Quirks of US Customary Units

Some would argue that the decline of manufacturing industry in the USA contributed to Mr Trump’s surprising victory in the Presidential election*. Others might say that manufacturing’s decline was due in part to the tardy adoption of the international system of measures. Here we look at some of the quirks of ‘English measures’, a throw back to the USA’s colonial past and still widely used in America today.

Many champions of the imperial system often point to survival of ‘English’ units in the United States to justify their contiued use in Britain. However, while US Customary aka ‘English’ units have many features in common with the imperial system, there are some differences. In particular, Americans uses some units that are virtually unknown in the UK and which many Britons would find curious and surprising. Here, Ronnie Cohen looks at some of the quirks of these units. All the information here can be found in Appendix C of the US National Institute of Standards and Technology (NIST) document, “General Tables of Units of Measurement”.

The Americans have two versions of the inch, foot, yard, statute mile and all the other related imperial units of length used on land. They have survey and international measures. Survey measures are only used for land survey data. Both are defined in terms of metric units. The survey foot is exactly 1200/3937 metres and the international foot is exactly 0.0254 x 39.37 survey foot. The survey mile and international mile differ by just 3 millimetres. This is equivalent to less than 2 parts of million. The difference between survey and international measures also affects area measurements, e.g.

  • One square survey foot = 1.000 004 square international feet
  • One square survey mile = 1.000 004 square international miles

As well as the use of survey measures, the NIST also provides definitions of some large land measures not seen in the UK. In the US, 1 section of land equals 1 square mile and 1 township equals 6 square miles. Hence 1 township = 36 sections = 36 square miles.

Here is some factual information provided by NIST about the origin of the statute mile and the international nautical mile that few people know:

“The term ‘statute mile’ originated with Queen Elizabeth I who changed the definition of the mile from the Roman mile of 5000 feet to the statute mile of 5280 feet. The international mile and the US statute mile differ by about 3 millimetres although both are defined as being equal to 5280 feet. The international mile is based on the international foot (0.3048 metres) whereas the U.S. statute mile is based on the survey foot (1200/3937 metres).

The international nautical mile of 1852 metres (6076.115 49 feet) was adopted effective July 1, 1954, for use in the United States. The value formerly used in the United States was 6080.20 feet = 1 nautical (geographical or sea) mile.”

The US has different volume measures for solids and liquids. Units for dry measures are approximately one-sixth larger than their equivalent liquid units. For example, one liquid pint equals 28.875 cubic inches whereas one dry pint equals 33.6003 cubic inches.

For liquid measures there are 16 fuid ounces in a pint, compared with 20 in the imperial system. The US fluid ounce, pint, quart and gallon differ from the imperial units of the same name. However, the yard, the avoirdupois pound, the troy pound, and the apothecaries pound are identical with the imperial units.

Another source of confusion over volume measures is the difference between standard liquid measures and apothecaries liquid measures. Standard and apothecaries liquid volumes are both based on the liquid gallon of 231 cubic inches. However, the breakdown of units for standard and apothecaries liquid volumes is different. Neither is compatible with the other.

The USA officially recognises two different hundredweights and tons. These are the short and long (a.k.a. gross) hundredweight and ton. Believe it or not, the USA uses both although the short measures are used for most purposes. NIST says that the gross or long ton and hundredweight are used commercially in the United States to only a very limited extent, usually in restricted industrial fields and that the units are the same as the British “ton” and “hundredweight”.

Other curiosities in the US customary system mentioned in the NIST document include:

  • 1 cable’s length = 120 fathoms (exactly) = 720 feet (exactly)
  • 1 hand = 4 inches
  • 1 league (land) = 3 U.S. statute miles (exactly)
  • 1 point (typography) = 0.013 837 inch (exactly)
  • 1 square (building) = 100 square feet
  • 1 cord (firewood) = 128 cubic feet (exactly)
  • 1 water ton (English) = 270.91 U.S. gallons = 224 British Imperial gallons (exactly)
  • 1 assay ton = 29.167 grams
  • 1 micro pound = 0.000 001 pound (lb)
  • 1 mil = 0.001 inch (exactly)

It is clear that the micropound and mil clearly borrow the decimal features from the metric system. The Gunter’s or surveyors chain foreshadowed the metric system (e.g. 1 furlong = 10 chains = 1000 links). These features of non-metric units show that their users clearly see the benefits of using a decimal-based measurement system. However, the metric system is almost entirely based on powers of 10 (i.e. all decimal-based). We could ask, if Americans want to benefit from decimal-based measurements, why don’t they just use the metric system?

