Category Archives: Metric Education

Joule in the Crown

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By The Metric Maven

The creators of the television series Futurama had a question about money in the future. Would there be any? After deciding there probably would be, they speculated about what form the currency might take. An early suggestion for a currency basis was the joule, but in the end they opted for the dollar. The joule seemed like a much better idea to me, what is more important to the “modern” world than energy? Energy has made life luxuriant when compared with the life our forefathers (and foremothers) experienced. The joule is the unit of energy in the metric system and would be universally recognized—well except in one country.

Recently a fellow from the local energy company knocked on my door and announced he needed to work on the gas meter. Apparently in the mid-1990’s a wireless reader was installed so it could be read remotely. The battery was at the end of its life and so it was to be replaced. I watched as the technician unscrewed the existing meter module, which has its units in cubic feet. He then replaced it with an identical module, which in the year 2014 still reads out in cubic feet of gas.

My utility company sends me a bill for energy usage each month. The word energy is even in their corporate name. Below is a scan of a recent bill’s comparison information section:

The gas and electric energy usage is offered in Kwh per month and in therms respectively. The Kwh stands for kilowatt-hours. A watt is a joule per second, so multiplying a value in watts by hours is pigfish talk. The recognized unit of time in SI is the second. For this bill, the first energy value given is 928 Kwh for the electrical energy used, but energy is internationally described in joules. When all the conversions are done, the electrical energy used for the month in SI is 3341 megajoules.

The natural gas usage is assumed to be in Therms. So what is a therm?  Well, in the US, it’s 100 000 BTU, and BTU are British Thermal Units, but not the British Thermal units used by the British, those are a bit different. These are American British Thermal Units—you know—the patriotic kind. Gas meters don’t directly measure the energy delivered, but instead the volume of gas delivered. According to Wikipedia:

Since (Natural Gas) meters measure volume and not energy content, a therm factor is used by (Natural) gas companies to convert the volume of gas used to its heat equivalent, and thus calculate the actual energy use. The therm factor is usually in the units therms/CCF. It will vary with the mix of hydrocarbons in the natural gas. Natural gas with a higher than average concentration of ethane, propane or butane will have a higher therm factor. Impurities, such as carbon dioxide or nitrogen, lower the therm factor.

The volume of the gas is calculated as if it was measured at standard temperature and pressure (STP). The heat content of natural gas is solely dependent on the composition of the gas, and is independent of temperature and pressure.

Therms “Explained” for Consumers.  It is noted that 10 therms is a decatherm (Dth) and not a dth as one might expect. This is very “metricy” sounding but clearly not metric. Therms are BTUs  (click to enlarge)

So we have to have a temperature correction, and apply a therm factor which is in therms/CCF. So what is a CCF?  Well, it’s centium cubic feet or 100 cubic feet. So  the first C is the roman numeral C and stands for 100. The second identical C stands for the word cubic and F is for foot. It is sometimes alternatively written as Ccf. MCF is also used for 1000 cubic feet. The M standing for the Roman numeral for 1000 The correction factor is used to calculate the value as if it were at STP (i.e. standard temperature and pressure). Obviously, accurate values for temperature are important in determining accurate values of natural gas usage. I assume that the average daily temperature has some relationship to this required correction factor. It does not have an obvious entry on my bill. Here is what my energy company states:

Therm Multiplier

Gas usage is defined in Therms, a measure of the heat, or energy content of natural gas in a billing period. One Therm equals 100,000 British Thermal Units (Btu). The energy content of gas changes depending on its source, the altitude and temperature at which it is delivered. After your meter measures your usage by volume (in hundreds of cubic feet and appearing on your bill as “Measured Usage”), this volume is multiplied by the Therm Multiplier to determine the units of energy consumed.

