Category Archives: Centimeters or Millimeters

Stickin’ it to Yardsticks

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By The Metric Maven
Bulldog Edition

One of my very first memories of linear measurement, is of my Grandfather’s upholstery shop. He had built all of his wooden  workbenches himself, and embedded wooden yardsticks into them for a convenient measure. Well, they looked like yardsticks, but were actually 54 inches. This was the size of “standard” upholstery cloth he often used.  There were also yardsticks of 36 inches around for  quick measurement. They were ubiquitous in my youth. Why?—because almost every business of one type or another gave them out as free advertising. Below is one from many years ago as an example.

Yardstick (Click to enlarge)

They seem as American as apple pie, but are actually a good example of how much the way we measure is a throwback to the 18th century. Even then they knew better. I explained the problem to a woman one day during a trip, and half-way through my explanation she spouted out “You make the way we measure sound like it’s difficult!”  I wasn’t sure if it was denial mixed with surprise and a hint of exasperation, or the shock of realization. She is no average girl, she has worked on large engineering bids in Korea and London. What’s wrong with our rulers? Let me begin at the beginning. Here is part of a yardstick with typical divisions labeled:

Yardstick with scales labeled

As every American knows from grade school instruction, a yardstick is divided into one inch divisions, half-inch, quarter-inch, and in the case of the yardstick shown, into eighth-inch divisions. Apparently that was close enough for most people, I don’t recall any complaints. The divisions are expressed as fractions, so if you have 1 + 1/2 + 3/4 + 7/8 you cannot add them directly to get 25/8 total. You must find a common denominator for them.

Essentially you have a ruler with 4 scales on it. By a scale I mean graduations you can read and add together directly. For instance if you measure a distance of 1 inch, and then measure 3 inches you can immediately add them together to make 4 inches. This is true for each fraction also, so 5/8  + 7/8 = 12/8 (= 3/2). To designate these scales on a yardstick, the line lengths are all different. Their vertical length is proportional to their horizontal linear graduation size, with 1, 2, 3 inches the longest and 1/8, 2/8, 3/8 the shortest vertical lines.

The Maven has one suggestion that would help make a yardstick much easier to use he-thinks. All of the fractional scales, (i.e 1, 1/2, 1/4 ..) are on top of one another, and share  many equal values. What I mean is  1 inch = 2/2 inch = 4/4 inch = 8/8 inch. So lets just get rid of all the scales except for the integer inches and the 1/8 inch graduations. The yardstick would now look like this:

Yardstick altered so only eighths show.

Now we can measure as precisely as possible with the smallest given graduation, that is, within 1/8 of an inch. The ruler does not have finer graduations, so no matter what you measure, it will be within about 1/8 of an inch. The great part is that now we can add measured values directly. Say we measure 2 3/8 inches and 6 7/8 inches. We can add them easily to get 8 10/8 inches or 9 and 2/8 inches. Now you may want to change it to 9 1/4 inches, but that value is no longer on our scale, so we would leave it in eighths.

The closest we can measure with this ruler is 1/8 inch which is 3.175 mm. If we go to 1/16 inch, that is 1.58 mm, so if we use a millimeter graduated rule we will be just slightly better than 1/25 of an inch. We already start out measuring much more precisely than a common yardstick, just by using millimeter graduations!

What most Americans think of as a metric ruler is shown below. I like showing it, because it’s from a thoughtless anti-metric diatribe, written at the turn of the twentieth century, which was presented before congress—and is wrong.

Centimeter-millimeter Ruler Mislabeld as a Millimeter Scale

It is designated to be a millimeter ruler according to the “distinguished” and “scholarly” author of The Metric Fallacy,” but it is not. It is a centimeter rule with millimeter graduations, what a mess! You may be thinking, “but Maven, you already showed us the same thing above is an improvement, isn’t it  better to have a version with centimeters and millimeters?” NO IT IS NOT. Yes this is the type of ruler that is attached to lower edge of inch rulers in the United States as an after-non-thought, and called a metric ruler. It’s clear whoever decided this “design” is a proper set of metric graduations has never actually used the metric system. Other English speaking fully metric nations, like Australia and New Zealand, have learned to eschew centimeters on rulers. Remember! The idea of metric is simplicity, full stop. Properly implemented metric is not harder than the current measurements, it’s much easier, as I will later show.

