Busting myths about the metric system

December 27, 2016 by Elizabeth Gentry, National Institute of Standards and Technology
Busting myths about the metric system
Credit: F. Webber/NIST

This week is the 41st anniversary of the Metric Conversion Act, which was signed on December 23, 1975, by President Gerald R. Ford. Normally, we celebrate by sharing metric education resources, but this year I want to use the occasion to dispel some common misconceptions about the U.S. relationship with the metric system.

You've probably heard that the United States, Liberia and Burma (aka Myanmar) are the only countries that don't use the metric system (International System of Units or SI). You may have even seen a map that has been incriminatingly illustrated to show how they are out of step with the rest of the world.

It's a compelling story and often repeated, but you might be surprised to learn that it's simply untrue!

While it's true that metric use is mandatory in some countries and voluntary in others, all countries have recognized and adopted the SI, including the United States.

Dr. Russ Rowlett at the University of North Carolina at Chapel Hill emphasizes on his website that becoming metric is not a one-time event but a process that happens over time. Every international economy is positioned somewhere along a continuum moving toward increased SI use. There are still countries that are amending their national laws to adopt mandatory metric policy and others pursuing voluntary metrication.

The Unites States was one of the original countries to sign the Treaty of the Meter in 1875, which is now celebrated annually on May 20, World Metrology Day. It's been legal to use the metric system since 1866, and metric became the preferred system of weights and measures for U.S. trade and commerce in 1988.

Countries which have not “officially” adopted the metric system (The United States, Myanmar, and Liberia) in gray. Credit: AzaToth [Public domain], via Wikimedia Commons

It's impossible to avoid using the metric system in the United States. All our measurement units, including U.S. customary units you're familiar with (feet, pounds, gallons, Fahrenheit, etc.), are defined in terms of the SI—and have been since 1893! The SI's influence is pervasive and felt even if most people don't know it. I envision U.S. metric practice like a huge iceberg. Above the water's surface, U.S. customary units appear to still be in full effect. In actuality, below the water's surface we find that all measurements are dependent on the SI, linked through an unbroken chain of traceable measurements.

Although U.S. customary units are still seen alongside metric units on product labels and merchandise literature, it's common for the goods themselves to be made using SI-based manufacturing processes. Why? While some businesses are concerned that consumers expect to see customary units on the package, when it comes to manufacturing processes, they are under constant pressure to stay competitive. Adopting the latest science and technology, developed using metric design practices, enables innovation. In addition, many industries extensively use international supply lines to develop, manufacture, and sell their products around the world.

I'm the coordinator of NIST's Metric Program. Because of my passion for all things metric, I encourage companies to investigate adopting metric practices whenever possible and show them how doing so can make a strategic economic impact for their organization. Changes in technology and extremely competitive domestic and global marketplaces can compel businesses with little previous experience to explore metric use. Many have found that going metric pays off, resulting in a competitive advantage.

If your business is considering making the switch to metric, I would encourage you to conduct small beta tests to explore how your customers react. Research can help ensure decisions aren't based on out-of-date information or preconceived notions. You might be pleasantly surprised by how quickly customers adapt—and how using metric benefits the bottom line.

Metric system use in the US lies along a continuum where some measures are entirely in metric and others are entirely devoid of it, at least at the consumer level. Credit: E. Gentry/NIST

And as always, if you need advice, be sure to give NIST a call; we're here to help!

Going Metric Pays Off

During the recent recession, lumber companies located in the U.S. Northwest saw their U.S. customer base shrink, but its Canadian and Japanese markets, both of which use metric, expand—especially after the 2011 earthquake and tsunami. Wood-product producers made adjustments so that their production systems could flex between metric and U.S. customary measures based on what their customers needed. Because so much of the world uses metric only, more and more U.S. companies are recognizing the benefits of as they find new international markets for their products.