Kwh “Explained” for Consumers (click to enlarge)

The multiplier is not broken down any further and does not spell out the individual contributions. Apparently the temperature, altitude, energy content and such are all wrapped into the Therm Multiplier. The comparison section on my bill is strange, as it has natural gas printed on a line above electric as if the top line is gas, and the bottom is electric. What appears to be the case is that the Kwh value (yes I used a capital K) is the amount of electrical energy usage and the therm value is the natural gas energy usage. It is assumed the customer knows and understands this energy demarcation from the Account Summary they’ve presented.

The most straightforward way for both electric and gas usage to be described, would be in terms of energy usage with a single, simple, internationally recognized unit, but they choose not to do this. Instead, the company uses kilowatt-hours and therms. In the case of kilowatt-hours, it is a pigfish unit, which is metaphorically based on metric, but not the actual metric unit for energy, and for therms it is a semi-imperial system unit for energy. Neither of them use the internationally  accepted unit for energy—the joule.

The comparison section of my energy bill could have been written  in a  much, much clearer way, that anyone could understand, using the metric system and gigajoules:

Comparison Information

Metric Comparison (click to enlarge)

When the bill is written this way, one can immediately see the difference in direct energy cost per gigajoule between Electric and Gas. Electricity is 4.85 times more expensive per joule when compared with natural gas. One can assume that the electric usage is essentially for operating appliances and gas is used for heating, just by looking at the energy usage from this year to last. This year was sixteen degrees colder than last year, and the amount of gas usage in gigajoules was different by a factor of 2.6. The previous energy use was lower for the warmer average temperature as one would expect. One also notices what is missing in this table, the comparison cost per gigajoule from the previous year for electric and gas. This would be a very useful way to gauge the change in cost from year to year. The way the energy bill is originally written one could easily confuse the columns. When presented this way, it is clear.

The way the energy usage is presented in the actual/original bill does not allow a consumer to directly compare energy prices—which are offered by an “energy” company. This is because two non-metric proxy units are used, kilowatt-hours and therms, which have a conversion factor between them of approximately 29 (i.e. 1 therm = 29.307 kilowatt-hours).

One cannot be certain about the origins of the format of the bill I received, but I could not help but think about the word confusopoly, which was introduced in Scott Adams’ book The Dilbert Future. According to Wikipedia:

The word is a portmanteau of confusion and monopoly (or rather oligopoly), defining it as “a group of companies with similar products who intentionally confuse customers instead of competing on price”. Examples of industries in which confusopolies exist (according to Adams) include telephone service, insurance, mortgage loans, banking, and financial services.

I would like to add energy companies to the list.

Australian Gas Meter — Photo by Peter Goodyear

Electricity and Gas are pretty basic, both are sold by energy content, so despite the view they are public utilities, one can only wonder if they are not following the confusopoly model when they present bills in Kilowatt-hours and Therms. My rework of my utility bill certainly looks simpler to understand than the one that uses “our traditional measurements.” When the metric system is implemented, people can readily see it’s a system.  When energy is discussed in any context using the metric system, it is always joules, so the energy content on food packages are in kilojoules, as is a person’s energy bill in gigajoules. The metric system allows for a more integrated and systematic understanding of the world by everyone. There will always be those who will try to use metric in a non-transparent manner, but it takes much more effort than when using the potpororri of “traditional” measures currently established in the US. The joule in the crown for energy description is the joule. No matter what energy is under discussion:

Australian Subway napkin with food energy in kilojoules (kJ).  An average person burns (i.e. radiates as heat) about 169 000  kJ per month (169 MJ) (courtesy of Peter Goodyear — click on image to enlarge)
US Subway Napkin with Calories (kilocalories) and grams of fat — The word energy does not appear on the  US napkin (click to enlarge)

Postscript:

On a side note, New Scientist on 2014-01-04 related that since the UK phased out incandescent light bulbs there has been a considerable drop in energy usage. They state:

The average amount of electricity needed annually to light a UK home fell from 720 kilowatt-hours in 1997 to 508 kWh in 2012, a drop of 29 percent.

