Category Archives: Metric Education

Technical Presentation and Metric

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By The Metric Maven

Let’s suppose for a moment that I was interested in promoting myself as an expert in the use of the  English language (which, for the record, I am definitely not) and specifically for technical explanation. Further suppose that in order to convince you of this literary expertise,  I sent you a slick bit of advertising copy which has this for its lead sentence:

I is expert in english and know how to show people the ways best to write groups of words for understanding.

How persuaded would you be that my claim of expertise with the English language is true? I suspect you might in fact question my literacy. When you see this construction, the very structure of the sentence serves to disqualify the author, and calls his competence into question. To a  majority of Americans it would be self-evident that this sentence was either a joke, or a sad commentary.

When I read technical trade magazines and other works written by those purporting to be technological guiding lights, I’m often very surprised that the measurement unit equivalent of the mangled sentence above is ubiquitous. Worse, its incongruous nature is often completely invisible to technical readers, and technical authors. I’m not here to  cast blame on particular people, this poor practice is common, but I will uses specific examples from trade magazines for illustration.  I will not directly cite the article, author, and title. The articles I cite are not the issue, it is the accepted use of poor measurement unit descriptions by people in the technical community that is the issue. My first example is from an article which is described as “Educational.”  It describes a type of printing roller called an Anilox Roller.  This roller has a large number of dimples etched into its surface which hold ink for printing. Here is what the author states:

Simply put, the anilox roller is a measuring cup made up of volume carrying pockets that have a particular unit of volume measurement called a “BCM/Square inch.” ….However, unlike measuring cups, there is no standard off the shelf anilox specification. Unfortunately, there is an infinite variety of anilox volumes…

So what is a BCM/Square inch? He explains:

Volume of ink available from an anilox is measured in BCM’s (billion cubic microns). Because the size of a micron (25,400 microns per inch) and the number of cells the laser can engrave into the ceramic, a second unit had to be added to get the volume unit up to an understandable number. BCM/square inch is the volume unit for North America.

The European anilox volume is measured in Cm3/M2 (cubic centimeters per square meter). I will not go through the difference between a micron and a centimeter. I will just move to the down and dirty conversion factors. A BCM is converted to European unit by multiplying the BCM by 1.55. The European unit is converted to a BCM by multiplying by 0.6455. For example, 12 BCM/in2 x 1.55 = Cm3/M2

Yes, the C of centimeter and the M of meter are capitalized in the original. I have tortured you and myself enough. Lets pause and talk about this for a moment. The mixing of metric and Ye Olde English units is bad enough, but giving a separate name to a clearly defined metric quantity of volume is unit proliferation at its worst.

So a BCM is a billion cubic microns, and it is a volume. The metric system has a nice unit for volume called the liter. Those of us who do not live in the 19th century use the term micrometer rather than micron. My understanding is that a billion is 109 and a cubic micrometer is 10-18 cubic meters, or, when the two are multiplied, they become 10-9 cubic meters. We know there are 1000 liters in a cubic meter. That means this volume is 10-6 liters or a microliter. Therefore a BCM is a microliter. Unless I’ve made a mistake converting, this means that 12 BCM/in2 is 12 µL/in2. The “rationale” used is that they had to choose units that give numbers that are understandable. Pat Naughtin argued for numbers to be expressed as integers when possible. He calls this his whole number rule and I’m at one with this view. The author is trying to express a volume contained in small dimples over a given area. One square inch is 645.16 square millimeters. The 12 µL/in2 is therefore 12 µL/(645.16 mm2). To keep with Naughtin’s convention, we shift to nanoliters and have 18.6 nL/mm2.

So instead of creating a ridiculous ad hoc pigfish measurement unit like BCM/in2 one could easily use nanoliters/square millimeter. This actually gives me some feeling for the volume of ink contained in an area. The Europeans embraced the pseudo-inch, also known as the centimeter. They use a square meter as the unit to project upon the Anilox Roller, which seems odd for a roller. When viewed by a pressman, an ink roller would never present anything like that size of an area to him. A millimeter area makes considerable sense. Even so, if the European’s insist that the centimeter be used, why not write the cubic centimeter as a milliliter and use 18.6 mL/m2. This is also a unit that may be easily visualized. This numerical value, 18.6 mL/m2, is the same as  18.6 nL/mm2 and is so easy to convert—just multiply by 1. The rewriting of the European specification with mL would also eliminate the possible confusion caused by using a ratio of length units (i.e. cm3/m2 = 1 µm) rather than using a volume unit in the numerator to provide clarity.