Explore further: US, Canada broker agreement to share dwindling cod fishing

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Eddorian
3 / 5 (2) Dec 31, 2016
The metric system is extremely useful in many ways, but the fractional approach of linear measures in the imperial system offers real advantages for activities like woodworking and furniture making. If an worker is handy with common fractions, measuring and cutting, finding centers, etc. are far easier and quicker than decimal approximations. The Imperial fraction system also offers advantages in layout without risking propagating errors due to decimal underflow. However, I would far prefer purchasing metric -dimensioned lumber where the stated size is accurate rather than notional.
julianpenrod
1 / 5 (7) Jan 01, 2017
In terms of a unit "arbitrarily" chosen as one ten millionth the distance from the equator to the North Pole, it's unusual that the speed of light comes out as almost exactly 3 times 10 to the 8th power meters per second, the radius of earth's orbit is almost exactly 50 light seconds, the year is almost exactly pi times 10 to the 7th power seconds, the earth at the equator moves almost exactly 1000 miles per hour, the moon is almost exactly 10 earth circumferences away, the spot for a geostationary orbit is almost 1 earth circumference above the surface of the earth, the moon's size fits almost exactly to the size of the sun seen from earth, the velocity of the moon in orbit is almost exactly 1000 meters per second, the diameter of the moon is almost exactly 100 times the radius of its orbit. There is a point where a number of "coincidences" becomes too much and someone has to suggest it was all designed.
adam_russell_9615
3.7 / 5 (3) Jan 01, 2017
Q: Why did the world not adopted metric time units?
A: Because the changeover would be too inconvenient - coincidentally, the same reason the US has not adopted kilometers!
antialias_physorg
not rated yet Jan 02, 2017
, the same reason the US has not adopted kilometers!

Why, exactly, is the kilometer an inconvenient unit?

Changing clocks to a decimal based system would be a major design change - whereas changing to meters just requires printing another number.
Guy_Underbridge
4.6 / 5 (9) Jan 02, 2017
In terms of a unit "arbitrarily" chosen...and someone has to suggest it was all designed

You used 'almost' for every example, and had to change units and measures to even get that to work.
Pretty much almost exactly BS
KelDude
not rated yet Jan 02, 2017
As a Canadian it drives me crazy that the US is still on the Imperial system. The article says the US is largely metric already, what crap. On the surface, day to day experiences are still pounds and inches. In Canada its Kilograms and meters but try to buy a scale, a car or a measuring tape that's only in metric, it's almost impossible. Speedometers in Canada have both on the gauge. All the thermometers out there are "both systems" yet we only use metric here. We are treated as a "spin off market" to the US so because they are still Imperial, we get everything bastardized with both units. Catch up you guys, it's easy once you change over. Reading science articles is particularly annoying with things like "25 pounds (12 Kg)" describing weights then later in the same article you see "12 kg (25 lbs)" as the convention to show both. The US has even crashed a billion dollar spacecraft onto mars because the engineers wrote the manual in metric and the "pilot" used them as Imperial. doomed!
Nik_2213
5 / 5 (1) Jan 02, 2017
Even the supposedly metric UK sells milk in pint multiples, but labels them as equivalent decimal litres...

And, d'uh, some weather forecasts still come through in 'F.

{ "Subtract 32, multiply by 5/9 for 'C." Of course, '-40' is the same in both systems... }
24volts
not rated yet Jan 02, 2017
It probably won't change until folks like me that were taught the old system completely die off. And even then it's going to take at least another generation or so. My kids and grandchildren were all taught the metric system but they still tend to use the old system most of the time.
RealScience
5 / 5 (1) Jan 02, 2017
@JP:
Not metric: the earth at the equator moves almost exactly 1000 miles per hour.

Regardless of metric: the moon is almost exactly 10 earth circumferences away, the spot for a geostationary orbit is almost 1 earth circumference above the surface of the earth, the moon's size fits almost exactly to the size of the sun seen from earth,... the diameter of the moon is almost exactly 100 times the radius of its orbit.

There is a point where a number of "coincidences" becomes too much and someone has to suggest it was all designed.

If it actually were all designed, these would all BE exact, and not 'almost exactly'.
Eikka
1 / 5 (1) Jan 03, 2017
If an worker is handy with common fractions, measuring and cutting, finding centers, etc. are far easier and quicker than decimal approximations


Working the traditional way, you don't measure in inches either because nothing ever comes to exact fractions - wood shrinks and grows with humidity and temperature, and you make errors in measurement anyhow, so you match piece to piece or cut the parts that are meant to be the same size against the same fence setting - not to a measuring tape.

Otherwise you end up with yawning gaps in your work with all the random errors you do.

So, Finding a center in metric is the same - you don't care where it lands to the millimeter just as you don't care what fraction of an inch it is - the actual number you'll find is often irrational as it involves Pi or the square root of 2 etc.

