John Quincy Adams and The Metric System

By The Metric Maven

Get Yourself Some Coffee Edition — This is long — You have been warned.

When I watched the HBO series John Adams, I was most interested in the portrayal of his son, John Quincy. He appeared to be the reluctant, competent son who was a genius in diplomacy. When one reads the Wikipedia entry on John Quincy Adams (JQA), it indicates that George Washington was so taken with his abilities that he did his best to keep him in government. JQA is also the person to whom many metric advocates look for early political affirmation of the metric system, which was yet again ignored by the US Government afterward. The report itself is an incredible tome. When JQA wrote it, the metric system had been around formally for about 25 years. The quotation one generally sees reproduced from this report, over and over and over, is found in this government document from 1969 about the history of the metric system. It implies that JQA was a very, very serious scholar of weights and measures:

We will delve into the actual body of JQA’s tome in this essay to reveal what he actually said. At the beginning of his work Quincy Adams describes the two systems. The metric system he sees as governed by:

By an uniformity of  identity, is meant a system founded on the principle of applying only one unit of weights to all weighable articles, and one unit of measures of capacity to all substances, thus measured, liquid or dry.

and the existing situation:

By an uniformity of  proportion, is understood a system admitting more than one unit of weights, and more than one of measures of capacity; but in which all the weights and measures of capacity are in a uniform proportion with one another.

and:

Our present existing weights and measures are, or originally were, founded upon the uniformity of proportion. The new French metrology is founded upon the uniformity of identity.

JQA then starts to discuss decimal arithmetic. He states: “The elementary principle of decimal arithmetic is then supplied by nature to man within himself in the number of his fingers.” So it would appear that John Quincy sees decimal arithmetic as a positive development, a natural one. After all we have 10 fingers. Then just as quickly he admonishes it: “But while decimal arithmetic thus, for the purposes of computation, shoots spontaneously from the nature of man and of things, it is not equally adapted to the numeration, the multiplication, or the division, of material substances, either in his own person, or in external nature.” One starts to get a very schizophrenic feeling when reading the report. Adams states:

The power of the legislator is limited over the will and actions of his subjects. His conflict with them is desperate, when he counteracts their settled habits, their established usages; their domestic and individual economy, their ignorance, their prejudices, and their wants: all which is unavoidable in the attempt radically to change, or to originate, a totally new system of weights and measures.

Considering the US Constitution gives the government the power to determine the weights and measures, the limit on the legislator is actually a function of his leadership, which in this case JQA argues for timidity in the extreme which is a form of self-limitation. Later JQA will try to rationalize this position.

John Quincy Adams (1767-1848)

JQA then launches into a history of the almost unlimited number of measurement values used in the ancient world. He then interjects: “…and it has since been noticed, that the power of the legislator is restricted to the inhabitants of his own dominions.”  and after mentioning how nice having a single system would be he states: “But this uniformity cannot he obtained by legislation. It must be imposed by conquest, or adopted by consent.” Adams is now contradicting the constitutional mandate that his father and others placed into the constitution. One must wonder if JQA was against the very idea of uniform measures when he makes this statement:  “is it not worth their while to inquire, whether an imperceptible improvement in the uniformity of things would not be dearly purchased by the loss of millions in the uniformity of persons ?” Adams then indicates that legislation just doesn’t work and offers up this statement:

In England, from the earliest records of parliamentary history, the statute books are filled with ineffectual attempts of the legislature to establish uniformity.

JQA then launches into a defense of the use of barleycorns for measurement. I guess I can be thankful that agricultural scientists have not been tasked to develop better barleycorn strains specifically to act as measurement standards.

But he seems to argue that much of the English legislation was not actually meant to establish uniform measures. He throws in this disparaging statement along the way: “The litre of the French system is a weight for nothing but distilled water, at a given temperature.” JQA demonstrates technical ignorance of the important concept of specific gravity, which relies on the mass of water, and is used to this day. This is followed by page after page of interrelationships between an almost uncountable number of measures used over the ages. He relates how they changed because of wars and political strife. The mad interrelationships, birth and death of measures is described for page after slumber inducing page. Then he offers an intermission to state: “Such was originally the system of English weights and measures, and such is it now in its ruins.” JQA then launches an attack aimed at those who seek uniformity in measure:

No further change in this portion of English legislation has yet been made. But the philosophers and legislators of Britain have never ceased to be occupied upon weights and measures, nor to be stimulated by the passion for uniformity. In speculating upon the theory, and in making experiments upon the existing standards of their weights and measures, they seem to have considered the principle of uniformity as exclusively applicable to identity, and to have overlooked or disregarded the uniformity of proportion. They found a great variety of standards differing from each other: and instead of searching for the causes of these varieties in the errors and mutability of the law, they ascribed them to the want of an immutable standard from nature. They felt the convenience and the facility of decimal arithmetic for calculation; and they thought it susceptible of equal application to the divisions and multiplications of time, space and matter. They despised the primitive standards assumed from the stature and proportions of the human body. They rejected the secondary standards, taken from the productions of nature most essential to the subsistence of man ; the articles for ascertaining the quantities of which, weights and measures were first found necessary. They tasked their ingenuity and their learning to find, in matter or in motion, same  immutable standard of linear measure, which might
be assumed as the single universal standard from which all measures and all weights might be derived. In the review of the proceedings in France relative to this subject, we shall trace the progress and note the results hitherto of these opinions, which have there been embodied into a great and beautiful system. In England they have been indulged with more caution, and more regard to the preservation of existing things. (page 45-46)

John Quincy launches into another apparently suspicious flood of words aimed at uniformity  as an end unto itself. He boldly appears to predict that the metric system as we know it today will never happen because: “Any change whatever in the system of the one [country], which would not be adopted by the other, would destroy all this existing uniformity.” (page 47) All of the countries of the world, with the exception of the one for whom JQA acted as a politician, have today embraced one uniform system—the metric system. In an almost backhanded and dismissive manner he then states:

If these ideas should be deemed too cold and cheerless for the spirit of theoretical improvement; if Congress should deem their powers competent, and their duties imperative, to establish uniformity as respects weights and measures in its most universal and comprehensive sense; another system is already made to their hands. If that universal uniformity, so desirable to human contemplation, be an obtainable perfection, it is now attainable only by the adoption of the new French system of metrology, in all its important parts. Were it even possible to construct another system, on different principles, but embracing in equal degree all the great elements of uniformity, it would still be a system of diversity with regard to France, and all the followers of her system. And as she could not be expected to abandon that, which she has established at so much expense, and with so much difficulty, for another, possessing, if equal, not greater advantages, there would still be two rival systems, with more desperate chances for the triumph of uniformity by the recurrence to the same standard of all mankind.

Any subtlety about the origin of the metric system, or enthusiasm for it, is not offered by John Quincy when he relates his view that:

The system of modern France originated with her Revolution. It is one of those attempts to improve the condition of human kind, which, should it even be destined ultimately to fail, would, in its failure, deserve little less admiration than in its success. It is founded upon the following principles:

1. That all weights and measures should be reduced to one uniform standard of linear measure.

2. That this standard should be an aliquot part of the circumference of the globe.

3. That the unit of linear measure, applied to matter, in its three modes of extension, length, breadth, and thickness, should be the standard of all measures of length, surface, and solidity.

4. That the cubic contents of the linear measure, in distilled water, at the temperature of its greatest contraction, should furnish at once the standard weight and measure of capacity.

5. That for every thing susceptible of being measured or weighed, there should be only one measure of length, one weight, one measure of contents, with their multiples and subdivisions exclusively in decimal proportions.

6. That the principle of decimal division, and a proportion to the linear standard, should be annexed to the coins of gold, silver, and copper, to the moneys of account, to the division of time, to the barometer and thermometer, to the plummet and log lines of the sea, to the geography of the earth and the astronomy of the skies; and, finally, to every thing in human existence susceptible of comparative estimation by weight or measure.

7. That the whole system should be equally suitable to the use of all mankind.

8. That every weight and every measure should be designated by an appropriate, significant, characteristic name, applied exclusively to itself.

This system approaches to the ideal perfection of uniformity applied to weights and measures; and, whether destined to succeed, or doomed to fail, will shed unfading glory upon the age in which it was conceived, and upon the nation by which its execution was attempted, and has been in part achieved.

Once again I get the feeling that I’m reading the description of a tennis ball bouncing from side to side of a tennis court. And if mankind has the ability to improve himself:

“…the metre will surround the globe in use as well as in multiplied extension; and one language of weights and measures will be spoken from the equator to the poles.