Jargon combination units like BCM/in2, which is a mix of metric and Ye Olde English units, is like my poorly executed sentence in English above. When examined, the unit expression is very, very poor engineering practice. This is either from ignorance, or it’s from willful obfuscation, which acts as an intellectual barrier to those who might embrace the trade. It may accidentally be the latter, but I suspect it is born from the former.

I have spent enough time harping on this “Educational Article.” I will toss out one more example. There has been considerable excitement in recent years about the development of 3D printers. If one has a computer model of a 3D object, it is possible to have that object fabricated in plastic using this printing device which puts down layers of melted plastic. I came across an article which compares available low cost 3D printing units. First the volume of the object which may be fabricated is described:

…the MakerBot Replicator 2, with a build envelope of 11.22 x 6 x 6.12 inches and the Cubify CubeX, with a build envelope of 10.82 x 10.43 x 9.49 inches (basically the size of a basketball).

A basketball has a volume of about 7.5 liters. The MakerBot Replicator 2 has a build envelope of 285 mm x 152.4 mm x 155.4 mm and the Cubifiy Cube X is 275 mm x 265 mm x 241 mm.

The resolution of the 3D printing is next described:

Resolution:  Of the two machines we considered, the Replicator 2 can print to a layer height of 100 microns. The CubeX can only go as fine as 125 microns, but it has options for 250 and 500 micron layers.

Once again, we in the US have never reformed our measurements and gone metric, so we use a 19th century term for the micrometer—the micron. The article goes on to discuss printing speed:

Speed: We recently built one part that took about 20 hours to finish at the highest resolution of 125 microns; it measured 9 inches tall by about 3 inches square. The same piece took about four hours at 500 microns.

Again we see a mixture of metric and Olde English. The resolution he first used was 125 micrometers. The printed part is about 228 mm x 76 mm x 76 mm. One can quickly see this is about 608 layers when the dimensions are all given in metric. This is about 118.4 seconds per layer. The volume of each layer is 76 mm x 76 mm x 0.125 mm or 722 cubic mm. Each layer printed is 722 microliters, so the volume deposit rate for the 125 µm resolution setting is about 6.1 microliters/second.

When the resolution was changed to 500 micrometers, it took four hours to print. The number of layers is now 152 which comes out to 94.73 seconds per layer. Each layer has 2888 µL which gives us 30.48 µL per second.

Considering that 3D printing is creating a volume, it might make sense to describe the printing speed in terms of microliters/second (µL/s) deposited. When set to 125 µm resolution the deposition speed is about 6.1 µL/s and when set to 500 µm resolution its 30.48 µL/s.

The fact that the US has not changed to the metric system produces an isolation, both from our own understanding of technical issues, and from the rest of the technical world. This in turn freezes our metric usage in the past, which is demonstrated by the constant use of the micron in US industry, rather than the micrometer. It reflects poorly on the technical writers of this nation that they do not appear to understand, that from a measurements standpoint, they sound completely innumerate. We in the US like to pat ourselves on the back as technologically advanced. Well at this point it’s more like we use technologically advanced equipment, which even our technical writers can only describe to us with a mismatched set of metric and pre-scientific units. We flatter ourselves at the expense of numerical understanding, even if we can’t perceive that it is happening.

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.

Long Distance Voyager

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By The Metric Maven

Bulldog Edition

When it comes to distance, the larger metric prefixes are generally neglected. Astronomers feel justified in using Astronomical Units to describe distances within the solar system. When distances become large enough, the ubiquitous light-year is then employed with great relish and awe. One of the arguments offered for the absence of the larger metric prefixes in astronomy, is that the distances are just too large, and the metric system is overwhelmed. The distances are just too astronomical for the metric system to handle!—or even convey their vastness! Generally, this manner of argument masks a provincial desire by a specialty of engineering or science to have its “own” special measurements. It is also stated that people can only relate to Km and smaller metric measures because the other distances are outside of their everyday experience.