Working from designs, you respect the units. There you get into real trouble with adding fractions instead of decimals, unless it's all in 1/16 or 1/32
Eikka
not rated yet Jan 03, 2017
If it actually were all designed, these would all BE exact, and not 'almost exactly'.


"I'm no mathematician, but it always blows my mind that there are exactly Pi radians in a circle."

The original definition of the meter was supposed to be the seconds pendulum. A weight tied to a string exactly 1 meters long from pivot to center of the mass will swing at 1/2 Hz, or make a half-swing in exactly one second - give or take the variation in the local force of gravity.

It didn't become the offical definition because they coincidentally noticed that the local gravity was variable when they attempted it. Still, it's a useful definition because it can be replicated to within 1-2% just about anywhere in the world.

So if you don't have a measuring tape, grab a rock and a piece of string and time it with a watch.
antialias_physorg
5 / 5 (3) Jan 03, 2017
the moon is almost exactly 10 earth circumferences away,

I'm curious: What exactly is the significance of the Earth-circumference to distance-Earth-Moon relation? It's like saying the height of a traffic cone is almost equal to the length of a platypus. While undoubtedly true I fail to see the significance in this 'correlation'.

But I'm sure JP will add it to the list of "coincidences that just mount up."

Eikka
not rated yet Jan 03, 2017
I'm curious: What exactly is the significance of the Earth-circumference to distance-Earth-Moon relation?


It's a geometric improbability if you think that the moon has always been in the same place instead of slowly receding.

Knowing that the moon does recede, it's merely curious that we should be alive exactly when it occurs.

Although if you were being precise, the earth-moon distance varies by 31,000 miles through the orbit. And it's 60.32 earth radii away on average, which is 9.6 circumferences (2pi * r) and not 10.

antialias_physorg
5 / 5 (4) Jan 03, 2017
It's a geometric improbability

By what measure? Just because we like the number 10 because of our 10 fingers? A decimal system is just a convenience - not a 'natural' one. Stuff sometimes happens to be close to an order of magnitude on an arbitray number scale. Wow. Amazing! I bet I can show such a coincidence for ANY two measures you care to name by just choosing an appropriate base (and no: doing math in base 7 is not any more difficult or 'unnatural' than doing it in base 10 or base 3785).

(And note: the Moon is not on a circular orbit. The ratio of Earth-Moon-Diameter to Earth circumference varies between roughly 8.96 to 10.12 between Perigee and Apogee...where exactly is the 'improbability in any of these numbers?)
Zorcon
5 / 5 (2) Jan 03, 2017
Why, exactly, is the kilometer an inconvenient unit?


Because politicians are terrified of low-information voters. Uttering a scary word like "kilometer" would be every bit as dangerous as proposing a dollar coin.

You would also have to teach everyone to divide by 10, but where would you find teachers who can do that? It would require a complete overhaul of the educational system!
Whydening Gyre
5 / 5 (2) Jan 03, 2017
@JP:
Not metric: the earth at the equator moves almost exactly 1000 miles per hour.

Regardless of metric: the moon is almost exactly 10 earth circumferences away, the spot for a geostationary orbit is almost 1 earth circumference above the surface of the earth, the moon's size fits almost exactly to the size of the sun seen from earth,... the diameter of the moon is almost exactly 100 times the radius of its orbit.

There is a point where a number of "coincidences" becomes too much and someone has to suggest it was all designed.

If it actually were all designed, these would all BE exact, and not 'almost exactly'.

The designed part is the math that we construct to parse all the "coincidences"..
Eikka
1 / 5 (1) Jan 03, 2017
By what measure? Just because we like the number 10 because of our 10 fingers?


Exactly because of that. The idea is, why should nature conform to numbers that are "nice" for us? If it appears to do so, that would be a "calling card from God" - a miracle of sorts, like finding a fair coin that nevertheless prefers to land on heads against all odds.

Of course, it doesn't - it's a fable.

(though a statistician might conclude you simply got incredibly lucky - a real gambler would say there's something else going on with the coin)
Eikka
1 / 5 (1) Jan 03, 2017
Why, exactly, is the kilometer an inconvenient unit?


In my experience, because nobody really knows what a kilometer is in practice. It's difficult to relate to, because it's too long to experience directly and the indirect means are prone to error, yet it's shorter than you imagine it to be when you actually walk it out.

If you ask someone to walk a kilometer, they go all over the place unless they're counting paces and taking care to step just that little bit more than what comes naturally so they don't accidentally pace in yards.