The establishment of this system of metrology forms an era, not only in the history of weights and measures, but in that of human science. Every step of its progress is interesting…..”

So JQA likes the metric system? He then relates that the French (before the revolution) attempted to have their king write to the British king, and see if they could not work out a method for using the seconds pendulum as a length standard. The length later chosen was the length of an arc of a meridian and JQA was not pleased. I fully understand this, and believe the choice of a meridian created a schism. JQA makes a quite reasonable objection to this choice:

She had already communicated by her own inspiration to the mind of Newton, that the earth was not a perfect sphere, but an oblate spheroid, flattened at the poles : and she had authenticated this discovery by the result of previous admeasurements of degrees of the meridian in different parts of the two hemispheres.

John Quincy Adams pounds out the details of the practical problems associated with using the earth as a “metrology standard.” To make matters worse he points out “The admeasurement [actual act of measurement] of the meridian was commenced at the very moment of the fanatical paroxysm of the French revolution.” The men tasked with the measurement ran into problems of epic proportions because of this. For those who might be interested, their problems are exhaustively related in the book The Measure of All Things by Ken Alder. JQA relates the use of metric prefixes and finds: “The theory of this nomenclature is perfectly simple and beautiful.” But then claims the French people have rejected their use, and relates this to the rejection of decimal currency in the US. He further launches into the “too many syllables” argument against metric notation, which will be echoed into at least the late 20th century.

John Quincy’s suspicion, that because of politics, war, and the inability of countries to come to a uniform weights and measures consensus appears to have been justified, when he relates how after the revolution a set of new names were given to sets of metric quantities.

JQA suspects that cities which are far away from Paris have probably retained their customary measures, or will revert. But strangely he then seems to argue that one should not get too down about the possibility of measurement uniformity in the future. I recalled upon my first reading of JQA’s report that it felt much like I would imagine the digestion of a pan-galactic gargle blaster might. Upon my second reading—I’m sure. He then believes he can identify the problem:

The French metrology, in the ardent and exclusive search for an universal standard from nature, seems to have viewed the subject too much with reference to the nature of things, and not enough to the nature of man.

JQA then returns to a sermon about how any metrology system must relate to the proportions of the parts of a human body (an average man I suspect?–not woman?–or child?–in what geographical location?). (BTW my index finger is very close to 100 mm, as is the width of my palm, and my hand span is close to 200 mm) He also revisits his attack on decimal arithmetic. Quincy Adams praises fractions and binary divisions and points out that even those who champion decimal arithmetic are now contemplating duodecimal (12) instead. This sounds like a stealth appeal to the foot and its division into inches. JQA sees the two systems thus:

The standard of nature of the English system is the length of the human foot, divided by the barley corn. That of the French system is an aliquot part of the circumference of the earth decimally divided.

Quincy Adams then launches into a long set of interlaced paragraphs which alternate between his reflections upon “The French System” and “The English System.” JQA then attacks the notion of using a seconds pendulum, argues that for voyages the length of a meridian it is great, but again returns to the complaint that metric is not suited for human needs. He asserts:

The foot of Hercules, the arm of Henry the First, or the barley-corn, are as sufficient for the purpose as the pendulum, or the quadrant of the meridian.

And then after arguing for “the foot of Hercules” as a measurement standard, which would be a standard based on the dimension a mythological person, he argues that making metrology too “sciency”  makes it less accessible to ordinary people:

It is a great and important defect of the systems which assume the meridian or the pendulum for their natural standard, that they never can be recurred to without scientific operations.

This is one great advantage which a natural standard, taken from the dimensions and proportions of the human body, has over all others.

Then I begin to hear imaginary violins in my head as I read:

Should the metre be substituted as the standard of our weights and measures, instead of the foot and inch, the natural standard which every man carries with him in his own person would betaken away; and the inconvenience of the want of it would be so sensibly felt, that it would be as soon as possible adapted to the new measures : every man would find the proportions in his own body corresponding to the metre, decimetre, and centimetre, and habituate himself to them as well as he could. If this conjecture be correct, is it not a reason for adhering to that system which was founded upon those proportions, rather than resort to another, which, after all, will bring us back to the standard of nature in ourselves.

