United States customary units

A table of weights from the secretaries of states, showing the number of pounds that their laws recognize as a bushel of different commodities. c. 1854

United States customary units are a system of measurements commonly used in the United States. Many U.S. units are virtually identical to their imperial counterparts, but the U.S. customary system developed from English units used in the British Empire before the system of imperial units was standardized in 1824. Several numerical differences from the imperial system are present.

The vast majority of U.S. customary units have been defined in terms of the metre and the kilogram since the Mendenhall Order of 1893 (and, in practice, for many years before that date).[1] These definitions were refined in 1959.[2]

The U.S. is the only industrialized nation that does not mainly use the metric system in its commercial and standards activities,[3] although the International System of Units (SI, often referred to as "metric") is commonly used in both the US Armed Forces and in fields relating to science, and increasingly in medicine, aviation, government as well as various sectors of industry.

Contents

History

The U.S. system of units is similar to the British imperial system.[4] Both systems derive from the evolution of local units over the centuries, as a result of standardization efforts in the United Kingdom; the local units themselves mostly trace back to Roman and Anglo-Saxon units. Today, these units are defined in terms of SI units.

In the Omnibus Trade and Competitiveness Act of 1988, the United States government designated the metric system of measurement as "the preferred system of weights and measures for U.S. trade and commerce". The legislation states that the federal government has a responsibility to assist industry, especially small business, as it voluntarily converts to the metric system of measurement. This process of legislation and conversion is known as metrication, and in the U.S. is most evident in labeling requirements on food products, where SI units are almost always presented alongside customary units.

However, metrication in the United States has been less forcefully imposed than in other countries,[5] and has encountered more resistance from industrial and consumer market forces, so customary units are still widely used on consumer products and in industrial manufacturing; only in military, medical, and scientific contexts are SI units generally the norm.

The customary system was championed by the United States-based International Institute for Preserving and Perfect­ing Weights and Measures in the late 19th century. Advocates of the customary system saw the French Revolutionary, or metric, system as atheistic.[6] An auxiliary of the Institute in Ohio published a poem reading:

Then down with every "metric" scheme
Taught by the foreign school,
We'll worship still our Father's God!
And keep our Father's "rule"!
A perfect inch, a perfect pint,
The Anglo's honest pound,
Shall hold their place upon the earth,
Till time's last trump shall sound![6]

One adherent of the customary system called it "a just weight and a just measure, which alone are acceptable to the Lord."[6]

There are anecdotal objections to the use of metric units in carpentry and the building trades, on the basis that it is easier to remember an integer number of inches plus a fraction than a measurement in millimeters,[7] or that inch measurements are more suitable when distances are frequently divided by two.[5]

Other countries had (or still have, unofficially) customary units of their own, sometimes very similar in name and measure to U.S. customary units, since they often share the same Germanic or Roman origins. Frequently, however, these units designate quite different sizes. For example, the mile ranged by country from one half to five U.S. miles; even foot and pound had varying definitions. Until the twentieth century the customary units of measure in the United States were sometimes just as variable. Historically, a wide range of non-SI units were used in the United States and in Britain, but many have fallen into disuse. This article deals only with the units commonly used or officially defined in the United States.

Units of length

Unit Divisions SI Equivalent
Exact relationships shown in boldface
International
1 point (p) 352.8  µm
1 pica (P) 12/p 4.233 mm
1 inch (in) 6/P 2.54 cm
1 foot (ft) 12 in 0.3048 m[8]
1 yard (yd) 3 ft 0.9144 m[8]
1 mile (mi) 5280 ft 1.609344 km
Survey
1 link (li) 3350 ft or 7.92 in 2.012 dm
1 (survey) foot (ft) 12003937 m 0.30480061 m[8]
1 rod (rd) 25 li or 16.5 ft 5.029210 m
1 chain (ch) 4 rd 2.011684 da m
1 furlong (fur) 10 ch 2.011 684 hm
1 survey (or statute) mile (mi) 8 fur 1.609347 km[8]
1 league (lea) 3 mi 4.828042 km
Nautical
1 fathom (ftm) 2 yd 1.8288 m
1 cable (cb) 120 ftm or 1.091 fur 2.19456 hm
1 nautical mile (NM or nmi) 8.439 cb or 1.151 mi 1.852 km

The system for measuring length in the United States customary system is based on the inch, foot, yard, and mile, which are the only four customary length measurements in everyday use. Since July 1, 1959, these have been defined on the basis of 1 yard = 0.9144 metres except for some applications in surveying.[2] This definition was agreed with the UK and other Commonwealth countries, and so is often termed international measure.