Driving a car, it's common to average a mile a minute. It becomes more challenging to think in increments of 1.67 km when relating time to distance.
RealScience
5 / 5 (2) Jan 03, 2017
In my experience, because nobody really knows what a kilometer is in practice. ...


Most people, even in the U.S., don't know what a mile is in practice either..

...counting paces

Agreed! For the few who remember that a mile is 1000 paces, this is one of the measurements that still is easier to approximate in imperial. Since I walk a lot I still pace a distances in miles at least once a year.

Driving a car, it's common to average a mile a minute. It becomes more challenging to think in increments of 1.67 km when relating time to distance.


1.6, not 1.67. But while a mile a minute on the highway is useful for short distances, 100 km per hour is perfect for long distances. And in town a kilometer per minute works well.

I find that it is great to know both systems - I do any math in whichever system the numbers are rounder in, and then convert at the end to whichever system I want the answer in.
antialias_physorg
not rated yet Jan 04, 2017
(though a statistician might conclude you simply got incredibly lucky - a real gambler would say there's something else going on with the coin)

Good gamblers are good statisticians. I'm currently reading up on the math (game theory) used by Texas Hold'em pros. Proficient gamblers are very well aware of falling into the trap of prematurely calling something 'off' just because it looks like a lucky/unlucky streak to a layman (because such a misjudgement will cost them a lot of money).

Pareidolia is the bane of a scientific mindset.
Itar_Pejo
3.7 / 5 (3) Jan 04, 2017
In science the metric system is absolute winner, especially when working with microscopic sizes. Much easier and less prone to errors is to write 2 Micrometers than 7.874e-5 inches. Do not even attempt to go into the Nano/Picometer sizes.

The Celsius scale is based on easily observable everyday water properties, 0 degrees is when water freezes and 100 is when it boils.
Guy_Underbridge
3.7 / 5 (3) Jan 04, 2017
Driving a car, it's common to average a mile a minute. It becomes more challenging to think in increments of 1.67 km when relating time to distance.

Driving a car, it's common to average 2km a minute. Dividing by two shouldn't be a major challenge.
Whydening Gyre
5 / 5 (2) Jan 04, 2017
Most people, even in the U.S., don't know what a mile is in practice either..

Well, I know it's 1.3 miles to the 7/11 in town. (approx 2km)
...counting paces

Agreed! For the few who remember that a mile is 1000 paces, this is one of the measurements that still is easier to approximate in imperial. Since I walk a lot I still pace a distances in miles at least once a year.

I did not know that! But it makes sense - 5.28 feet per pace (right,left)...
... It becomes more challenging to think in increments of 1.67 km when relating time to distance.

1.6, not 1.67.
Technically, closer to 1.61... :-)
... it is great to know both systems - I do any math in whichever system the numbers are rounder in, and then convert at the end to whichever system I want the answer in.[/q}
Exactly! Added benefit of keeping the brain challenged!
RealScience
5 / 5 (1) Jan 04, 2017
In science the metric system is absolute winner


As much as I prefer metric for MOST science, it is far from an "absolute winner".
Examples that spring to mind of non-metric or quasi-metric units range from the very big:
Light years, parsecs and red-shit Z for distances, measuring stars in solar masses and planets in Jupiter and Earth masses, measuring orbits in AU; down through the Richter scale and volcano index; to the very small (measuring energy and even mass in electron volts). Even minutes, hours and years are non-metric, and yes, scientists use these terms.

If someone asks you your age do you answer in megaseconds?
Or do you, too, use non-metric when it is more convenient?

Much easier and less prone to errors is to write 2 Micrometers than 7.874e-5 inches

Picking a round number in metric and then complaining that it is easier than in imperial is biased. 3 mils is a lot easier that 76.2 micrometers, for example.
RealScience
5 / 5 (1) Jan 04, 2017
I did not know that! But it makes sense - 5.28 feet per pace (right,left)...

Exactly - I count every right foot. (And 'mile' is related to 'mil' for 1000).

Technically, closer to 1.61... :-)

True enough, but 1.6 is correct to two places and it is a very nice number for math in one's head.