So, all we will do if the metric system is implemented is to revert to body parts anyway, so just forget bothering with it. He then argues that the values of metric are just as arbitrary as those used currently. Quincy Adams believes the metric system is nice, but it’s not perfect, so let’s keep our distance. After all: “Of all the nations of European origin, ours is that which least requires any change in the system of their weights and measures.” Really!? JQA continues to argue that the current measures are “natural” and metric is not.

As I read this incredibly long, repetitive and circular document, it struck me that what is being argued in its pages may not be about measurement at all, but about man’s place in the universe. It’s like a proxy war about whether man is at the center of the universe and the planets and sun revolve around the earth, versus an inanimate universe where man is not at the center, and the earth orbits the sun. The current English measures are “man centered” he argues, and the metric system is impersonal and based on science (in his view science is not nature–or natural of course, that could undermine his argument).

Away he goes again. JQA relates ad nausium dozens of measurements and their relationships in different states of the union. Page after page is filled with antique relationships about which no one would care if the metric system were substituted for the current mess. John Quincy asserts that if the metric system were introduced, it would only end up augmenting the current farrago of weights and measures. The old ones would remain as they could not be eschewed. Introducing metric would only make matters worse.  He uses this as an argument to explain why the metric system can never achieve uniformity. It is the same argument that will be used 85 years later by Frederick A. Halsey against metric in the metric hearings of the early 1900s.

Finally after 117 pages, JQA points out that the reason he has begun this endless set of prose is because of a provision in the constitution:

in reference to that part of the resolutions of both Houses, which requires the opinion of the Secretary of State with regard to the measures which it may be proper for Congress to adopt in relation to weights and measures, it may be proper to state the extent of what can be done by Congress. Their authority to act is comprised in one line of the constitution, being the fifth paragraph of the eighth section and first article; in the following words: to fix the standard of weights and measures.”

Quincy Adams then proceeds to argue that: “To fix the standard, appears to be an operation entirely distinct from changing the denominations and proportions already existing, and established by the laws, or immemorial usage.”

I now recall why I found reading this document to be torturous. So he claims fixing the weights and measures is not deciding or legislating the weights and measures.  I hope you readers appreciate my wading through this malarial swamp of prose—that is if you have made it this far without giving up, or having fallen asleep.

JQW then proceeds to argue that legislation has never brought uniform measurement before, so forget even bothering to try. It’s a fools errand. How many times has he hit this chestnut over the last 188 pages?—don’t tell me, I don’t want to know. Not long after this assertion he offers a set of options:

1. To adopt, in all its essential parts, the new French system of weights and measures, founded upon the uniformity of identity.

2. To restore and perfect the old English system of weights, measures, moneys, and silver coins, founded upon the uniformity of proportion. [note that JQA appears to be arguing that the implementation of decimal currency by the US in 1786 should be repealed. Apparently he wanted to return to the almost endless and irrational set of English coins?]

3. To devise and establish a system, in which the uniformities of identity and of proportion shall be combined together, by adaptations of parts of each system to the principles of the other.

4. To adhere, without any innovation whatever, to our existing weights and measures, merely fixing the standard. (page 119)

Ok, spoiler alert!  For those of you who didn’t know—we chose number four. So we have one mystery left, which option did John Quincy Adams endorse? Well, this probably nails it:

In the mean time, should Congress deem it expedient to take immediate steps for accomplishing a more perfect uniformity of weights and measures within the United States, it is proposed that they should assume as their principle, that no innovation upon the existing weights and measures should be attempted.

Oh, if you’re confused, it says: “don’t do anything.” But if you do “here are some non-metric suggestions, and discussion of possible standards—for our non-system.”  So how is it that many pro-metric persons think JQA was pro-metric?  Perhaps they read the last page of the document, and didn’t realize that he had previously argued against any change, recommended none, and if there was to be change, it should be to further the “development” of the current set of measures. Here is what the last page states:

“France first surveyed the subject of weights and measures in all its extent and all its compass. France first beheld it as involving the interests, the comforts, and the morals, of all nations and of all after ages. In forming her system, she acted as the representative of the whole human race, present and to come. She has established it by law within her own territories; and she has offered it as a benefaction to the acceptance of all other nations. That it is worthy of their acceptance, is believed to be beyond a question. But opinion is the queen of the world; and the final prevalence of this system beyond the boundaries of France’s power must await the time when the example of its benefits, long and practically enjoyed, shall acquire that ascendency over the opinions of other nations which gives motion to the springs and direction to the wheels of power.

