Handbook 44 – 2009 Appendix B – Units and Systems of Measurement 

Appendix B 

Units and Systems of Measurement 

Their Origin, Development, and Present Status 

1. Introduction 

The National Institute of Standards and Technology (NIST) (formerly the National Bureau of Standards) was established 

by Act of Congress in 1901 to serve as a national scientific laboratory in the physical sciences, and to provide 

fundamental measurement standards for science and industry. In carrying out these related functions the Institute 

conducts research and development in many fields of physics, mathematics, chemistry, and engineering. At the time of 

its founding, the Institute had custody of two primary standards – the meter bar for length and the kilogram cylinder for 

mass. With the phenomenal growth of science and technology over the past century, the Institute has become a major 

research institution concerned not only with everyday weights and measures, but also with hundreds of other scientific 

and engineering standards that are necessary to the industrial progress of the nation. Nevertheless, the country still looks 

to NIST for information on the units of measurement, particularly their definitions and equivalents. 

The subject of measurement systems and units can be treated from several different standpoints. Scientists and engineers 

are interested in the methods by which precision measurements are made. State weights and measures officials are 

concerned with laws and regulations that assure equity in the marketplace, protect public health and safety, and with 

methods for verifying commercial weighing and measuring devices. But a vastly larger group of people is interested in 

some general knowledge of the origin and development of measurement systems, of the present status of units and 

standards, and of miscellaneous facts that will be useful in everyday life. This material has been prepared to supply that 

information on measurement systems and units that experience has shown to be the common subject of inquiry. 

2. Units and Systems of Measurement

The expression “weights and measures” is often used to refer to measurements of length, mass, and capacity or volume, 

thus excluding such quantities as electrical and time measurements and thermometry. This section on units and 

measurement systems presents some fundamental information to clarify the concepts of this subject and to eliminate 

erroneous and misleading use of terms. 

It is essential that the distinction between the terms “units” and “standards” be established and kept in mind. 

A unit is a special quantity in terms of which other quantities are expressed. In general, a unit is fixed by definition and is 

independent of such physical conditions as temperature. Examples: the meter, the liter, the gram, the yard, the pound, the 

gallon. 

A standard is a physical realization or representation of a unit. In general, it is not entirely independent of physical 

conditions, and it is a representation of the unit only under specified conditions. For example, a meter standard has a 

length of one meter when at some definite temperature and supported in a certain manner. If supported in a different 

manner, it might have to be at a different temperature to have a length of one meter. 

2.1. Origin and Early History of Units and Standards.

2.1.1. General Survey of Early History of Measurement Systems. – Weights and measures were among the 

earliest tools invented by man. Primitive societies needed rudimentary measures for many tasks: constructing 

dwellings of an appropriate size and shape, fashioning clothing, or bartering food or raw materials. 

Man understandably turned first to parts of the body and the natural surroundings for measuring instruments. Early 

Babylonian and Egyptian records and the Bible indicate that length was first measured with the forearm, hand, or 

finger and that time was measured by the periods of the sun, moon, and other heavenly bodies. When it was 

necessary to compare the capacities of containers such as gourds or clay or metal vessels, they were filled with plant 

seeds which were then counted to measure the volumes. When means for weighing were invented, seeds and stones 

served as standards. For instance, the “carat,” still used as a unit for gems, was derived from the carob seed. 

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Appendix B – Units and Systems of Measurement Handbook 44 – 2009 

Our present knowledge of early weights and measures comes from many sources. Archaeologists have recovered 

some rather early standards and preserved them in museums. The comparison of the dimensions of buildings with 

the descriptions of contemporary writers is another source of information. An interesting example of this is the 

comparison of the dimensions of the Greek Parthenon with the description given by Plutarch from which a fairly 

accurate idea of the size of the Attic foot is obtained. In some cases, we have only plausible theories and we must 

sometimes select the interpretation to be given to the evidence. 