If I need more accuracy I use 1.6 and keep track of the ~1/2% error (effectively 1.608).
For multiplying errors add, so for miles cubed to kilometers cubed it would be 1.6 cubed = 4.096 (because 16 cubed is 2^12 or 4096), and the error would triple to 1.5%, so 4.10 (4.096 rounded off + 0.06 (1.5% of 4) = 4.16 cubic kilometer - let's check: Google says 4.168!

If I need more accuracy than that, I get out my calculator and use 1.609... to however many places are needed.
Eikka
not rated yet Jan 04, 2017
1.6, not 1.67. But while a mile a minute on the highway is useful for short distances, 100 km per hour is perfect for long distances.


100 mph is perfect for long distances. Too bad you're mostly not allowed to.

I was rather thinking about driving at 100 kph. Common speed limits just cause inconvenient fractions; 80 is 1.333... and 100 is 1.666... km/min. It's even more annoying if you happen to be Swedish, because they have a 70 kph limit. I've sometimes entertained myself while commuting trying to calculate the time of arrival in my head, and it's easier in miles because you can pretty much assume 30 and 60 mph averages for town/highway.

And in town a kilometer per minute works well.


I've seen 30,40 kph downtown and 50,60 kph in between. Trouble is, you get traffic lights and roundabouts so you're never really doing 60 kph average speed even if that's the limit, so the point is a little bit moot.
Eikka
5 / 5 (1) Jan 04, 2017
The Celsius scale is based on easily observable everyday water properties, 0 degrees is when water freezes and 100 is when it boils.


Except that the boiling point drops by a degree for every 1000 ft of elevation due to air pressure, so it's harder to get right without knowing where exactly you are. You also need pure water to get the correct freezing point.

That was the convenience of the Farenheit system - you don't need pure water to calibrate your thermometer to a reasonable accuracy - instead you're adding impurities because the low point is measured by adding salt to ice - the temperature drops to the melting point of saturated brine. The other point of reference was your own armpit, because the daily average human body temperature varies less than a degree whether you're 6000 ft up in the hills or down by the coast.

Today that's irrelevant, because you no longer need to build and calibrate your own thermometers.
Eikka
5 / 5 (2) Jan 04, 2017
Or do you, too, use non-metric when it is more convenient?


The irony is, liter is not an SI unit - it's a convenience unit the same as the gallon or the quart.

If you were really hardcore metric by the MKS system, you'd be buying your milk in cubic meters. Cubic decimeters would be allowed in a pinch.
RealScience
5 / 5 (1) Jan 04, 2017
The irony is, liter is not an SI unit - it's a convenience unit ...
If you were really hardcore metric by the MKS system, you'd be buying your milk in cubic meters. Cubic decimeters would be allowed in a pinch.


Yes, the informal metric units get used a lot - Angstrom, for example, instead of tenths of a nanometer. And for metal layer on a semiconductor wafer, kiloAngstroms are often used. Or milliliters. And then there are mixed units like km/h (kph) in which hour is not a metric unit.

I was rather thinking about driving at 100 kph. Common speed limits just cause inconvenient fractions; 80 is 1.333... and 100 is 1.666... km/min.


Those are inconvenient decimals, but 1.333 and 1.666 are very convenient fractions: 4/3 and 5/3.

When I'm on a U.S. highway where the speed limit is 70 mph, I got 120 km/h (just under 75 mph), or 2 km per minute. That's also a convenient 20% less than a minute per mile (or 25% more that a mile per minute).
Whydening Gyre
5 / 5 (2) Jan 04, 2017
Bottom line is - they're both different ways of describing the same thing.
Like - languages.
Different brains acclimate to different languages. If you don't practice with both you'll defer to the one you've had the most exposure to.
Itar_Pejo
3 / 5 (2) Jan 04, 2017
@RealScience I was thinking absolute winner of Metric over the US system of units though, since the article was more or less about that. And of course I use megaseconds for my age, it makes me seem much younger.

" Picking a round number in metric and then complaining that it is easier than in imperial is biased. 3 mils is a lot easier that 76.2 micrometers, for example. "

That is true but micrometer is still a relatively 'large' measurement, how about the picometer to mils conversion for example?

RealScience
5 / 5 (1) Jan 04, 2017
@... of course I use megaseconds for my age, it makes me seem much younger.


And you get to celebrate a megasecond milestone over 30 times as often as a yearly birthday!
And, of course celebrate for 10,000 seconds rather than just a day - you must be exhausted from all of the partying....

That is true but micrometer is still a relatively 'large' measurement, how about the picometer to mils conversion for example?