So  the average energy use by a UK home in 1997 was 2592 megajoules/year  and in 2012 was 1829 megajoules/year

Unfortunately New Scientist can play fast and loose with energy quantities and power values. On 2014-03-08 in an article about using batteries for energy storage from wind power they state on page 20:

Last year California passed legislation requiring the state’s energy companies to create more than 1.3 gigawatts of energy storage between them by 2020.

One could blame this technical faux pas on scientifically illiterate California legislators, but one would expect New Scientist to note this mistake, and possibly comment on it. Energy storage is in joules, the amount of energy flow out of the batteries is watts (joule/second). It is like equating the amount of water behind a dam with the flow rate of water leaving it.

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.

Lies, Damned Lies, and Scientific Notation

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By The Metric Maven

Bulldog Edition

My first extended use of scientific notation was in my introductory chemistry class, Chem 147, at a large university. Anyone who has taken a chemistry class will certainly remember 6.022 x 1023 as Avagardro’s number. It appears to be nice, compact and expressive. I was certainly beguiled with scientific notation as I watched my professor manipulate magnitudes large and small with apparent ease. The numbers would cause one to think, “that’s really big”, or “that’s really small.” It all seemed so nice and orderly—and useful. The one question I did not ask was: “what is the actual relation of the magnitudes expressed on the blackboard to the physical world?”

What happened next did not really provide an answer, but introduced another question. I had purchased a Hewlett-Packard RPN calculator, which has a beautifully written manual. It was while perusing the manual that I ran across settings for the display. I could have fixed, scientific and engineering notation displayed. Engineering notation?—I had not heard of it. It was never mentioned in High School. I then saw a small table which showed it. Scientists use the term order of magnitude to describe a power of ten. This is the superscript used in scientific notation. Engineering notation had categorized scientific notation into groups which differ by three orders of magnitude. It automatically eschews the prefix cluster around unity (i.e centi, deci, deca and hecto). In a millisecond I was enamored with engineering notation, but it would be many, many years before I really understood the beauty and utility of it.

The current set of three magnitude multipliers is eight. This group spans a range from 103 to 1024. The current set of magnitude reducers is also eight which covers  10-3 to 10-24. The entire range is 10-24 to 1024. When this range is expressed using scientific notation there are 48 different and separate magnitudes to wrap one’s mind around. With engineering notation it is 16. What is incredibly useful when one uses engineering notation, is the seamless integration of linguistic expression and numerical expression.

Let me back up for a moment, and explain what I mean. When I was taking classes on circuit theory we used a number of components, the most prominent being resistors. Resistors are marked with colors, and the colors are coded for resistance values. I recall looking for a specific resistor I needed in my small stash and slowly working out the color sequence from a chart. My professor looked over my shoulder and said here, and picked one out immediately. I asked how he figured it out, and he said “I don’t, I just see the colors and I know.” It seemed impossible, but within two years—I could “see” the colors as numbers—and seldom needed a chart.

Within a couple of years I had a similar experience with engineering notation. When I would see 11.5 mm it would immediately be punched into my calculator as 11.5 x 10-3. If I saw 1.575 GHz it would go into my calculator as 1.575 x 109. The language designation and the numerical magnitude were indistinguishable. Without thought, my mind knew the equivalence between the prefixes and numbers. The prefixes milli, micro, nano, kilo, mega and giga required no thought, they were 10-3, 10-6, 10-9, 103, 106, 109. The engineering prefixes meld literacy and numeracy. Scientific notation has no such general linguistic equivalents. They are barren in providing an idea of their size using compact language. The use of scientific notation actually obscures numerical comparison. Here is an example from an article about Global Warming from New Scientist; it expresses four possible scenarios with respect to the amount of energy we use:

Let’s compare the scientific notation values from the article with engineering notation using Pat Naughtin’s Whole Number Rule:

Global Energy Use:

Scientific                     Engineering

1)   8 x 1020 joules            800 Exajoules
2)   1 x 1021 joules          1000 Exajoules
3)   8 x 1020 joules            800 Exajoules
4)   1.75 x 1021 joules     1750 Exajoules

Which column provides you with a better numerical “feeling,” as well as the ability to directly express the size of the number involved, as a number? If we lived in an effectively metric and numerate country, every pupil in grade school would have been taught, and know, that Exa is 1018. Despite living in non-metric America, I’m sure they’ve probably heard of Exabyte drives.