When international measure was introduced in the English-speaking countries, the basic geodetic datum in North America was the North American Datum of 1927 (NAD27), which had been constructed by triangulation based on the definition of the foot in the Mendenhall Order of 1893, that is 1 foot = 12003937 meters: this definition was retained for data derived from NAD27, but renamed the U.S. survey foot to distinguish it from the international foot.[2] For most applications, the difference between the two definitions is insignificant — one international foot is exactly 0.999998 of a U.S. survey foot, for a difference of about 18 inch (3 mm) per mile — but it affects the definition of the State Plane Coordinate Systems (SPCSs), which can stretch over hundreds of miles.[9]

The NAD27 was replaced in the 1980s by the North American Datum of 1983 (NAD83), which is defined in meters. The SPCSs were also updated, but the National Geodetic Survey left the decision of which (if any) definition of the foot to use to the individual states. All SPCSs are defined in meters, but seven states also have SPCSs defined in U.S. survey feet and an eighth state in international feet: the other 42 states use only meter-based SPCSs.[9]

State legislation is also important for determining the conversion factor to be used for everyday land surveying and real estate transactions, although the difference (2 ppm) is of no practical significance given the precision of normal surveying measurements over short distances (usually much less than a mile). Twenty-four states have legislated that surveying measures should be based on the U.S. survey foot, eight have legislated that they be made on the basis of the international foot, and eighteen have not specified the conversion factor from metric units.[9]

Units of area

Unit Divisions SI Equivalent
Exact relationships shown in boldface
1 square survey foot (sq ft or ft2) 144 square inches 0.09290341 m2
1 square chain (sq ch) or (ch2) 4356 feet2 (survey) or 16 sq rods 404.6873 m2
1 acre 43560 sq ft (survey) or 10 sq ch 4046.873 m2
1 section 640 acres or 1 sq mi (survey) 2.589998 km2
1 survey township (twp) 36 sections or 4 sq leagues 93.23993 km2

The most widely used area unit with a name unrelated to any length unit is the acre. The National Institute of Standards and Technology contends that customary area units are defined in terms of the square survey foot, not the square international foot.[8] Conversion factors are based on Astin (July 27, 1968)[10] and National Institute of Standards and Technology (2008).[11]

Units of capacity and volume

Volume in general
Unit Divisions SI Equivalent
1 cubic inch (cu in) or (in3) 16.387064 mL[12]
1 cubic foot (cu ft) or (ft3) 1728 cu in 28.31685 L
1 cubic yard (cu yd) or (yd3) 27 cu ft 764.559 L
0.7645549 m3
1 acre-foot (acre ft) 43560 cu ft
1613.333 cu yd
1.233482 ML
1233.482 m3

The cubic inch, cubic foot and cubic yard are commonly used for measuring volume. In addition, there is one group of units for measuring volumes of liquids, and one for measuring volumes of dry material.

Other than the cubic foot, cubic inch and cubic yard, these units are differently sized from the units in the imperial system, although the names of the units are similar. Also, while the U.S. has separate systems for measuring the volumes of liquids and dry material, the imperial system has one set of units for both.

Fluid volume

Liquid volume
Most common measures shown in italic font

Exact conversions in bold font

Unit Divisions SI Equivalent
1 minim (min) ~ 1 drop or 0.95 grain of water 61.61152 μL
1 US fluid dram (fl dr) 60 min 3.696691 mL
1 teaspoon (tsp) 80 min 4.928921 mL
1 tablespoon (Tbsp) 3 tsp or 4 fl dr 14.78676 mL
1 US fluid ounce (fl oz) 2 Tbsp or 1.041 oz av of water 29.57353 mL
1 jigger (jig) 3 Tbsp 44.36028 mL
1 US gill (gi) 4 fl oz 118.2941 mL
1 US cup (cp) 2 gi or 8 fl oz 236.5882 mL
1 (liquid) US pint (pt) 2 cp or 16.65 oz av of water 473.1765 mL
1 (liquid) US quart (qt) 2 pt 0.9463529 L
1 (liquid) US gallon (gal) 4 qt or 231 cu in 3.785412 L
1 (liquid) barrel (bbl) 31.5 gal or 12 hogshead 119.2405 L
1 oil barrel (bbl) 42 gal or 23 hogshead 158.9873 L
1 hogshead 63 gal or 8.421875 cu ft
or 524.7 lb of water
238.4810 L