For example, does the fact that the length of the double-cubit of early Babylonia was equal (within two parts per 

thousand) to the length of the seconds pendulum at Babylon suggest a scientific knowledge of the pendulum at a very 

early date, or do we merely have a curious coincidence? By studying the evidence given by all available sources, and 

by correlating the relevant facts, we obtain some idea of the origin and development of the units. We find that they 

have changed more or less gradually with the passing of time in a complex manner because of a great variety of 

modifying influences. We find the units modified and grouped into measurement systems: the Babylonian system, 

the Egyptian system, the Phileterian system of the Ptolemaic age, the Olympic system of Greece, the Roman system, 

and the British system, to mention only a few. 

2.1.2. Origin and Development of Some Common Customary Units. – The origin and development of units of 

measurement has been investigated in considerable detail and a number of books have been written on the subject. It 

is only possible to give here, somewhat sketchily, the story about a few units. 

Units of length: The cubit was the first recorded unit used by ancient peoples to measure length. There were several 

cubits of different magnitudes that were used. The common cubit was the length of the forearm from the elbow to 

the tip of the middle finger. It was divided into the span of the hand (one-half cubit), the palm or width of the hand 

(one sixth), and the digit or width of a finger (one twenty-fourth). The Royal or Sacred Cubit, which was 7 palms or 

28 digits long, was used in constructing buildings and monuments and in surveying. The inch, foot, and yard evolved 

from these units through a complicated transformation not yet fully understood. Some believe they evolved from 

cubic measures; others believe they were simple proportions or multiples of the cubit. In any case, the Greeks and 

Romans inherited the foot from the Egyptians. The Roman foot was divided into both 12 unciae (inches) and 

16 digits. The Romans also introduced the mile of 1000 paces or double steps, the pace being equal to five Roman 

feet. The Roman mile of 5000 feet was introduced into England during the occupation. Queen Elizabeth, who 

reigned from 1558 to 1603, changed, by statute, the mile to 5280 feet or 8 furlongs, a furlong being 40 rods of 

51⁄2 yards each. 

The introduction of the yard as a unit of length came later, but its origin is not definitely known. Some believe the 

origin was the double cubit, others believe that it originated from cubic measure. Whatever its origin, the early yard 

was divided by the binary method into 2, 4, 8, and 16 parts called the half-yard, span, finger, and nail. The 

association of the yard with the “gird” or circumference of a person’s waist or with the distance from the tip of the 

nose to the end of the thumb of Henry I are probably standardizing actions, since several yards were in use in Great 

Britain. 

The point, which is a unit for measuring print type, is recent. It originated with Pierre Simon Fournier in 1737. It 

was modified and developed by the Didot brothers, Francois Ambroise and Pierre Francois, in 1755. The point was 

first used in the United States in 1878 by a Chicago type foundry (Marder, Luse, and Company). Since 1886, a point 

has been exactly 0.351 459 8 millimeters, or about 1

/72 inch. 

Units of mass: The grain was the earliest unit of mass and is the smallest unit in the apothecary, avoirdupois, Tower, 

and Troy systems. The early unit was a grain of wheat or barleycorn used to weigh the precious metals silver and 

gold. Larger units preserved in stone standards were developed that were used as both units of mass and of monetary 

currency. The pound was derived from the mina used by ancient civilizations. A smaller unit was the shekel, and a 

larger unit was the talent. The magnitude of these units varied from place to place. The Babylonians and Sumerians 

had a system in which there were 60 shekels in a mina and 60 minas in a talent. The Roman talent consisted of 

100 libra (pound) which were smaller in magnitude than the mina. The Troy pound used in England and the United 

States for monetary purposes, like the Roman pound, was divided into 12 ounces, but the Roman uncia (ounce) was 

smaller. The carat is a unit for measuring gemstones that had its origin in the carob seed, which later was 

standardized at 1

/444 ounce and then 0.2 gram. 

