U.S. customary units

The U.S. customary units is the non-metric system of units of measurement that is presently used in the United States, alongside the metric system. It is similar to the Imperial system once used in the United Kingdom and the Commonwealth, but has some differences. Both systems derive from the units which developed over the centuries in England. U.S. customary units are defined in terms of SI units.

The official policy of the United States government is to designate the metric system of measurement as the preferred system of weights and measures for U.S. trade and commerce. This process known is known as metrication. In practice, this process in the United States is not very far advanced. The United Kingdom is more advanced in the process than the United States, and in most Commonwealth countries (such as Australia and New Zealand) the process is largely completed, although some informal usage of non-metric units remains.

Historically a wide range of non-metric units have been used in the US and UK, and in England before that, but many of these have fallen into disuse. This article will mainly deal with those commonly used or officially defined in the US.

See also: SI, Imperial units, History of Weights and Measures, conversion of units, Informal conversion of common units.

Table of contents 1 Units of Length 2 Units of area 3 Units of mass 3.1 Avoirdupois weight 3.2 Apothecaries weight 3.3 Troy weight 4 Units of capacity and volume 4.1 Volume in general 4.2 Liquid Volume 4.3 Dry Volume 5 Cooking Measures 6 Grain Measures 7 Units of Temperature 8 Other Units

Units of Length

The system for measuring length in the U.S. customary system is based on the inch, foot, yard and mile. However, for each of these units there exist two slightly different definitions, yielding two different systems of measure - international measure, and U.S. survey measure. The relationships between the different units within each measure is the same, but each measure has a slightly different definition in terms of metric units.

One inch international measure is exactly 25.4 mm, while one inch U.S. survey measure is defined so that 39.37 inches is exactly one metre. For most applications, the difference is insignificant (about 3 millimetres per mile). International measure is used for everyday use, engineering, and commerce in the United States, while survey measure is only used for surveying.

International measure uses the same definition of the units involved as is used in the UK and other Commonwealth countries. U.S. survey measure uses an older definition of these units which the United States used prior to adopting international measure.

• 1 inch (in)
• 1 foot (ft) = 12 in exactly
• 1 yard (yd) = 3 ft exactly
• 1 mile (mi) = 1760 yd exactly

• 1 rod (rd) = 16.5 ft exactly (also called pole or perch)
• 1 furlong (fur) = 40 rd exactly = 660 ft exactly
• 1 mile = 8 furlongs = 5280 ft exactly

Sometimes, for surveying purposes, units known as Gunther's Chain Measure (or equivalently Surveyor's Chain Measure) are used. These units are defined as follows:

• 1 link (li) = 7.92 in exactly
• 1 chain (ch) = 100 li = 66 ft exactly

To measure depths at sea, fathoms are used:

• 1 fathom = 6 feet exactly
• 1 cable length = 120 fathoms exactly (US Navy definition, there are others)

Units of area

The units of area in the U.S. customary system are based on the square inch[?] (sq in). Since the U.S. customary system has two differing definitions of the inch, there are also two differing definitions for the square inch. But presuming international measure is used, 1 square inch is exactly 645.16 mm².

• 1 square foot[?] (sq ft) = 144 sq in exactly
• 1 square rod[?] (sq rd) = 272.25 sq ft exactly
• 1 acre = 160 sq rd exactly = 43560 sq ft exactly
• 1 square mile (sq mi) = 640 acres exactly
• 1 section[?] = 1 sq mi exactly

Units of mass

There have historically been four different English systems of mass: Tower weight, Troy weight, avoirdupois weight, and apothecaries weight. Tower weight fell out of use (due to legal prohibition) centuries ago, and was never used in the United States. Troy weight is still used to weigh precious metals. Apothecaries weight, once used in pharmacy, has been largely replaced by metric measurements. Avoirdupois weight is the primary system of mass in the the U.S. customary system.

There is some confusion as to whether these are units of mass, or of force. The pound avoirdupois is legally defined as a unit of mass, though in physics the term "pound" can represent "pound-force" (a unit of force properly abbreviated as "lbf").

Troy weight, avoirdupois weight and apothecaries weight are all defined in terms of the same basic unit, the grain. However, they consist of various units (pounds, ounces, etc.) with the same name but different definitions in terms of the grain and in terms of each other. The pound and ounce in apothecaries and troy weight are the same, but each system has different subdivisions.