NIST says that the assay ton is used in assaying and that the assay ton bears the same relation to the milligram that a ton of 2000 pounds avoirdupois bears to the ounce troy; hence the mass in milligrams of precious metal obtained from one assay ton of ore gives directly the number of troy ounces to the net ton.

The Americans use a variety of different barrels that vary in size betwee 31 and 42 gallons. In this context, the term “gallon” refers to the US liquid gallon. Cranberries have a barrel all to themselves while all other fruits, vegetables, and other dry commodities use a different barrel. A variety of other barrels are established by law or usage.

  • 1 standard barrel for fruits, vegetables, and other dry commodities, except cranberries = 7056 cubic inches = 105 dry quarts = 3.281 bushels, struck measure
  • 1 standard barrel just for cranberries = 5826 cubic inches = 86 + 45/64 dry quarts = 2.709 bushels, struck measure
  • 1 federal liquid barrel = 31 gallons (the basis for federal taxes on fermented liquors)
  • a widely used state liquid barrel = 31½ gallons
  • a cistern measurement barrel in one state = 36 gallons
  • 1 federal proof spirits barrel = 40 gallons
  • 1 oil barrel = 42 gallons (this barrel is recognized for liquids by 4 states)

There are different bushels for heaped and struck measure:

  • 1 bushel (U.S.) struck measure = 2150.42 cubic inches (exactly)
  • 1 bushel, heaped (U.S.) = 2747.715 cubic inches = 1.278 bushels, struck measure
  • 1 bushel (British Imperial) (struck measure) = 1.032 US bushels, struck measure = 2219.36 cubic inches

The heaped US bushel is frequently recognised as 1¼ bushels, struck measure.

Cups, teaspoons and tablespoons remain in common use for recipes in the US and I do not mean kitchen utensils but standard US measurements. Now that recipes in the UK are overwhelmingly metric, I suspect that most Britons would have no idea what quantities cups, teaspoons and tablespoons represent if they saw them in a recipe. These measurements are rarely seen in the UK. So if you are curious to know what they represent, here they are (Note that measures represent US volume measures, which all differ from UK volume measures.).

  • 1 cup, measuring = 8 fluid ounces (exactly) = ½ liquid pint (exactly)
  • 1 tablespoon, measuring = 3 teaspoons (exactly) = 4 fluid drams = ½ fluid ounce (exactly)

NIST provides the following caution of the ‘teaspoon’:
“The equivalent ‘1 teaspoon = 1 1/3 fluid drams’ has been found by the Bureau to correspond more closely with the actual capacities of ‘measuring’ and silver teaspoons than the equivalent ‘1 teaspoon = 1 fluid dram’, which is given by a number of dictionaries.” Dram is the US spelling of the British drachm.

The US is far behind the UK in metrication so you are bound to find a lot of alien measurement units still used in the USA that have long been abandoned in the UK.

As well as all the measurement units mentioned in this article, the NIST document mentions the rod, pole, perch, furlong (now confined to horse racing in the UK), link, Gunter’s or surveyors chain (now confined to railways in the UK), gill, quart, minim, dram, peck, grain, pennyweight, scruple, quarter, fathom and league. Most of these units will be unfamiliar to young Britons.

Are you baffled by the system of US customary units? They are really complex and cumbersome to work with. When imperialists defend the use of imperial units in the UK because of US usage, do they really know all the strange features of US customary units? I guess not. Clearly the US is not an ideal model for our usage of measurement.