The picometer to mils conversion is easy - a mil is 25.4 million picometers, no calculator needed (thanks to a micron being a million picometers).

The smallest imperial unit that I actually ran into was a micro-inch, or 1/1000 of a mil. Micro-inches turn out to be a convenient unit in plating metals. Interestingly it was on the same project where other metal thickness were measured in kiloAngstroms, and a kiloAngstrom is 4 microinches (that's 3.937 for WhydeningGyre, just as a meter is 39.37... inches).
Eikka
not rated yet Jan 06, 2017
Those are inconvenient decimals, but 1.333 and 1.666 are very convenient fractions: 4/3 and 5/3.


Except that's just pushing the problem along the road, because then you have to fit thirds in the calculation with halves, quarters, eights... e.g. what's 4/3 plus 3/4?? Suddenly it becomes a whole lot more complex to do it in your head. That's why odd fractions are generally not used with the US customary measures. If you're going to use fractions, 1/2^n are nicer.

RealScience
not rated yet Jan 06, 2017
I have no problem with halves, thirds and quarters in my head (I learned math before there were pocket calculators). 4/3 + 3/4 is 16/12 + 9/12 = 25/12 = 2 and 1/12.

The great thing about 1/2^n fractions is that one can approximate them physically because it is easy to divide a length in half as many times as is needed, and easy to convert something like 11/16 to 1/2 + 1/8 + 1/16.

I generally use feet for coarse work like fencing, inches and fractions for carpentry, and metric for most other things. For temperatures I only use Fahrenheit for cooking, and use Celsius of Kelvins for everything else.

Where metric is really good, however, is when a project involve a huge range of measurements, because it is easier to convert nanometers to kilometers than it is to convert micro-inches to miles, of square meters to hectares than square feet to acres.
Eikka
not rated yet Jan 07, 2017
I have no problem with halves, thirds and quarters in my head (I learned math before there were pocket calculators).


It stil introduces extra steps, and the result won't conform to 1/n^2 so the same issue keeps popping up over and over.

Fortunately you can just approximate it as 13/8 km/min and get over it.

Eikka
not rated yet Jan 07, 2017
Where metric is really good, however, is when a project involve a huge range of measurements, because it is easier to convert nanometers to kilometers than it is to convert micro-inches to miles, of square meters to hectares than square feet to acres.


When does that ever happen though?

RealScience
not rated yet Jan 07, 2017

When does that ever happen though?


Very funny!
(A Mars Climate Orbiter millions of miles away with foot-pounds of thrust crosses a range of scales even if done entirely in imperial...)

In case you aren't being humorous:

I hit conversions involving acres and square feet in agricultural research - scaling pounds per square foot to tons per acre (and occasionally I've dealt with cubic feet of water per second draining or filling a reservoir with a capacity measured in acre-feet.

I only once had nanometers and km together (in the mass of a hypothetical gossamer mirror for a 1 km space telescope that would have ~100nm of silver on a few microns of plastic film).

But an ugly conversion I often run into is solder or epoxy listed in BTUs per hour per foot per degree F (or per ft^2 per inch) for thermal conductivity, when the chip to cool is measured (even in imperial) in inches and in Watts. That's one where metric is MUCH nicer!
Eikka
not rated yet Jan 08, 2017
That's one where metric is MUCH nicer!


That's also where you'd expect a simple conversion factor to exist, because it's just W/mK with another name - much like gallons and liters. Since the chips and traces are measured in inches (mills/thous) it's less work to convert Watts to BTU/h than the other way around.

Something like BTU per hour per foot per degree F sounds daunting when you put it like that, but it's a simple constant (k-value) that is used as such in the formulas. At worst you have to convert it once for the size of unit you're dealing with, such as square mils.

You'd do the same in metric as well, because otherwise you're dealing with a unit that is ridiculously large (square meter) to the size of the device (square centimeter or millimeter) which means you have to write those pesky 10^-3 and 10^-6 multipliers everywhere and damn if you forget to carry them along.
Eikka
5 / 5 (1) Jan 08, 2017
And metric too has stupid units, like the Pascal, which is approximately the weight of a deciliter of water (2/5ths of a standard coffee mug) spread evenly over a square meter.

It's so small that any useful pressure or tension measured in it has a prefix of million - MPa. Hence why material properties are expressed in MPa which is equal to Newtons per square millimeter, which is a bitch of a unit when you're dealing with objects larger than a toothpick - like bridges and skyscrapers.