I have had the privilege of working with some incredibly talented engineers, including the Engineer, who designed the high gain dish antenna which resides on the front of the Voyager spacecraft. His name is Michel, and I once shared an office with him. The Voyager antenna would at one time have been within millimeters of Michel, it was then moved about 4000 Kilometers away from him so it could be launched into space on September 5, 1977 (1977-09-05). It ascended from our planet, which has a circumference of 40 Megameters. Michel’s antenna then passed the orbit of the moon which is about 384 Megameters from Earth. One could argue that the Voyager spacecraft was now in the realm of the solar system. At that point, its distance from the sun might be a more meaningful reference point to describe its distance from us. The Earth is approximately 150 Gigameters from the sun.

Gigameters is a useful length to describe the distances of our planets from the sun, as well as the current location of the Voyager spacecraft (2014-04-04). Michel’s antenna is part of the singular human-constructed object we call Voyager 1, and is further away from the Earth than any other space probe in history—and likely to remain so. Despite the fact that Voyager is now beyond our solar system, its distance is still readily describable in terms of Gigameters. Below is a table of planetary distances and Voyager 1 and 2:

I don’t recall any astronomers ever using Gigameters in school or on television, even though it is a convenient unit. Astronomers define their own “yardstick” which they call an astronomical unit. This astronomical unit is defined as the distance from the earth to the sun, therefore 1 AU = 150 Gigameters. I don’t see why modern astronomers, by which I mean astronomers who have been born after 1960, don’t use Gigameters instead. The prefix Giga was officially adopted in 1960. A Gigameter is certainly as convenient of a unit as an AU, and it’s tied to the meter, which is the universal measurement length used by science, and by 95% of the worlds population. When a person, even an American, sees the symbol Km, they see kilometers. The lack of use of the designation Gm for Gigameters by astronomers makes it unfamiliar and seemingly awkward. It is only the lack of general use which makes this so.

When Astronomers begin to describe distances outside of our solar system, they generally turn to another unit they coined which is unique to astronomers—the light-year. Wikipedia gives the definition of  a light-year as:

1 light-year     = 9460730472580800 metres (exactly)

This is where, if I were forced to write it in meters, I would use the three digit space convention to parse it. The three digit grouping allows a person to identify the appropriate metric prefixes with ease:

1 light-year     = 9 460 730 472 580 800 metres (exactly)

This expression allows one to immediately recognize the metric prefixes as one moves from right to left as: one, Kilo, Mega, Giga, Tera, Peta, and determine that 1 light-year = 9.461 Petameters (Pm). In my view the light-year is more of a “gee whiz” measurement metaphor than an actual length. It is like the kilowatt-hour. There is a metric prefix which is of sufficient magnitude to describe distances which have magnitudes in terms of light-years and it is Peta. The hypothetical Oort cloud is believed to be about 7.5 Petameters away, which when compared with stars, it not  far away.

Almost everyone knows that alpha-centari is the star closest to Earth (other than the sun). It is 4.366 light-years distant. This is 41.4 Petameters. So even when we are discussing the distances to stars, there is a sufficient metric prefix. The light year is not required, at least not after 1975, when Peta was adopted as a metric prefix. Here is a list of nearby stars, and a more distant one also in Petameters:

Constellation of Orion Betelgeuse is the upper left star which is about 6 Em from Earth. Rigel is on the lower right and about 8 Em from Earth — Click to enlarge                    (Wikimedia Commons)

Betelgeuse is a red giant which is in the upper left corner of the constellation Orion. On a clear night in Montana, when I lived far away from the city lights, I could clearly see its red color. Stars beyond Betelgeuse are at distances that may require the introduction of another metric prefix.  This would be the prefix Exa.  One could categorize stars which are “near” earth as those up to 1000 Pm and those beyond 1 Em (Exameter) as “far away” stars. This would make Alpha-Centari, Barnard’s Star and Sirius all nearby stars. Far away stars would include Betelgeuse (6.1 Em) and Rigel (7.7 Em). The farthest currently known star which is still inside of the Milky Way Galaxy is  UDF 2457. It is 558 Em distant.