Source: http://www.nist.gov/pml/wmd/pubs/upload/appc-16-hb44-final.pdf

*An example is the article by Martin Geissler, a reporter for ITV News, published in the Evening Standard on Tuesday 8 November but clearly written earlier in Ohio, headed ‘Crushed hopes and anger in the Rust Belt: this is how Trump could win’.

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29 Responses to Quirks of US Customary Units

  1. John Frewen-Lord says:

    Ronnie:

    " In the US, 1 section of land equals 1 square mile and 1 township equals 6 square miles. Hence 1 township = 36 sections = 36 square miles."

    Shouldn't that be 6 miles square (i.e. 6 mi x 6 mi)?

    The hand (4 in) is commonly used in equestrian circles to measure the height of horse (from the ground to its withers) throughout the world, even in metric countries. I doubt that will change as it is so embedded in equestrian 'culture'.

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  2. BrianAC says:

    LOL.
    Do we really need to know this?
    I got bogged down in the first mile.
    Makes we wonder even more why any sane, rational person should favour these pathetically stupid measures.

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  3. Ezra Steinberg says:

    I was born in the USA and educated in American schools and yet I am totally unfamiliar with most of the units mentioned in this post.

    Yikes! What a mess! Still, I hope we will convert over here to metric while I am still alive and cognitively alert. 😉

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  4. Han Maenen says:

    Ever heard of the 'commercial acre'? Here it is: US unit of land area that is only 82.6 percent of an acre. Invented by the real estate dealers, it measures 36000 square feet, 4000 square yards, 3342.8 square meters, or 0.334 hectare, and is a legal unit in several states.''

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  5. John Steele says:

    If you backtrack the origin of most of the measures, you will learn that they are pre-Imperial British measures. We were independent by the time of the Imperial Act and never adopted any of its new provisions. Particularly our gallon and bushel are the Queen Anne wine gallon and Winchester bushel, defined the same as Parliament redefined them circa 1700.

    The NIST list essentially preserves the definition of every archaic measure ever used here. However, the list of measures we actually use is greatly simplified vs the NIST list.

    We survey in decimal feet and used to survey in chains and links (decimal chains). I don't think the rod or it's aliases or furlongs have ever been much used here. The township and section are part of the Public Land Survey System and most of the center of the country was surveyed in this system; most land surveys start from the corner and central markers of these sections. The township is approximately a square 6 miles on a side. However, a square grid can only be imposed so far on a round earth and 19th century surveyors made mistakes. There are townships and sections which are "off" as intended adjustments or errors. The survey monuments prevail and define sections. The US road system is largely built on section and half-section lines.

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  6. Ronnie Cohen says:

    @John Frewen-Lord

    Here is the full table of area conversions given by NIST on page 5 of Appendix C – General Tables of Units of Measurement:

    Units of Area
    144 square inches = 1 square foot
    9 square feet = 1 square yard = 1296 square inches
    272¼ square feet = 1 square rod
    160 square rods = 1 acre = 43 560 square feet
    640 acres = 1 square mile
    1 mile square = 1 section of land
    6 miles square = 1 township = 36 sections = 36 square miles

    I got all the info from there in good faith. You can find a link to the "Appendix C – General Tables of Units of Measurement" document near the bottom of this article.

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  7. Daniel Jackson says:

    The election of Donald Trump could have a profound effect on metrication in the US, especially on those areas where metrication was successful. If Trump goes against the grain and keeps his election promises, there is a possibility metrication in the US could be reversed.

    Trump has promised to put America first. He wants to abolish all trade agreements and force companies that moved to metric countries to return to the US. Whether this is achievable or practical is yet to be seen. Trump has never been involved in manufacturing and doesn't know what is best for industries, he works completely on emotion. If the workers in domestic metric factories start to make a noise about working in metric and insist on a return to USC, will Trump step in and put pressure on these industries to do so?

