United States customary units

United States customary units are a system of measurements commonly used in the United States. The United States customary system (USCS or USC) developed from English units which were in use in the British Empire before American independence. However, the British system of measures was overhauled in 1824 to create the imperial system, changing the definitions of some units. Therefore, while many U.S. units are essentially similar to their Imperial counterparts, there are significant differences between the systems.

The majority of U.S. customary units were redefined in terms of the meter and the kilogram with the Mendenhall Order of 1893 and, in practice, for many years before.^[1] These definitions were refined by the international yard and pound agreement of 1959.^[2] Americans primarily use customary units in commercial activities, as well as for personal and social use. In science, medicine, many sectors of industry and some of government, metric units are used. The International System of Units (SI), the modern form of the metric system, is preferred for many uses by the U.S. National Institute of Standards and Technology (NIST).^[3]

History

The United States system of units is similar to the British imperial system.^[4] Both systems are derived from English units, a system which had evolved over the millennia before American independence, and which had its roots in Roman and Anglo-Saxon units.

The customary system was championed by the U.S.-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.^[5] An auxiliary of the Institute in Ohio published a poem with wording such as "down with every 'metric' scheme" and "A perfect inch, a perfect pint".^[5] One adherent of the customary system called it "a just weight and a just measure, which alone are acceptable to the Lord."^[5]

The U.S. government passed Omnibus Trade and Competitiveness Act of 1988, which made the metric system "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 as it voluntarily converts to the metric system, i.e., metrification. This is most evident in U.S. labeling requirements on food products, where SI units are almost always presented alongside customary units. According to the CIA Factbook, the United States is one of three nations (the others being Liberia and Burma) that have not adopted the metric system as their official system of weights and measures.^[6]

U.S. customary units are widely used on consumer products and in industrial manufacturing. Metric units are standard in science, medicine, as well as many sectors of industry and government, including the military.^[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 foot-inch measurements are more suitable when distances are frequently divided into halves, thirds and quarters, often in parallel. The metric system also lacks a parallel to the foot.^[8]

Other nations 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; foot and pound also had varying definitions. Historically, a wide range of non-SI units were used in the U.S. and in Britain, but many have fallen into disuse. This article deals only with the units commonly used or officially defined in the U.S.

Units of length

Unit	Divisions	SI Equivalent
Exact relationships shown in boldface
International
1 point (p)		352.777778 µm
1 pica (P̸)	12 p	4.233333 mm
1 inch (in)	6 P̸	25.4 mm
1 foot (ft)	12 in	0.3048 m[9]
1 yard (yd)	3 ft	0.9144 m[9]
1 mile (mi)	5280 ft or 1760 yd	1.609344 km
US Survey
1 link (li)	^33⁄50 ft or 7.92 in	0.2012 m
1 (survey) foot (ft)	^1200⁄3937 m	0.30480061 m[9]
1 rod (rd)	25 li or 16.5 ft	5.02921 m
1 chain (ch)	4 rd or 66 ft	20.11684 m
1 furlong (fur)	10 ch	201.1684 m
1 survey (or statute) mile (mi)	8 fur	1.609347 km[9]
1 league (lea)	3 mi	4.828042 km
International Nautical[9]
1 fathom (ftm)	2 yd	1.8288 m
1 cable (cb)	120 ftm or 1.091 fur	219.456 m
1 nautical mile (NM or nmi)	8.439 cb or 1.151 mi	1.852 km

For measuring length, the U.S. customary system uses 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 meters except for some applications in surveying.^[2] The U.S., the United Kingdom and other Commonwealth countries agreed on this definition, and so it 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 = ¹²⁰⁰⁄₃₉₃₇ meters: this definition was retained for data derived from NAD27, but renamed the US 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 US survey foot, for a difference of about ¹⁄₈ inch (3 mm) per mile – but it affects the definition of the State Plane Coordinate Systems (SPCSs), which can stretch over hundreds of miles.^[10]