When we approach the dimensions of the Milky Way Galaxy, we may want to describe the distances from the galactic center. The diameter of our galaxy dwarfs the distance from the sun to Betelgeuse. It is 1 000 000 Petameters across or, shifting metric prefixes, is approximately 1 Zettameter (Zm) in extent. From this information, we know that no star within our galaxy is more than a zettameter away.

The Andromeda Galaxy is 24 Zm from Earth and is visible with the unaided eye.                      (Wikimedia Commons)

Interestingly, we can directly see a distance which is much farther than the dimension our galaxy with the unaided eye. The nearest spiral galaxy is Andromeda, and it can be viewed with the “naked eye.” The Andromeda Galaxy is 2 540 000 light-years away or approximately 24 Zettameters (Zm). This is rather close. It is only 24 times the diameter of our galactic disk. The Andromeda galaxy is expected to collide with our Milky Way Galaxy in 3.75 billion years and form a large elliptical galaxy. Andromeda is not the nearest galaxy overall. The Sagittarius Dwarf Elliptical Galaxy is actually a satellite Galaxy of the Milky Way, that is, it orbits our galaxy. It is only 0.77 Zettameters from our galaxy (or 766 Exameters). This places it just a couple of hundred Exameters beyond the farthest known star within the Milky Way Galaxy.

Here is a short list of local group galaxies which are over one Zettameter away:

The Sombrero Galaxy is 265 Zm from Earth (Wikimedia Commons)

Sextans B is near the end of what is known as the local group of galaxies. The local group encompasses a diameter of about 100 Zettameters (Zm). Clearly there are lots of galaxies which are further away, so which one is the farthest known? The current candidate for the furthest galaxy is MACS0647-JD which is a whopping  125 825 Zettameters (Zm). We can see that we are well beyond a 1000 difference. Has the metric system let us down because of this astronomical distance? No, it has not, at least not since 1991. In 1991 both the Zetta prefix, and the Yotta prefix were added. The Yotta prefix allows us to write the distance to the farthest confirmed galaxy as 126 Yottameters (Ym). The end of the observable universe is approximately 435 Yottameters (Ym). The diameter of the universe is 870 Ym. Astronomical distances do not crush the metric system. There is no need for astronomers to resort to a light-year or AU or parsecs to describe astronomical dimensions. The metric system can in fact be useful to classify astronomical distances. For instance:

click to enlarge
Neil deGrasse Tyson — Host of Cosmos

The latest incarnation of Cosmos has been interesting to watch, but I can only wince when I hear Neal deGrasse Tyson use miles, billions of kilometers, astronomical units, and light-years to describe the cosmos. This archaic measurement usage seems like a lack of respect for the metric system on the part of the Cosmos producers. It is 34 years after the original series was aired. When the original Cosmos aired, the Zetta and Yotta prefixes had not been added to SI. One could see why metric might not have been invoked. Indeed, SI was not large enough to encompass the universe, but like the universe, it expanded. Unfortunately, the root cause for the lack of the metric system in Cosmos could possibly have an even less desirable origin—it could just be unawareness. It is even possible it is the product of a culturally encouraged unfamiliarity. This culturally sanctioned ignorance, if that is the root source, was fortified at the same time as the first airing of Cosmos in 1980. It was in that year that Ronald Reagan quashed any possibility of measurement reform in the US, by disbanding the metric board. This disbanding was an attack on modernity and efficiency, mantled in a red herring of cost savings. It was a narcotic of intellectual flattery perpetrated by a cultural embargo, which has numbed the minds of the American public to the spectrum of metric prefixes, and in turn, it has cost lives. If there is another edition of Cosmos 34 years from now, I can only hope, that by then, it uses the metric system.

Related essay: Neil deGrasse Tyson and The Metric System

This essay was edited on 2016-10-15 to conform with The Elements of Bile.

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.