# 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:

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.