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 US survey feet and an eighth state in international feet: the other 42 states use only meter-based SPCSs.^[10]

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 US 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.^[10]

Units of area

Unit	Divisions	SI Equivalent
Exact relationships shown in boldface
1 square survey foot (sq ft or ft^2)	144 square inches	0.09290341 m^2
1 square chain (sq ch or ch^2)	4356 sq ft (survey) or 16 sq rods	404.6873 m^2
1 acre	43560 sq ft (survey) or 10 sq ch	4046.873 m^2
1 section	640 acres or 1 sq mile (survey)	2.589998 km^2
1 survey township (twp)	36 sections or 4 sq leagues	93.23993 km^2

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.^[9] Conversion factors are based on Astin (July 27, 1968)^[11] and National Institute of Standards and Technology (2008).^[12]

Units of capacity and volume

Volume in general
Unit	Divisions	SI Equivalent
1 cubic inch (cu in) or (in^3)		16.387064 mL[13]
1 cubic foot (cu ft) or (ft^3)	1728 cu in	28.31685 L
1 cubic yard (cu yd) or (yd^3)	27 cu ft	764.554857984 L 0.764554857984 m^3
1 acre-foot (acre ft)	43560 cu ft 1613.333 cu yd	1.233482 ML 1233.482 m^3

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 inch, cubic foot 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	61.611519921875 μL
1 US fluid dram (fl dr)	60 min	3.6966911953125 mL
1 teaspoon (tsp)	80 min	4.92892159375 mL
1 tablespoon (Tbsp)	3 tsp or 4 fl dr	14.78676478125 mL
1 US fluid ounce (fl oz)	2 Tbsp or 1.0408 oz av of water	29.5735295625 mL
1 US shot (jig)	3 Tbsp	44.36029434375 mL
1 US gill (gi)	4 fl oz	118.29411825 mL
1 US cup (cp)	2 gi or 8 fl oz	236.5882365 mL
1 (liquid) US pint (pt)	2 cp or 16.65 oz av of water	473.176473 mL
1 (liquid) US quart (qt)	2 pt	0.946352946 L
1 (liquid) US gallon (gal)	4 qt or 231 cu in	3.785411784 L
1 (liquid) barrel (bbl)	31.5 gal or ^1⁄2 hogshead	119.240471196 L
1 oil barrel (bbl)	42 gal or ^2⁄3 hogshead	158.987294928 L
1 hogshead	63 gal or 8.421875 cu ft or 524.7 lb of water	238.480942392 L

One US fluid ounce is ¹⁄₁₆ of a US pint, ¹⁄₃₂ of a US quart, and ¹⁄₁₂₈ of a US gallon. The teaspoon, tablespoon, and cup are defined in terms of a fluid ounce as ¹⁄₆, ¹⁄₂, and 8 fluid ounces. The fluid ounce derives its name originally from being the volume of one ounce avoirdupois of water, but in the US it is defined as ¹⁄₁₂₈ of a US 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 (20 oz).

A 23.7 US fl oz (700 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 U.S., 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. The gill is often referred to as a "half-cup".

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 US dry gallon is less commonly used, and was not included in the handbook that many states recognize as the authority on measurement law.^[14][15] However pecks, or bushels are sometimes used—particularly for grapes, apples and similar fruits in agricultural regions.

Units of mass

Conversions

Type	Unit	Divisions	SI equivalent
Avoirdupois	1 grain (gr)	^1⁄7000 lb	64.79891 mg
	1 dram (dr)	27 ^11⁄32 gr or 8.859 carats	1.7718451953125 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	50.80234544 kg
	1 ton (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)	^1⁄7000 lb av or ^1⁄5760 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
Most common measures shown in italics Exact conversions shown in bold

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 U.S. The imperial system, which is still used for some measures in the United Kingdom and other 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 United Kingdom, 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,^[16] 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 U.S., 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

Common volume measures in English-speaking countries
(Comparable measures listed for comparison purposes.)