With this typical American style ruler we would have to measure say 2 cm 5 mm and 5 cm 7 mm to get 8 cm 2 mm. What we have again is two scales, one centimeter and one millimeter. We are forced to use two units, centimeters and millimeters, because of the ruler’s design.This may seem comfortable to a culture which measures people with values like five foot ten inches, but it is still not optimum, and is cumbersome. I would bet that the yardsticks given out in Monticello Iowa, in 1980, were centimeter-millimeter ones. This would probably cause most people there to see no advantage, and ignore the metric side. Here is the ad for yardsticks with metric graduations from the June 25, 1980 Monticello Express:

We will now convert the centimeter/millimeter ruler from 1904, with the magic of computer imaging software, to a true, single scale, millimeter metric ruler:

Correctly designated millimeter ruler — Now just the spelling needs fixing (click to enlarge)

Now this is a simple ruler anyone can use. If you measure 52 mm and 72 mm you can easily add them to get 124 mm. If the free yardsticks offered to Iowans in 1980 had been marked this way, some of the local residents might have immediately realized the advantages of using it. In my view, the mixed graduations of centimeters and millimeters on American rulers have held back metrication considerably. Dual rules, millimeters and inches, also are bad for metrication–but that’s another blog. Don’t use centimeters!—ever! Here is an example of a section from a 300 mm Australian ruler I use in my Engineering work:

Modern metric ruler from Australia (click to enlarge)

I tend not to need a ruler which is more than 600 mm long. It is people in metric countries, who design with fabric, that use full meter sticks with millimeter graduations—Like my grandfather’s larger yard stick. Here is a picture of a person using a meter stick with mm graduations:

Meter Stick with millimeter graduations (click to enlarge)

For the average person, there are only three distance measurement units that are important, millimeters, meters, and kilometers, that’s it. The others, such as micrometers and nanometers, are generally only used by technical professionals.

I spoke with my friend Thern, the Mechanical Engineer, about all of this. He has experience building houses, and said “If we used metric tape measures with only millimeters, people who have been unable to accurately read inch measures for their entire careers, would finally be able to do so accurately, and with way fewer errors when building houses.”

In the Jan-Feb issue of Metric Today in 2005, the story of Professional Engineer Robert Bullard  is detailed. He had the temerity to design a house exclusively in metric–in Florida. He faced multiple layers of metric discrimination trying to get his drawings approved by regulators. The attitude was “you don’t like it–then sue us.”  Bullard was inspired to go metric when he had his first experience with a metric design. The construction design was completed by a draftsman much faster than the US designs with which he had exclusive experience. Overall the entire design was about 20% more efficient

Quoting from the Metric Today article, we see Robert Bullard’s builder, Blake Cougle agreeing with Thern about our current measurement system:

Cougle then turns his critical eye onto U.S. workers, who, he claims, even fail to show mastery of American customary units of measurement. “[U.S. laborers] can’t handle fractions of inches,” he said. “They might use a ruler, but they often end up just counting courses (concrete blocks). You’d be amazed.”

Actually, because I understand how baroque our rulers are in the US, I’m not that amazed.

This is why Australia saves 10%-15% in material costs for building construction every year compared with America. What is a good use for all these old yard sticks?  Perhaps they can be broken up and used to fix tables with unequal legs. Some people already use them to make art. The time has long ago arrived in America to drop by a lumber yard and expect them to hand out wooden meter sticks for advertising—in metric only. Demand millimeter Metersticks not Yardsticks.

Related essays:

The American “Metric” Ruler

The Design of Everyday Rulers

America’s Fractional Mind

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 not of direct importance to metric education. It 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.

Metamorphosis and Millimeters

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By The Metric Maven

Bulldog Edition

On a lark, I decided to read a book about bees entitled Fruitless Fall. I was quite surprised that a book about bees could be so interesting. The keeping of beehives is ancient. The traditional, conical shaped, stepped mud/clay beehive was used until 1851. It was then that Reverend Lorenzo Lorraine Lanstroth (1810-1895), of Philadelphia, envisioned an entirely new and radical bee hive design. The Langstroth bee hive did not require a bee keeper to destroy the bee hive in order to harvest the honey. There were numerous other bee hive design improvements Langstrom introduced in an amazing flurry of engineering creativity. Author Rowan Jacobsen describes the affect the introduction of this new bee hive had on this ancient practice:

“….it changed everything. Within a decade the Langstroth hive had swept the United States. In another decade, it was standard throughout the world. And it has endured with only minor improvements  ever since.

It seems remarkable that not a single individual, in the previous eight thousand years of beekeeping history, hit upon this idea. It looks obvious in retrospect, but then so do a lot of revolutionary ideas.” (page 32)

Clay Beehive Used for 8,000 years

This set of prose reminded me how humans can become trapped and arrested by tradition. For generation after generation they repeat received technical methods without questioning if they are optimum or may be improved. The issue is considered to be settled, and therefore not to be re-examined.

