrepreneur was looking to bring his company into the 21st century, he might well be looking to get rid of the cabinets he already has. The classic American five-drawer filing cabinet may not be quite as much a museum piece as a 1960s console “Hi-Fi” cabinet, but they’re getting there fast.

      Finally, I’m not sure I understand you, but I’ve never seen an engineer do what you seem to suggest, that is “take” measurements, as opposed to reading marked dimensions, from a drawing. It sounds like incredibly bad practice. The only time I’ve ever seen anything like this done was during drawing “checking,” back in the olden days of hand-drawn engineering. Once a drawing is copied, you cannot depend on it for absolute scale. Even when photocopiers are set to copy 1:1, “actual size,” they generally don’t: the actual magnification is seldom known, or controlled by any specification. Many copiers are designed to magnify very slightly on their 1:1 setting, so that page edges don’t show in the copies. And the last thing you want is your technicians taking dimensions from a drawing by measurement.

      Filing cabinets and hand-drawn engineering as reasons for baulking at international standards? You might want to check out some of the currently available CAD software. What it can do boggles the mind.

      • I was trying to suggest reasons because reasons can be overcome if you can deal with them.

        Apparently, Americans have no reasons, they just don’t use A4 because they HATE A4. Ok, but that will be hard to deal with.

        Yes, I am aware if you fuss with it A4 will fit in the file holder. Then if the paper moves 1-2 mm, it gets caught under the rails and you can’t pull the file out. I do deal with “some” a4, and it is a nuisance. (If there is an top and bottom margin, I trim it a little so it fits better, or the more logical approach, pdf and print to fit on letter.)

        I agree with you on dimensioned drawings and most engineering drawings are. I’ve seen a lot of architectural drawings, garden plans, etc which only give a scale, and in many cases the scale is not exactly right. Scale drawings should be avoided, but they aren’t.

        A4 isn’t widely used, because it is a PITA to try to use A4 in the US. But, you need some small solutions that would cause a few “first adopters” to be more willing to use it. If you made A4 supplies widely available at the same price, the stores wouldn’t sell enough before the usage ramped up, and they would drop the line. At present US usage, the alternative to having to buy it online is not being able to buy it at all. You have to cause enough people using it to make those online sales look appealing and create some b&m competition.

  3. While it cost the average “American” family several hundreds of dollars or more to replace the analog CRT TV with a new digital TV, I don’t remember hearing anyone complain about it much. It was a government mandated change and it happened. The government did help folks out by subsidizing the purchase of a converter box if they couldn’t buy a new TV that was digital ready. I guess if a change can make a football game look better, Americans will happily buy it.

    A4 paper can be purchased at Staples. I don’t think they stock it in the stores, but you can buy it on line. Funny they describe it in inches and pounds, though.

    • Once I went to Staples for A4 paper and was irate when I found out they didn’t have it.

      The real WTF is that the American paper sizing “system” includes 8.5 x 11 inch sheets as well as 8.5 x 14 inch sheets, but there are no 8.5 x 12 inch sheets. I mean, really? A foot-long size would have all the logic of A4, as well as being as American as guns and money.

      • There is a 9″ x 12″ architectural size (and a series based on doubling up) but I don’t think it is used much any more.

  4. The reason they settled on 16:9 is missing from your Wikipedia article –
    You need to ask why not a square or 1.5?

    The math says – 16/9 = 1.777 which is not the ideal – 1.61803 – what is known as the golden rectangle. It is close and leave a bit extra for auto-panning.
    I think physiology beats efficiency in this case.

    I don’t think you can extend the issue of paper stock to digital aspect ratio.
    11 /8.5 = about 1.3 and 17/11 is also wrong at 1.54 (but close) – but metric paper at 2^(1/2) – 1.414 is also not very close to the golden ratio.

    My hunch is that the 11 x 17 was supposed to be close to this ratio?

    • The useful property of a rectangle with sides in the ratio of 1:1.414141… is that if you fold the sheet of paper halfway along its longest side you end up with two rectangles of half the area of the original sheet with their sides in the proportion of 1:1.414141… again.

      This is why an A4 sheet of paper is half the area of an A3, an A3 is half the area of an A2 and so on.

      • The aspect ratio of sqrt(2) is the only aspect ratio that preserves its aspect ratio when folded in two. The US parer sizes have the property that each smaller sheet is half the area, but they alternate between two aspect ratios.