The use of engineering notation allows for a nice continuum of numerical expressions, which are immediately expressible in words alone—yet express an exact numerical magnitude. Scientific notation promotes unit proliferation. For many years, light was expressed in angstroms. One would have to recall that an angstrom is 10-10 meters. There is no metric prefix. There is no clue in the word angstrom as to what  its magnitude might be. In recent years the angstrom has been thankfully abandoned and light is generally expressed with nanometers, which I immediately know is 10-9 meters, just from the prefix nano. There are cases where values which are outside of the range of SI notation appear in engineering and scientific research work. Scientific notation alone must be used for this work.  But in all these cases it should remain without prefix designation as a value in scientific notation.  No googol for 10100 or logoog for 10-100 period. If they’re too big for SI one should leave them unnamed—until they are officially.

I came across the notes for a university course on the environment when I was searching to find out how many joules of energy are in a given quantity of gasoline. I came across this table which has the answer:

Energy Unit  ————————————————————–  Joules Equivalent (S.I.)

This is a clear example of an instructor believing that scientific notation allows for a meaningful comparison of values. Your friendly neighborhood Maven sees exactly the opposite. This person does not use any SI units in the “Energy Unit” column. There are gallons, pounds, tons, a barrel (which is in reality actually statistical), and a cubic foot. Not one metric unit appears on the left and only scientific notation is found on the right, with joules assumed for the column. I have sympathy for the instructor. This is a difficult set of numbers to express because of their large dynamic range, but metric prefixes can help considerably, and should have been employed. I will reorder the table, change it to metric in the left hand column, and compare a one kilogram mass of each substance:

Alternative Table — (click to enlarge)

I believe the use of increasing energy content is a good way to compare these energy sources. The new table shows that the energy density of the majority of the substances we use to supply energy have similar magnitudes. Five of the seven entries are from 20-53 megajoules. The large amount of energy in Uranium-235 is clearly evident when we keep the megajoule prefix, although it’s a very large number. The kilogram of AA batteries is only 0.211 megajoules. When we start with kilograms, the “conversion” of coal and uranium entries to megagram quantities (i.e. “metric tons”) may be done in one’s head. When pounds are used, one needs to multiply by 2000 to obtain a short ton and 2240 to convert to long tons. There is no designation within the table that explains which ton is used. Clearly in a course about environmental concerns, the most efficient and succinct way of presenting energy numbers is desired. The use of a mixture of units and scientific notation obscures the fact that most of the substances have similar energy content.

I see very poor expression of numbers and numerical data in popular science magazines, technical papers, and the worst, mass media publications. When I took English, I demonstrated a complete inability to internalize its grammatical intricacies. What I was told by the instructor was that the worst use of grammar could be found in newspapers and magazines. One could see the irony that these were people making a living using the English language, ostensibly professionals, who used poor grammar. When I first realized how badly numerical data was often presented in technical papers, I had a kinship with my English teacher that I had never experienced before. The lack of the metric system in the US, stunts the ability of professionals to express numbers in a cogent manner. The lack of the metric system in the US prevents teachers from instructing children at the earliest age possible about how to use metric prefixes, as they will not experience them in this society. The lack of the metric system in the US encourages the continued overuse of scientific notation which is an opaque way to express numbers. The lack of the metric system helps to keep us innumerate.

Updated 2014-05-30

Related essay:

The Expanding Universe

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.