This in turn made me think of centimeters. When I was first introduced to millimeters and centimeters in college, it was expected that one be proficient in both. Multiple choice exam questions preyed on those who might confuse the two units. This seemed most prevalent in chemistry and physics classes, but vanished in my engineering classes. Oddly, I never realized this absence until years later, and after some reflection.

At that time, the Engineering Department was teaching the use of “scientific calculators.” The HP calculators used Reverse Polish Notation (RPN). I purchased a Hewlett Packard 29C calculator. When I read the manual, I discovered it had three display settings. One was called fixed, which was just numbers with a fixed number of places beyond the decimal point. The second I expected, it displayed scientific notation. I expected  this would be the setting I would use for the next few years of school. The third option came as a surprise, it said “Engineering Notation.” Well, I thought, I’m going to be an engineer, let’s see how this setting works. What I discovered was that the engineering display setting output numbers in groups of three orders of magnitude.

Table of Engineering Notation (to 12)

What this means in practice is that if I was computing a capacitor or inductor value for instance, the output would match commonly used prefixes on electronic parts.When I computed inductance it would adjust the output to be a whole number raised to ten to the minus ninth, which would be nanohenries or nH. Capacitance would appear as picofarads (pF), nanofarads (nF), microfarads (uF) and track all the standard component value designations. I thought it was beautiful.

There was one odd sticking point, when metric distances were displayed, the unit grouping would be kilometers, meters, millimeters, micrometers, nanometers, picometers and so on. All were a difference of 1000, which meant there was no automatic output for centimeters. If one wanted a centimeter, then the decimal point would need to be moved appropriately. This absence of the centimeter did not produce any epiphany, and for many, many years after that, I continued to embrace the idea of centimeters.

About four years ago I decided to purge all imperial units from my engineering work. I obtained a wooden meter stick from Canada with centimeter markings and alternating colors for each decimeter. Compared with the imperial rulers I’d used, the meter stick seemed much, much simpler and I was poised to embrace it.

I have a fortnightly breakfast with my good friend Sven, and on one occasion mentioned my new centimeter meter stick purchase. Sven gingerly tried to assert that perhaps there were some metric units that should not be used, or at least de-emphasized  as much as possible. Centimeters was first among them in his view. I blanched at the notion. Centimeters were the first metric unit to which I had been introduced during my university study. Clearly my friend was being “too hard” on centimeters, they must be useful, because everyone used them. The notion of eliminating centimeters appeared to be an absurd idea—when I first heard it—but my viewpoint would begin to change as I began to think more about it—and use metric in my work.

I spoke with my friend Thern, who is a mechanical engineer, and mentioned the centimeter discussion I had with Sven. Thern had a quiet measured reply, in the form of a question: “Have you ever seen an engineering drawing in centimeters?”  I realized I had not—and I had seen a considerable number of metric Engineering Drawings. This metric intervention by my friends began to initiate questioning within my mind about the utility of centimeters, but I still thought that they were necessary units. They’re part of SI—right?

I had begun using a small milling machine to create printed circuit boards. The work was all done in millimeters and I dutifully used my centimeter ruler to check dimensions. One day an Australian friend’s gift of a 300 mm and 600 mm set of steel rules arrived. It was then that I realized how much conversion I was doing in my head from millimeters to centimeters. It was as if a decades long fog had been lifted, and I could finally see very clearly. I began to obtain all millimeter based tools and purged the centimeter ones from my tool chest.

I started to wonder just why centimeters had been introduced in the first place. I, then began to suspect centimeters had been introduced so there would be a unit which was similar to an inch in magnitude, and that a 100 part division had worked so well with decimal money—people would quickly catch on to the centimeter. Just as 100 cents equal one dollar so 100 centimeters would equal one meter. The public would accept and embrace metric with more ease if they could relate to the divisions of a dollar.

The centimeter has been around for 200 years, so I expected it was obviously an important choice for a measurement unit. This belief faded quickly when put into practice, and like the bee keepers who were exposed to Langstroth’s innovation after 8000 years of clay beehives, I soon began to question the utility or desirability of the centimeter. When I next met with Sven for breakfast, I had become a fire-breathing opponent of centimeters, which caught my friend by surprise. Only a short time before, I had been arguing centimeters were not a big deal.  A lot had happened since I last spoke with him.