One fluid ounce is 116 of a U.S. pint, 132 of a U.S. quart, and 1128 of a U.S. gallon. The fluid ounce derives its name originally from being the volume of one ounce avoirdupois of water, but in the U.S. it is defined as 1128 of a U.S. gallon. Consequently, a fluid ounce of water weighs about 1.041 ounces avoirdupois.

The saying "a pint's a pound the world around" refers to 16 US fluid ounces of water weighing approximately (about 4% more than) one pound avoirdupois. An imperial pint of water weighs a pound and a quarter.

A 20 US fl oz (591 mL) bottle displaying both US and Metric units.

There are varying standards for barrel for some specific commodities, including 31 gal for beer, 40 gal for whiskey or kerosene, and 42 gal for petroleum. The general standard for liquids is 31.5 gal or half a hogshead. The common 55 gallon size of drum for storing and transporting various products and wastes is sometimes confused with a barrel, though it is not a standard measure.

In the United States, single servings of beverages are usually measured in fluid ounces. Milk is usually sold in half pints (8 fluid ounces), pints, quarts, half gallons, and gallons. Water volume for sinks, bathtubs, ponds, swimming pools, etc., is usually stated in gallons or cubic feet. Quantities of gases are usually given in cubic feet (at one atmosphere).

Minims, drams and gill are rarely used currently.

Dry volume

Dry volume
Unit Divisions SI Equivalent
1 (dry) pint (pt) 33.60 cu in 0.5506105 L
1 (dry) quart (qt) 2 pt 1.101221 L
1 (dry) gallon (gal) 4 qt or 268.8025 cu in 4.404884 L
1 peck (pk) 2 gal 8.809768 L
1 bushel (bu) 4 pk or 1.244 cu ft 35.23907 L
1 (dry) barrel (bbl) 7056 cu in or 3.281 bu 115.6271 L

Small fruits and vegetables are often sold in dry pints and dry quarts. The U.S. dry gallon is less commonly used, and was not included in the handbook that many states recognize as the authority on measurement law.[13][14] However pecks, or bushels are sometimes used—particularly for grapes, apples and similar fruits in agricultural regions.

Units of mass

Unit Divisions SI Equivalent
Most common measures shown in italic font

Exact conversions shown in bold font

Avoirdupois
1 grain (gr) 17000 lb 64.79891 mg
1 dram (dr) 27 1132 gr 1.7718451953 g
1 ounce (oz) 16 dr 28.349523125 g
1 pound (lb) 16 oz 453.59237 g
1 US hundredweight (cwt) 100 lb 45.359237 kg
1 long hundredweight 112 lb 50.80224544 kg
1 short ton 20 US cwt or 2000 lb 907.18474 kg
1 long ton 20 long cwt or 2240 lb 1016.0469088 kg
Troy
1 grain (gr) 17000 lb av or 15760 lb t 64.79891 mg
1 pennyweight (dwt) 24 gr or 7.776 carats 1.55517384 g
1 troy ounce (oz t) 20 dwt 31.1034768 g
1 troy pound (lb t) 12 oz t or 13.17 oz av 373.2417216 g

There have historically been five different English systems of mass: tower, apothecaries', troy, avoirdupois, and metric. Of these, the avoirdupois weight is the most common system used in the U.S., although Troy weight is still used to weigh precious metals. Apothecaries weight—once used by pharmacies—has been largely replaced by metric measurements. Tower weight fell out of use in England (due to legal prohibition in 1527) centuries ago, and was never used in the United States. The imperial system, which is still used for some measures in the U.K. and commonwealth countries, is based on avoirdupois, with variations from U.S. customary units larger than a pound.