    An advantage to Trump's desire to tear up trade agreements, like NAFTA is it could also pave the way for Canada to complete metrication. Canada may have to seek other markets for their goods and those markets will not allow them to sneak in USC. Mexico may close itself off to American goods completely and less USC influence will result. China may see itself free of having to provide USC on packages or product descriptions even when these products are fully metric. TV screen sizes could finally be expressed in centimetres only.

    It can take decades for Trump to accomplish his goals, but in the meantime a lot of internal damage can result.

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  8. jackthesmilingblack says:

    At least a US quart is almost one litre. As near as YUCK is to swearing.

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  9. John Steele says:

    @Ronnie Cohen

    "Miles square" is a potentially confusing statement

    6 square miles or 6 miles squared both represent 6 areas of land 1 mile x 1 mile; however, 6 miles square can mean a square 6 miles on a side. That final "d" makes a huge difference and can be overlooked. In my view, that makes it an awkward phrase.

    "6 miles square = 36 square miles" makes clear the first phrase refers to a square 6 miles on a side, whether or not it is a good way to refer to it

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  10. John Frewen-Lord says:

    @Daniel:

    "...also pave the way for Canada to complete metrication. Canada may have to seek other markets for their goods and those markets will not allow them to sneak in USC."

    Two points here:

    1. Canada was much more metric than it is today - in fact, metrication was almost complete, back in the mid 1980s, until Brian Mulroney abolished the Canadian Metric Board and signed the original Free trade Agreement with the USA, many provisions of which reversed Canada's metrication program, or at least allowed dual measures.

    2. For at least 40 years now, many in Canada have exhorted the country to depend far less on the USA than it does - i.e. become far more of an international high-tech economy and less of 'hewers of wood and drawers of water' primarily for the USA. However, the easy option has always been to sell raw materials to the US without adding much value to them. If NAFTA is torn up, or at least heavily modified, that just might be the spur for Canada to rethink its economy, and make it much more high tech. That alone would force Canada to become more metric.

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  11. Michael Glass says:

    I doubt that Donald Trump is going to make much difference to American weights and measures. Lincoln Chafee's call for America to adopt the metric system apparently fell on deaf ears, so I don't think we'll see any great movement soon.

    However, there may be an increasing use in medicine. See http://www.modernhealthcare.com/article/20150501/NEWS/150509993
    and
    http://www.teammetric.org/the-metric-system-and-healthcare/
    Confusion between pounds and kilograms can cause medical emergencies.

    There were moves in Oregon and Hawaii to pass metrication bills through their state governments. However, that appears to have faded away.

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  12. Charlie P says:

    @Michael Glass

    Unit confusion doesn't only occur between metric and imperial/USC. One of the biggest unit related wories wrt "medical emergencies" is the confusion between ?g (microgram) and mg - which can result in a 1000x overdose! Is it really such a good idea for any unit symbol (or abbreviation) to need a character which isn't readily found on a keyboard or one which when hand-written may be indistinguishable from another? I don't think so.

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  13. Alex Bailey says:

    @Charlie P

    If you use metric exclusively it is less likely that you’ll get your milli and micro mixed up; those who use them professionally will have been trained to do so and so in most cases should not be making that sort of mistake, it’s only when you get folks who leave work in the evening and then have their minds flooded with the plethora of archaic imperial/USC units that confusion creeps in, especially when under stress.

    The fact you can’t find a symbol on your keyboard is irrelevant.

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  14. Daniel Jackson says:

    @Charlie P:

    This may have occurred in the past, but it is no longer cited as an issue firstly due to better education of medical personnel to recognise the difference between an m and a ? (mu), which looks more like a "u" than an "m". Secondly, this was due to a misreading of handwritten prescriptions. But that isn't an issue anymore as the handwritten prescription is obsolete. Now, doctors send prescriptions electronically to pharmacies or chemists.

    In the hospital environment the latest concerns now deal with misdosings due to the confusion between kilograms and pounds. Medicines being dosed in milligrams or millilitres per kilogram of body mass create a dosing error when someone uses pounds instead of kilograms to calculate the correct dose.