One of the first metric tools I purchased years ago was a dial calipers. Whenever I used it, I seemed to have a terrible time reading it without difficulty. One day while measuring a device for analysis, I continued to stumble making measurements. I thought to myself that I had owned this tool for a long time and perhaps I might consider purchasing a new one. It was at that point I realized how odd perception is. I had been using this set of metric calipers for almost seven  or eight years. It was only now that I realized the dial was in millimeters and the slide was in centimeters. To my astonishment my mind had been looking at the lower slide, realizing it was centimeters, then automatically converting to millimeters and then adding that value to that on the dial. I was doing this without a conscious realization of performing the centimeter to millimeter conversion. I only perceived my calipers “were hard to read accurately.” I found and purchased a metric only set of calipers with millimeters on both the dial and the slide. I was amazed how much easier they were to read.

Caliper with mm and cm (top) Caliper with mm only (Bottom)

I had now started to become radically antagonistic to centimeters, and of the opinion they were archaic and should be dropped from general use. It would be later that I would listen to the late Pat Naughtin’s video and audio lectures which describe how industries that embraced millimeters converted quickly from imperial to metric, and those that chose centimeters so far had not, even after many decades had passed.  Pat found this to be a surprising, and somewhat counter-intuitive result. He has written essays about why he thinks this centimeter-millimeter difference occurs [PDF]. My personal experience combined with Pat Naughtin’s work, convinced me centimeters should be eliminated.

The most enlightening moment in Pat Naughtin’s lectures for me, was when he related that centimeters had been completely banned from use in Australian building construction. All the blueprint dimensions are in millimeters. Centimeters are never to be used in a calculation, never written down or used in any way—period. The choice of millimeters allowed for the use of integer only numbers—simple numbers as Pat would call them.. No decimal point would ever be needed. This choice reduced errors in cutting and measuring so much, that compared with imperial, 10-15% is saved on construction costs. They have saved this ever since their metric conversion in the 1970s.  The American guide to metric construction (yes-there is one) also bans centimeters. It only took Australia about one year to convert their entire construction industry to metric using millimeters.

This example (Australian construction) and others made me realize that the viewpoint that big numbers were somehow unwieldy and awkward to use, was simply folklore. It is a myth which has been passed down from generation to generation. I suspect this is a psychological holdover from using Roman Numerals. The full power of Arabic (Indian) numerals has not been realized out of an irrational concern about “large numbers” somehow being incomprehensible. In practice, these large numbers are most accessible to the least numerate on a project. This is completely opposite of what generations of mathematical folklore claims.

This was a real metric epiphany for me. I realized that for John and Jane Q. Public, it was possible to implement the metric system in the US, in a manner that almost completely eliminates the need for decimal points.  In everyday life one could generally use milliliters (mL), millimeters (mm) and grams (g) almost exclusively. No decimal points needed. The wisdom Pat Naughtin delivered in his lectures and writings has been distilled down to an informal set of Naughtin’s Law’s.

Engineering notation eliminates the prefix cluster around unity found in the current embodiment of SI. The prefix cluster around unity is deci, centi, deka, and hecto. The existence of these vestigial prefixes decreases the utility and ease of use of the metric system.

For cooking one can use milliters, millimeters and grams—period. 1250 grams–no problem—big numbers won’t hurt you—embrace them. In other parts of daily life, Kilometers, Kilograms and Liters would work just fine for Jane and John Q. Public. They might run into milligrams now and then in medicine, but this is a compact set of units compared with the almost endless number of units in Imperial. Engineers and Scientists would be the only ones that would need to know what most of the other prefixes mean off the top of their heads. There is one odd-man-out: Celsius. I discuss this in my blog Making The Milligrade. With a change to milligrade, almost all everyday work could be done without the need for decimal points. The advantages would be enormous.

From my research,  it appears that the way to introduce the metric system in the US, so that its adoption is the most difficult for the public, and thus delay its implementation for decades, even with mandatory legislation, is to: 1) Use centimeters 2) Use dual scales 3) Use the prefix cluster around unity. Current dual-scale rulers sold in the US have centimeter-millimeter scales. In my viewpoint this obscures the utility of metric, and has made metric look like just another kind of inch.

Much like the wholesale abandonment of mud/clay bee hives for Langstrom’s type,  I’m convinced that the time of the centimeter has long passed, if it was ever appropriate. We should expunge it from SI, and use only millimeters, and prefixes separated by 1000. If this version of the metric system were implemented in the US, its great utility and efficiency might almost make-up for the years of cost savings lost, by not introducing metric into the US by law. This will be true only if we don’t continue to dawdle and ignore the problem.

Related essays:

Familiarity Versus Simplicity

Building a Metric Shed

Who Says!?

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 not of direct importance to metric education. It 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.