        The aspect ratio preservation is the distinctive feature of the ISO paper sizes. Besides the A series paper, there is a B series, a C series, and a slightly different Japanese B series (usually designated JB). All have sqrt(2) aspect ratio.

  5. Hi The article mentions 1923 and Germany. This is the time after World War One and there was much anti -German feeling in the United States, so much that many german speakers stopped using german outside the home. Maybe the reason not to adopt a paper size invented in Germany? One can read “God bless you Mr Rosewater” and other stories of Kurt V. Jr.

  6. I think the article fails to address that the 8.0″ x 10.5″ was an oddball size used ONLY by the US government. US Letter (8.5′ x 11″) was in wide commercial usage at the time the government adopted its special size . It was certainly the norm for typing paper, student notebook filler, etc. when I was in school and college in the 50’s and 60’s.

    I think the government recognized the disadvantage of an oddball size, and using the existing commercial standard in the US was the logical choice in 1979. I doubt ANY A4 was in use in the United States then, although multinationals use a far amount now.

  7. According to Wikipedia:

    Letter or US Letter is the most common paper size for office use in North America, Bolivia, Colombia, Venezuela, the Philippines and Chile.[1] It measures 8.5 by 11 inches (215.9 mm x 279.4 mm). US Letter size is a recognized standard adopted by the American National Standards Institute (ANSI) whereas the A4 is the International Standard (ISO) used in most countries.

    So, it seems the US & Canada are not alone.

    • In this citation on paper size in Wikipedia it states:

      By 1977 A4 was the standard letter format in 88 of 148 countries. Today the standard has been adopted by all countries in the world except the United States and Canada. In Mexico, Costa Rica, Colombia, Venezuela, Chile and the Philippines the US letter format is still in common use, despite their official adoption of the ISO standard.

      What was stated in the essay: ‘Today “metric paper” is used by all countries with the exception of the United States and Canada.’

      • But A4 has SOME availability and use in the United States, and nobody “forbids” its use. I think you have measure which is “mostly commonly” used, ie which has a larger market share.

        As a proof of “some use,” note the USMA newsletter is printed on A3, which folded becomes A4. I’m sure there is some other use.

        I do wish it was more available. I’d like to keep a ream around for some things that are better printed on A4. I’m not ready to reformat things that are formatted for US letter, and I’m not ready to buy a case of A4. From time to time, I have found and bought a ream of A4, but at the moment I’m out.

      • I can see the South American countries going for A4 as American influence is waning and European and Chinese influence is increasing. European, Chinese and other countries already using A series will insist upon it in their businesses and force a change.

        Foreign companies operating in the US may also require it and thus create somewhat of a demand, such that A4 paper is somewhat available in the US even if not as easy as letter, etc.

        I would suspect that a country like Venezuela where there is strong anti-American feelings in the government, especially when Chavez was in power, would be good enough reason to switch. I was there a few times in the mid to late ’90s but don’t remember what paper size they used.

        I do remember being told before going that Venezuela used gallons for gasoline, only to find out when I got there they used litres. So if they did make a switch from gallons to litres, they could have also made a switch in the size of paper.

        I did a Google Search on “Papel A4 en Venezuela” and it is available, but so is “Oficio”, which means “job”, “career”, etc.

      • Also, if you go to the article link I posted, and select “talk”, there is a section on Mexico that references the article you mention:


        According to Mexico adopted the ISO standard in 1964. The only countries using letter et al. are US and Canada. This should be sorted out. —Preceding unsigned comment added by Mutluluk (talk • contribs) 03:09, 11 February 2008 (UTC)

        Letter is still widely used in (at least northern) Mexico; office stationery stores in Baja and Sonora stock noticeable quantities of the stuff. knoodelhed (talk) 19:30, 14 February 2009 (UTC)
        Letter size is a de facto standard in Mexico, where you can not buy a single A4 page at all. The ISO standard never came into effect in practice in Mexico. —Preceding unsigned comment added by Robgomez (talk • contribs) 23:53, 2 July 2009 (UTC)

        Letter is widely used in Chile. You can buy A4, but most people either don’t know what it is or can’t tell the difference with letter. (talk) 16:13, 7 April 2010 (UTC)

        This may be true in the other countries listed in the link I posted. The country officially uses A4, but it is not used in practice.

        Even with these exceptions, the overwhelming majority uses A series paper and it is the exceptions that have to accommodate the A series and not the other way around.

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