Pounds per square inch makes much more sense. With Pascals it's like trading in Zimbabwean dollars: "Very cheap, it's only million million million million.... and two dollars, fifty nine cents."
RealScience
not rated yet Jan 08, 2017
That's also where you'd expect a simple conversion factor to exist...
...
BTU per hour per foot per degree F ...sounds daunting... at worst you have to convert it once for the size of unit you're dealing with, such as square mils.


Yup. I got tired of doing the math and finally just remembered 7-to-1 if ft and 0.6-to-1 if ft^2/inch. Now I only have to figure out whether to divide or multiply...

You'd do the same in metric as well, because otherwise you're dealing with a unit that is ridiculously large (square meter) to the size of the device (square centimeter or millimeter)...

That's easy: 400 W/mK (copper) is 4 W/cmK is 0.4W/mmK..

you have to write those pesky 10^-3 and 10^-6 multipliers everywhere and damn if you forget to carry them along.

'm' and 'μ' are pretty easy to write, and factors of 1000 are relatively easy to spot.

RealScience
not rated yet Jan 08, 2017
And metric too has stupid units, like the Pascal...

It's so small that any useful pressure or tension measured in it has a prefix of million - MPa. ... which is equal to Newtons per square millimeter, which is a bitch of a unit when you're dealing with objects larger than a toothpick - like bridges and skyscrapers.

Pounds per square inch makes much more sense...


Yeah, a Pascal is wimpy for sure - I deal with micro-channel cold plates and even there pressure drops are in kPa, while strengths are in MPa, and stiffnesses are in GPa.

I'm fine with kPa (100 kPa being ~1 atmosphere is often nice), but if I want to know if something is safe I still think in psi, and the same for adhesive strength.
And for steel I still think in imperial, but ksi .. and then for stiffness I'm back to metric and think in GPa.

Whydening Gyre said it well:
If you don't practice with both you'll defer to the one you've had the most exposure to.


Eikka
not rated yet Jan 09, 2017
'm' and '�Ľ' are pretty easy to write, and factors of 1000 are relatively easy to spot.


That was for actually computing the formula. You have to convert all the mm and µm into 10^-3 and 10^-6 so the magnitudes of the actual numbers match. Alternatively you can write a whole bunch of zeroes everywhere in your solution and tap that into your calculator. That's why the "exp" button is in there.

It's not so bad for linear measures, but I always mess up the area and volume, because the conversion factor between a cubic meter and a cubic millimeter isn't 1,000 but 1,000,000,000 and going over quickly you automatically think, "Oh, milli... that's 10^-3..."

Eikka
not rated yet Jan 09, 2017
What also causes confusion is the fact that the metric units aren't actually evenly spaced. You go meter, decimeter, centimeter, millimeter, micrometer, nanometer... or the other way around meter, decameter, hectometer, kilometer...

You go a factor of 100 up from cm to m, but a factor of 10 down to mm.

It's a power of 10^(-) 0,1,2,3,6,9,12... so going from centimeters to nanometers you have to remember this arbitrary sequence. Always causes undergraduates to scratch their heads when you ask how many centimeters is a nanometer, because it's not a neat "shift decimal point by a thousand" question. One is 1E-2 and the other is 1E-9 and if you're clever you divide 1E-9 / 1E-2 which is 1E(-9+2), so it's 1E-7 or 0.0000001 cm.

There you have to remember that it's 0. and then one less zero than the exponent. Some people go and write 0. and count seven zeroes and a 1, which is 1E-8. Worse still, if the number wasn't 1 but say 14, they go 0.000000014 which isn't 14E-7 but 14E-9.
Eikka
not rated yet Jan 09, 2017
That's easy: 400 W/mK (copper) is 4 W/cmK is 0.4W/mmK..


Is it? Shouldn't the heat flow increase as the thickness of your insulator decreases?

You get the actual thermal flow by k*A/L which has the units of W/mK * m so it simplifies to Watts per Kelvin as long as all your lengths are in the same unit - doesn't matter if it's meters, centimeters or inches because the units cancel out.

So, you can just as well say 400 Watts per foot-Kelvins. It's the exact same number as long as your insulator area is in square feet and the insulator thickness is also in feet.