The pound avoirdupois, which forms the basis of the U.S. customary system of mass, is defined as exactly 0.453 592 37 kg. All the other units of mass are defined in terms of it.

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 British Imperial system is identical to that in the U.S. customary system.

Avoirdupois weight

• 1 ton (t) = 20 cwt exactly = 2000 lb exactly
• 1 hundredweight[?] (cwt) = 100 lb exactly
• 1 pound (lb) = 16 oz exactly = 7000 gr exactly = 0.453 592 37 kg exactly
• 1 ounce (oz) = 16 dr exactly = 437.5 gr exactly = 0.028 349 523 125 kg exactly
• 1 dram[?] (dr) = 27.34375 gr exactly
• 1 grain (gr) = 64.79891 mg exactly

There ton and hundredweight above are sometimes referred to as the "short" ton, and the "short" hundredweight, to distinguish them from the British Imperial ton and hundredweight, which are larger and hence are referred to as the "long" ton and "long" hundredweight. The long ton and hundredweight have limited use in the United States, although they are officially recognized as units. Any unqualified reference in the U.S. to "ton" or "hundredweight" means the short ton and hundredweight mentioned above. Sometimes the terms "net" and "gross" are used instead of "short" and "long", respectively.

• 1 long ton[?] = 2240 lb exactly
• 1 long hundredweight[?] = 112 lb exactly

Apothecaries weight

The grain has the same definition as for Avoirdupois weight

• 1 scruple (s ap) = 20 gr exactly
• 1 dram apothecaries (dr ap) = 3 s ap exactly
• 1 ounce apothecaries (oz ap) = 8 dr ap exactly = 480 gr exactly
• 1 pound apothecaries (lb ap) = 5760 gr

The pound and ounce apothecaries are identical to the pound and ounce Troy.

Troy weight

The grain has the same definition as for Avoirdupois weight

• 1 pennyweight (dwt) = 24 gr exactly
• 1 ounce troy (oz t) = 20 dwt exactly = 480 gr exactly
• 1 pound troy (lb t) = 12 oz t exactly = 5760 gr exactly

Units of capacity and volume

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.

Technically speaking, since these units are defined in terms of the inch, it would make a difference whether international or survey measure was used. However, in practice, the difference between the two definitions would be imperceptible, and in any case in defining volumes international measure is used.

Volume in general

• 1 cubic inch (in³ or cu in) = 16.387064 cm³ exactly
• 1 cubic foot (ft³ or cu ft) = 1728 cu in
• 1 cubic yard (yd³ or cu yd) = 27 cu ft
• 1 acre-foot = 43,560 cu ft or 325,851 gallons

Liquid Volume

• 1 gallon (gal) = 230.907 cu in exactly = 4 qt exactly
• 1 quart (qt) = 2 pt exactly
• 1 pint (pt) = 4 gi exactly = 16 fl oz exactly
• 1 gill (gi) = 7.21875 cu in exactly = 4 fl oz exactly
• 1 fluid ounce[?] (fl oz) = 8 fl dr exactly
• 1 fluid dram[?] (fl dr) = 60 min exactly
• 1 minim (min)

Dry Volume

• 1 bushel[?] (bu) = 2150.42 cu in exactly = 4 pk exactly
• 1 peck (pk) = 8 qt exactly
• 1 quart (qt) = 2 pt exactly
• 1 pint

Cooking Measures Measures of volume used in cooking. Note that differing cooking measures are used in other countries; see cooking measures for more information.

• 1 cup = 8 fl oz exactly
• 1 tablespoon (tbsp) = 0.5 fl oz exactly
• 1 teaspoon = 1/3 tbsp exactly
• 1 stick (of butter) = 1/4 pound exactly

Grain Measures These are derived from the volume measures.

• 1 bushel (maize) = 56 lb exactly = 25.401 kg approx.
• 1 bushel (wheat) = 60 lb exactly = 27.215 kg approx.

Units of Temperature

• Traditionally, degrees Fahrenheit are used in the United States to measure temperatures.
• Pure water freezes at 32°F.
• Water saturated with common salt freezes at 0°F.
• Water boils at 212°F at 1 atmospheric pressure.
• Conversion formula: <math>F=\frac{9}{5}C+32</math>

Other Units

• British thermal unit
• horsepower
• calorie
• degree Rankine
• board-foot
• R-value

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Source: Appendix C, NIST Handbook 44, 2002 edition. http://ts.nist.gov/ts/htdocs/230/235/h442002.htm