Respectfully submitted.
JOHN QUINCY ADAMS.
Department of State, February 22, 1821.

This is Mayor Maynot, from a short-lived animated series based on the movie Beetlejuice. Hizzoner tried to be all things to all his constituents: he was notorious for speeches in which every sentence contradicted the preceding sentence.

This could be read as an endorsement or even praise of the metric system by a person who is pro-metric. But it can also be read another way. Adams may well be accusing the French of cultural hubris with his statement: “she acted as the representative of the whole human race, present and to come.” In other words JQA is complaining that they appointed themselves arbiters of world measurement, without consulting  the rest of the world. Who do they think they are! How could this system possibly be legitimate? JQA also stresses that it took laws to establish the use of the metric system in France. This statement is used to imply there was no free choice by the French people to “voluntarily” use the metric system, and therefore it is used only under duress by these oppressed persons. Adams then argues that the metric system’s actual merits, as decided by the rest of the world, will determine whether it is adopted or not. This appears to be an early form of a technical Darwinism argument against metric.  The preceding statement by JQA: “That it [the metric system] is worthy of their [The French] [emphasis mine] acceptance, is believed to be beyond a question” may well imply that it is worthy for the French, but not a worthy system for Anglo-Saxons. This is what I suspect was his actual meaning.

In order to make some sense of this meandering, wandering and schizophrenic prose, one probably should look at the time in which Quincy Adams lived and his personal back ground. JQA was an envoy to France from 1778-1779. He became fluent in French and was well acquaintedwith other European languages. He had broad experience with the Europe of the time. John Quincy Adams supported George Washington’s decision for the US to have no involvement in the hostilities taking place in France during the revolution. Adams made it clear that he felt the US should stay out of European affairs. In affairs of the heart JQA decided that marriage to a British woman was a useful entanglement. From what little I know about Quincy Adams, it appears that as a personality he was “all business” and not much to have around socially. His photograph makes him look like Ebeneezer Scrooge’s grouchy brother.  In 1821 only four countries had adopted the metric system. These were France, Belgium, Luxembourg and The Netherlands. To JQA the metric system would hardly seem universal. He stated in his report:

During the conquering period of the French Revolution, the new system of French weights and measures was introduced into those countries which were united to the empire. Since the severance of those countries from France, it has been discarded, excepting in the kingdom of the Netherlands,….”

Worse yet the metric system was associated with political upheaval in France, from which John Quincy Adams had decided the US should distance itself. He also argued against foreign entanglement, so that he would argue to either change nothing or improve what we have makes sense. As his entire career was as a diplomat, it is not surprising that he would create a document that anyone who casually read only parts of it, could readily see as pro-metric or pro-English depending on their point of view. I have no idea why some authors have called this a celebrated document. It is almost a prose Rorschach test. Right after he recommends no change he then turns around and seems to praise France’s effort at a metric system. When the prose is read carefully, it appears it may well be sarcasm. The Report on Measures appears to have been a document designed for some type of diplomatic consumption, and should not be celebrated, it should be seen for what it was, a 268 page empty suit of a document, written by a person with little technical background.

I have found one person who took issue with this report and wrote a critique of it. The person was Frederick A.P. Barnard (1809-1889) who is discussed in an earlier essay. He had this to say about John Quincy’s attraction to British Measures:

The Metric System of Weights and Measures, Fredrick A.P. Barnard,  American Metric Bureau 1879 pg 82

Barnard further stated:

…I esteem [JQA’s Report on Measures] to have been a serious public misfortune. It effectually extinguished all hope of metrological reform in the United States for half a century. (pg 112)

He also points out that John Quincy Adams continued to discourage any legislation over the remainder of his long career. I agree with Barnard’s assessment.

I apologize for this long drawn-out blog to nowhere, which only serves to tell you that John Quincy Adams’ Report on Measures was essentially anti-metric (as near as I can tell) and simply appears to have existed so congress could feel good about doing nothing.  Its effect was to squelch any discussion of US metric implementation for at least another 50 years after its publication. I can only promise you I will never write a blog about this report again—if I can help it.

Related Essays:

How Did We Get Here?

John F. Shafroth: The Forgotten Metric Reformer

Testimony from the 1921 Metric Hearings

The Metric Hearings of 1975 — The Limits of Social Norm in Metrication

A Tale of Two Iowans

Australian Metrication & US Procrastination


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.

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.