    A second and major source of errors especially in the home dosing involving children that is a major concern is the use of teaspoons for dosing instead of millilitres. But that is changing, at least in the US, with medicines now being sold with instructions in millilitres only and millilitre only dosing cups or oral syringes given with each product sold.

    https://hal.archives-ouvertes.fr/hal-00555327/document

    http://foodpsychology.cornell.edu/research/stop-spoon-dosing-milliliter-instructions-cause-fewer-dosage-errors-spoon-instructions

    http://www.carelinemedical.com/products/Non-Sterile-Graduated-Plastic-Medicine-Cups-3/?gclid=CI3u27yOv9ACFYeUfgodwVoDuQ

    There is a reason the medical industry switched to metric dosing. There were obviously major and long forgotten mistakes made with the apothecary system that metrication cleared up that otherwise would still be a plague.

    It is best to update your information before presenting it as modern fact when in reality the problem was long ago solved unless passing on dated information is intended to bring attention to your campaign to retain obsolete units.

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  15. John Steele says:

    Charlie P

    Do you mean µ. There are many ways to create it
    Alt0181 on Windows (1250) Western Latin code page, Alt+b5 if you have installed extended alt codes for Unicode, Hex character b5 or decimal 181 in any valid unicode representation, or html, or as a named html character, the word micro preceded by & and terminated by ;
    We'll see if the last works here µg
    Even if named html character fails, you can see what was meant.

    Note that electrical engineers have similar (non)problems with ? for ohm

    I don't like the American medical practice of using mcg. I would prefer to see "ug" used in fonts that can't include µ even if it means getting rid of the awkward phase unified atomic mass unit (u) which has a synonym dalton (Da). The handwriting argument is no longer valid (here) as Obamacare has forced electronic medical records (well, I suppose only for doctors who actually prefer being paid). Also doctors transmit the prescriptions to pharmacies electronically to cut abuse.

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  16. Michael Glass says:

    @Charlie P

    The milligram/microgram confusion is a real problem, as can be seen here: http://www.cwladis.com/math104/lecture2.php

    This is bad enough without the added complications of using the Apothecary System and the Household System, also mentioned on the same web page. Abolishing the use of the other systems won't make dosing errors a thing of the past, but it will make things very much better.

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  17. Charlie P says:

    @Daniel

    Let me just restate for you Daniel… I do not advocate or campaign for any one system over another. I am happy and comfortable with both. What I deplore though is the arrogance of trying to force the use of one system over another without popular support, and by the dishonest use of false reasoning and misrepresentation of “evidence” to “justify” such a change. Let us discuss the facts without skewing and misrepresentation and let’s not attack contributors for having the “wrong” opinions.

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  18. BrianAC says:

    Maybe what the world needs is an 'SI' keyboard that includes all the SI symbols. If USA were ever to join the party we may just get one.

    Personal typing is one thing though, I would expect 'professionals' to do better.

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  19. BrianAC says:

    No, then do not work!

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  20. Ezra Steinberg says:

    Interestingly enough, I just noticed that the Kroger brand (a very generic brand sold in many stores) of tall kitchen garbage bags lists the thickness of the bags on the package in micrometers using the symbol for micro and the symbol for meter (thus "um" but with the real symbol for mu).

    I am actually surprised that such a generic brand actually uses the correct symbol for micro. Could this be a good sign? (I sure hope so.)

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  21. Michael Glass says:

    @CharlieP

    I am puzzled at your criticism of Daniel's contribution to this discussion. When it comes to public safety, the use of one system of measurement has obvious advantages.

    * There is no standardised size for teaspoons. It is far better to insist on accurate measurement of medicines in millilitres.

    * You appear to have accused Daniel of dishonestly using false reasoning and misrepresenting “evidence.” That's not fair. If you found any of his statements false or questionable, explain in detail. Broad brush accusations are not helpful.

    Finally, one suggestion:

    * The milligram/microgram confusion could be dealt with by banning the milligram in medicine. Use thousands of micrograms instead.

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  22. Daniel Jackson says:

    @ Charlie

    Well, who are you to say what side popular support is taking? As of late a number of online newspapers have taken up the story of the Luddite who went around for 16 years vandalising signs because they were in metric. The overwhelming comment support is pro-metric.