Measure	Australia	Canada	UK	US	US FDA[17]
Teaspoon	5 mL	5 mL	4.74 mL	4.93 mL	5 mL
Dessertspoon	10 mL	—	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 U.S. (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).

Units of temperature

Degrees Fahrenheit are used in the U.S. 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 American 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 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 = 1 ft × 1 ft × 1 in = 2.360 dm³
• 1 British thermal unit (Btu) ≈ 1055 J
• 1 ton of refrigeration (12,000 Btu/h) = 3.517 kW
• 1 calorie (cal) = 4.184 J
• 1 food calorie (kilocalorie, large calorie) (kcal, Cal) = 4.184 kJ
• 1 foot-pound (energy) ≈ 1.356 J
• 1 hand = 4 in = 10.16 cm
• 1 horsepower ≈ 745.7 W
• 1 R-value (ft²·°F·h/Btu) ≈ 0.1761 R_SI (K·m²/W)
• 1 slug = 1 lb_f·s²/ft
• 1 U (rack unit) = 1.75 in = 44.45 mm
• Various combination units are in common use, including the foot-pound (ft-lb) and the pound per square inch (psi); these are straightforwardly defined based on the above basic units.

Sizing systems are used for various items in commerce, several of which are U.S.-specific:

• US standard clothing size
• American wire gauge
• Scoop (utensil) sizes, numbered by scoops per quart

Other names for U.S. customary units

The United States Code refers to these units as "traditional systems of weights and measures".^[18]

Other common ways of referring to the system in the U.S. are: "Standard", "Customary", or, erroneously: "Imperial", or "English" (which refers to the pre-1824 reform measures used throughout the British Empire). Another term is the foot–pound–second (FPS) system, as opposed to centimeter–gram–second (CGS) and meter–kilogram–second (MKS) systems.

Tools and fasteners with sizes measured in inches are sometimes called "SAE bolts" or "SAE wrenches" to differentiate them from their metric counterparts. The Society of Automotive Engineers originally developed fasteners standards using U.S. units for the U.S. auto industry; the organization now uses metric units.^[19]

See also

Acre-foot Board foot Conversion of units Cord (unit)

Fahrenheit (vs. Celsius vs. Kelvin) History of measurement, systems, and units of measurement Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States (1790)

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. 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 note that 999,998 = 3937 × 254.
3. Laws and Metric Program. U.S. National Institute of Standards and Technology, 2010
4. "English units of measurement". The Columbia Encyclopedia 6th ed. 2001-2007. archived copy.
5. Gardner, Martin (1957). "The Great Pyramid".
6. "Appendix G - Weights and Measures". The World Factbook. Washington, D.C.: Central Intelligence Agency. Retrieved August 28, 2012.
7. Robyn Williams (February 8, 1998) "Trouble with the Metric System". Australian Radio National, Ockham's Razor.
8. Ed Tenner, (May 2005). "The Trouble with the Meter" Technologyreview.com
9. 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
10. "Frequently Asked Questions about the National Geodetic Survey". National Geodetic Survey. Retrieved May 16, 2009. |contribution= ignored (help)
11. 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.
12. National Institute of Standards and Technology. (2008). Guide for the Use of the International System of Units (SI).
13. 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
14. 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.
15. Summary of State Laws and Regulations in Weights and Measures. (2005) National Institute of Standards and Technology.
16. NIST Handbook 44, Appendix C, General Tables of Units of Measurement, page C-6 Avoirdupois Units of Mass
17. "Title 21, 101.9 Nutrition labeling of food" (PDF). Code of Federal Regulations. US Government Printing Office. 2012-04-12. Retrieved 2014-11-02. For nutrition labeling purposes, 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.
18. 15 U.S.C. § 205b
19. "Rules for SAE Use of SI (Metric) Units" (PDF). Society of Automotive Engineers, Inc. May 1999. Retrieved July 2012.

External links

• Rowlett's A Dictionary of Units of Measurement