The pound avoirdupois, which forms the basis of the U.S. customary system of mass, is defined as exactly 453.59237 grams by agreement between the U.S., the U.K. and other English-speaking countries in 1959. Other units of mass are defined in terms of it.

The avoirdupois pound is legally defined as a measure of mass, but the name pound is also applied to measures of force. For instance, in many contexts, the pound avoirdupois is used as a unit of mass, but in some contexts, the term "pound" is used to refer to "pound-force". The slug is another unit of mass derived from pound-force.

Troy weight, avoirdupois weight, and apothecaries' weight are all built from the same basic unit, the grain, which is the same in all three systems. However, while each system has some overlap in the names of their units of measure (all have ounces and pounds), the relationship between the grain and these other units within each system varies. For example, in apothecary and troy weight, the pound and ounce are the same, but are different from the pound and ounce in avoirdupois in terms of their relationships to grains and to each other. The systems also have different units between the grain and ounce (apothecaries' has scruple and dram, troy has pennyweight, and avoirdupois has just dram, sometimes spelled drachm). The dram in avoirdupois weighs just under half of the dram in apothecaries'. The fluid dram unit of volume is based on the weight of 1 dram of water in the apothecaries' system.

To alleviate confusion, it is typical when publishing non-avoirdupois weights to mention the name of the system along with the unit. Precious metals, for example, are often weighed in "troy ounces", because just "ounce" would be more likely to be assumed to mean an ounce avoirdupois.

For the pound and smaller units, the U.S. customary system and the British imperial system are identical. However, they differ when dealing with units larger than the pound. The definition of the pound avoirdupois in the imperial system is identical to that in the U.S. customary system.

In the United States, only the ounce, pound and short ton—known in the country simply as the ton—are commonly used, though the hundredweight is still used in agriculture and shipping. The grain is used to describe the mass of propellant and projectiles in small arms ammunition. It was also used to measure medicine and other very small masses.

Grain measures

In agricultural practice, a bushel is a fixed volume of 2150.42 cubic inches. The mass of grain will therefore vary according to density. Some nominal weight examples are:-

  • 1 bushel (corn) = 56 lb = 25.4012 kg
  • 1 bushel (Wheat) = 60 lb = 27.2155 kg
  • 1 bushel (Barley) = 48 lb = 21.7724 kg

In trade terms a bushel is a term used to refer to these nominal weights. Although even this varies. With oats, Canada uses 34 lb bushels and the USA uses 32 lb bushels.

Cooking measures

Measure Australia Canada UK USA FDA[15]
Teaspoon 5 mL 5 mL 4.74 mL 4.93 mL 5 mL
Dessertspoon 9.47 mL
Tablespoon 20 mL 15 mL 14.21 mL 14.79 mL 15 mL
Fluid ounce 28.41 mL 29.57 mL 30 mL
Cup 250 mL 250 mL 284.13 mL 236.59 mL 240 mL
Pint 568.26 mL 473.18 mL
Quart 1136.52 mL 946.35 mL
Gallon 4546.09 mL 3785.41 mL

The most common practical cooking measures for both liquid and dry ingredients in the United States (and many other countries) are the teaspoon, tablespoon and cup, along with halves, thirds, quarters and eighths of these. Pounds, ounces, fluid ounces, and common sizes are also used, such as can (presumed size varies depending on product), jar, square (e.g., 1 oz avdp. of chocolate), stick (e.g., 4 oz avdp. butter) or fruit/vegetable (e.g., a half lemon, two medium onions).

Some common volume measures in English-speaking countries are shown at right. The volumetric measures here are for comparison only.

Units of temperature

Degrees Fahrenheit are used in the United States to measure temperatures in most non-scientific contexts. The Rankine scale of absolute temperature also saw some use in thermodynamics. Scientists worldwide use the kelvin and degree Celsius. Several technical standards are expressed in Fahrenheit temperatures and U.S. medical practitioners often use degrees Fahrenheit for body temperature.

The relationship between the different temperature scales is linear, but the scales have different zero points so that conversion is not simply multiplication by a factor: pure water is defined to freeze at 32 °F = 0 °C and boil at 212 °F = 100 °C at 1 atm; the conversion formula is easily shown to be:

F = \frac{9}{5}C + 32 or inversely as C = \frac{5}{9}(F - 32).