    The evidence for change is real. Your opinions may not be wrong, but your "facts" sure are. You are just in denial.

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  23. Daniel Jackson says:

    @Ezra

    It could be that the person who designed he label was well aware of the correct unit symbol and could be a metric supporter.

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  24. Stan says:

    Many of the units described in the article are probably little known nowadays. It does however illustrate one important point about most non-metric units. They are application specific and were invented by different standards authorities working in different areas of industry.

    Metric was invented as a clean break designed to rationalise measurement into a single coherent system that can be used in all applications.
    There is an unfortunate tendency even nowadays to invent new units unnecessarily. The units of alcohol for example which is actually 10 ml. We still use the calorie for energy in food as though it is somehow different from energy measured in joules.

    We'd all be better off if we understood the importance of keeping things simple and not preserving false variants for what amount to purely emotional reasons.

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  25. John Steele says:

    @Ezra

    The FTC rules for the FPLA specify µm as the symbol for micrometer in "these and no other" language. If they read the rules, doing it wrong is not permitted.

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  26. John Steele says:

    @Charlie P

    Exactly how would you deal with a 1 µg dose in Imperial? The apothecary system has no smaller unit than the grain. Decimals or fractions? 0.000 0154 gr or 1/64800 gr. Do you seriously believe that would involve fewer mistakes?

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  27. Charlie P says:

    @Michael

    I am puzzled by your suggestion that I criticised Daniel's contribution in that post. Please read it again and you'll see you are wrong. I was: a) clarifying that I do not advocate or campaign for any one system (in reply to Daniel's assertion that I "campaign to retain obsolete units"), b) restating my dislike of the use of false reasoning and misrepresentation (which is a regular occurrence on these pages) with the goal of forcing the use of one system against popular opinion.

    I hope your misinterpretation of my post was not a deliberate attempt to undermine my points with gratuitous ad hominem. Perhaps you'll now retract it.

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  28. Mark Williams says:

    @Charlie P:

    Pull the other one---the double-standard evident in your MO is glaringly obvious, to `advocate or campaign' only against metric using FUD. Just because it is circumspectly worded does not preclude it from being a campaign and one intended to favour imperial (not a system).

    Where can we find your posts on the internet bemoaning that imperial glyphs are not `readily found on a keyboard' or, more critically, not even in baseline computer character sets or general-purpose typefaces---unlike the µ micro symbol µ? Or making up fairy stories (reasonable description, given that you provide zero corroboration) about the plausibility of 1000x imperial overdoses? What `facts without skewing and misrepresentation' do you have regarding `popular support' for forced imperial, bearing in mind that popular is not the same as noisy or contrived? `Arrogant', `dishonest' `false reasoning': take that beam out of your own eye!

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  29. Michael Glass says:

    @Charlie P

    I'll accept that you did not mean to criticise Daniel personally. A careful reading of what you wrote makes that interpretation possible. However, broad-brush attacks on "faulty reasoning" and "misrepresentation" are not helpful because they could apply to anything or everything that anybody wrote and that you don't happen to agree with.

    While you accept the use of both Imperial and metric measures, I feel sure that you would see the problem of having two or more sets of measurements in a medical context. You have rightly drawn attention to the milligram/microgram confusion, and I agree with you. This is a prime example of the confusion that can arise between two measures. Therefore I feel sure that the same logic applies to using teaspoons to measure medicines, when teaspoons are not of a standard size.

    You express concern that a move on medical measures may be done "with the goal of forcing the use of one system against popular opinion." I'm not aware that there is any great demand to save the teaspoon for measuring medicines. Perhaps, then, you see the move in the United States for using metric measures in medicines as the thin edge of the wedge, and you would therefore resist it on that account.

    If that is your concern, I think this is a case of putting ideology ahead of public safety.

    Perhaps you could clarify your thinking on this matter. Do you or do you not object to having medicines measured by the millilitre? If not - or if so - why?

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