Stickin’ it to Yardsticks

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.