Other units

  • 1 Board-foot = 2.360 dm³
  • 1 British thermal unit (Btu) ~ 1055 J
  • 1 Calorie (cal) = 4.184 J
  • 1 Large calorie (kilocalorie, food calorie) (Cal, kcal) = 4.184 kJ
  • 1 Hand = 10.16 cm
  • 1 Horsepower ~ 746 W
  • 1 R-value (ft²·°F·h/Btu) ~ 0.1761 RSI (K·m²/W)
  • 1 Slug (mass) = 1 lbf·s²/ft
  • Various combination units are in common use, including the foot-pound and the psi; these are straightforwardly defined based on the above basic units.

Other names for U.S. customary units

The United States Code refers to these units as "traditional systems of weights and measures".[16]

A pejorative name sometimes used by advocates of metrication is FFU for Fred Flintstone Units.[17]

See also

References

  1. ^ T. C. Mendenhall, Superintendent of Standard Weights and Measures, Order of April 5, 1893, published as Appendix 6 to the Report for 1893 of the Coast and Geodetic Survey.
  2. ^ a b c Astin, A.V., Karo, H. A. and Mueller, F. H. (June 25, 1959). Doc 59-5442, "Refinement of Values for the Yard and the Pound." Federal Register. When reading the document it helps to bear in mind that 999,998 = 3937 × 254.
  3. ^ "Appendix G - Weights and Measures". The World Factbook. Washington: Central Intelligence Agency. January 17, 2007. https://www.cia.gov/library/publications/the-world-factbook/appendix/appendix-g.html. Retrieved February 4, 2007. 
  4. ^ "English units of measurement". The Columbia Encyclopedia 6th ed. 2001-2007. archived copy.
  5. ^ a b Ed Tenner, (May 2005), "The Trouble with the Meter"
  6. ^ a b c Gardner, Martin (1957). ["The Great Pyramid". [http://www.skeptically.org/skepticism/id15.html. 
  7. ^ Robyn Williams (February 8, 1998) "Trouble with the Metric System". Australian Radio National, Ockham's Razor.
  8. ^ a b c d e Roberts, R.W. (February 3, 1975). Federal Register republished in Barbrow, L.E. and Judson, L. V. (1976) Weights and Measures of the United States. National Bureau of Standards Special Publication 447. p. 36
  9. ^ a b c National Geodetic Survey (undated). "Frequently Asked Questions about the National Geodetic Survey". http://www.ngs.noaa.gov/faq.shtml#Feet. Retrieved May 16, 2009. 
  10. ^ Astin, A. V. (July 27, 1968). Federal Register. Republished in Barbrow, L.E and Judson, L.V. Weights and Measures of the United States: A Brief History. National Bureau of Standards Special Publication 447. pp. 34–35.
  11. ^ National Institute of Standards and Technology. (2008). Guide for the Use of the International System of Units (SI).
  12. ^ The recommended symbol for the liter in the United States is 'L' per National Institute of Standards and Technology. (1995.) Guide for the Use of the International System of Units (SI). Special Publication 811. http://physics.nist.gov/Pubs/SP811/sec06.html#6.1.2
  13. ^ 93rd Conference on Weights and Measures. (2009). Specifications, Tolerances, and Other Technical Requirements for Weighing and Measuring Devices (NIST Handbook 44). National Institute of Standards and Technology.
  14. ^ Summary of State Laws and Regulations in Weights and Measures. (2005) National Institute of Standards and Technology.
  15. ^ "Food and Drugs: FDA Food Labeling". U.S. Government Printing Office. April 1, 2004. http://edocket.access.gpo.gov/cfr_2004/aprqtr/21cfr101.9.htm. 
    For Nutrition facts labeling "a teaspoon means 5 milliliters (mL), a tablespoon means 15 mL, a cup means 240 mL, 1 fl oz means 30 mL, and 1 oz in weight means 28 g."
  16. ^ 15 U.S.C. § 205b
  17. ^ Michael Milstein (March 2001). "Metric Mayhem". Air & Space Magazine. http://www.airspacemag.com/flight-today/mayhem.html. Retrieved March 2011. 

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