Then, for convenience, you could convert Watts into BTU/h and Kelvins into F, and you're back where we started - a simple constant that doesn't actually need to be converted to anything as long as you keep your units consistent, which is the simpler way of doing things.
RealScience
not rated yet Jan 09, 2017
That's easy: 400 W/mK (copper) is 4 W/cmK is 0.4W/mmK..


Is it? Shouldn't the heat flow increase as the thickness of your insulator decreases?

NO. If the scale is reduced by 10, the thickness and hence the heat flow per AREA increases by 10x. But the area is reduced by 100x, so the total heat flow (Watts) is reduced by 10x.

You get the actual thermal flow by k*A/L which has the units of W/mK * m so it simplifies to Watts per Kelvin as long as all your lengths are in the same unit - doesn't matter if it's meters, centimeters or inches because the units cancel out.


NO. There is only an 'm' in the denominator so the constant does NOT simplify to as a W/K.

There are TWO length units in area (square units), and only ONE in thickness so they do NOT cancel. the thickness only cancels ONE of the TWO units in area, leaving ONE unit.

- example to follow -
RealScience
not rated yet Jan 09, 2017
Example:

A copper cube a meter on a side has its bottom face in boiling water, a block of ice on the top face, and the sides insulated so heat flows from bottom to top with no lateral heat flow.

The hot face has an area of 1 m2 to carry the heat, and a thickness of 1 m to resist the heat flow.
Area/ thickness is 1 m2 / 1 m = 1 m.
Plugging 1 m into 400 W/mK gives 400W * 1 m / mK.
4*100 is 400, and m cancels m, so that reduces to 400 W/K.
The temperature difference is 100 K (Kelvins), which at 400 W/K is 40,000 W.

Now let's do it in cm:
The hot face has an area of 100 cm * 100 cm = 10000 cm2 to carry the heat and 100 cm of thickness to resist the heat.
Area / thickness is 10000 cm2 / 100 cm = 100 cm.

Plugging 100 cm into 4 W/cmK gives 4W * 100 cm / cmK.
4*100 is 400, and cm cancels cm, so that reduces to 400 W/K.
The temperature difference is still 100 K, which at 400 W/K is 40,000 W.
QED

If we had used 400 W/cmK we would have been off by 100x!
Eikka
not rated yet Jan 11, 2017
NO. There is only an 'm' in the denominator so the constant does NOT simplify to as a W/K.


That doesn't make sense.

It's a temperature difference across an object that conducts heat - once the dimensions are put in there are no more free variables that would influence the outcome. When the dimensions of the conductor are known, the result -must- simplify to W/K.

Examining the units:

A/L = m^2/m = m

When you multiply W/mK by m, as in kA/L, that cancels out the other m in the denominator and it leaves W/K. That much is plainly obvious.
RealScience
not rated yet Jan 11, 2017
Yeah, the first time I ran into W/mK I said "where's the area? where's the thickness? Why use such a silly unit?"

For a given chip, AFTER you put in the area and the thickness you must get a constant number of degrees per power for that chip.
So for 1 cm2 chip with 100 um (1/100 cm) of copper at 4 W/cmK, you get 1/400 K/W = 0.0025 W/K.
And you'll get 0.0025 Kelvins per Watt no matter what length measurement you use.
So yes, the thermal resistance of a GIVEN CHIP in K/W is indeed a constant that does not depend on the length unit used.

However that does NOT mean that the CONSTANT in the thermal conductivity value for a MATERIAL is independent of the length unit. If we measure that same chip in millimeters, its area is now 100 times a larger number while its thickness is only a 10 times larger number, to the constant used for the thermal conductivity of the material must also change by 10x to compensate.

So 4 W/cmK is 0.4 W/mmK (or ~120 W/footK or 10 W/inchK).
Eikka
5 / 5 (1) Jan 11, 2017
If we had used 400 W/cmK we would have been off by 100x!


Ah yes, I was doing the math right but thinking in factor of two instead of power of two. That gave me the intuition that as the absolute unit thickness doubles (conductance halves) the area would increase to keep a constant ratio. What a mixup!

RealScience
not rated yet Jan 11, 2017
Yes, it took me a while to convince myself that it made sense.

But after I had converted units a few times by converting both area and length a few times, I finally got lazy and tried just scaling the constant for the material linearly.
It worked (it gave the same answer with less effort), and after I checked it a few more times and it still worked, I finally internalized it and now it make sense to me...

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