Goods of commerce were originally traded by number or volume. When weighing of goods began, units of mass 

based on a volume of grain or water were developed. For example, the talent in some places was approximately 

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equal to the mass of one cubic foot of water. Was this a coincidence or by design? The diverse magnitudes of units 

having the same name, which still appear today in our dry and liquid measures, could have arisen from the various 

commodities traded. The larger avoirdupois pound for goods of commerce might have been based on volume of 

water which has a higher bulk density than grain. For example, the Egyptian hon was a volume unit about 11 % 

larger than a cubic palm and corresponded to one mina of water. It was almost identical in volume to the present 

U. S. pint. 

The stone, quarter, hundredweight, and ton were larger units of mass used in Great Britain. Today only the stone 

continues in customary use for measuring personal body weight. The present stone is 14 pounds, but an earlier unit 

appears to have been 16 pounds. The other units were multiples of 2, 8, and 160 times the stone, or 28, 112, and 

2240 pounds, respectively. The hundredweight was approximately equal to two talents. In the United States the ton 

of 2240 pounds is called the “long ton.” The “short ton” is equal to 2000 pounds. 

Units of time and angle: We can trace the division of the circle into 360 degrees and the day into hours, minutes, and 

seconds to the Babylonians who had a sexagesimal system of numbers. The 360 degrees may have been related to a 

year of 360 days. 

2.2. The Metric System.

2.2.1. Definition, Origin, and Development. – Metric systems of units have evolved since the adoption of the first 

well-defined system in France in 1791. During this evolution the use of these systems spread throughout the world, 

first to the non-English-speaking countries, and more recently to the English-speaking countries. The first metric 

system was based on the centimeter, gram, and second (cgs) and these units were particularly convenient in science 

and technology. Later metric systems were based on the meter, kilogram, and second (mks) to improve the value of 

the units for practical applications. The present metric system is the International System of Units (SI). It is also 

based on the meter, kilogram and second as well as additional base units for temperature, electric current, luminous 

intensity, and amount of substance. The International System of Units is referred to as the modern metric system. 

The adoption of the metric system in France was slow, but its desirability as an international system was recognized 

by geodesists and others. On May 20, 1875, an international treaty known as the International Metric Convention or 

the Treaty of the Meter was signed by seventeen countries including the United States. This treaty established the 

following organizations to conduct international activities relating to a uniform system for measurements: 

(1) The General Conference on Weights and Measures (French initials: CGPM), an intergovernmental 

conference of official delegates of member nations and the supreme authority for all actions; 

(2) The International Committee of Weights and Measures (French initials: CIPM), consisting of selected 

scientists and metrologists, which prepares and executes the decisions of the CGPM and is responsible for 

the supervision of the International Bureau of Weights and Measures; 

(3) The International Bureau of Weights and Measures (French initials: BIPM), a permanent laboratory and 

world center of scientific metrology, the activities of which include the establishment of the basic standards 

and scales of the principal physical quantities and maintenance of the international prototype standards. 

The National Institute of Standards and Technology provides official United States representation in these 

organizations. The CGPM, the CIPM, and the BIPM have been major factors in the continuing refinement of the 

metric system on a scientific basis and in the evolution of the International System of Units. 

Multiples and submultiples of metric units are related by powers of ten. This relationship is compatible with the 

decimal system of numbers and it contributes greatly to the convenience of metric units. 

2.2.2. International System of Units. – At the end of World War II, a number of different systems of measurement 

still existed throughout the world. Some of these systems were variations of the metric system, and others were 

based on the customary inch-pound system of the English-speaking countries. It was recognized that additional steps 

were needed to promote a worldwide measurement system. As a result the 9th GCPM, in 1948, asked the ICPM to 

conduct an international study of the measurement needs of the scientific, technical, and educational communities. 

Based on the findings of this study, the 10th General Conference in 1954 decided that an international system should 

be derived from six base units to provide for the measurement of temperature and optical radiation in addition to 

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Appendix B – Units and Systems of Measurement Handbook 44 – 2009 

mechanical and electromagnetic quantities. The six base units recommended were the meter, kilogram, second, 

ampere, Kelvin degree (later renamed the kelvin), and the candela. 

In 1960, the 11th General Conference of Weights and Measures named the system based on the six base quantities the 

International System of Units, abbreviated SI from the French name: Le Système International d’Unités. The SI 

metric system is now either obligatory or permissible throughout the world. 

2.2.3. Units and Standards of the Metric System. – In the early metric system there were two fundamental or base 

units, the meter and the kilogram, for length and mass. The other units of length and mass, and all units of area, 

volume, and compound units such as density were derived from these two fundamental units. 

The meter was originally intended to be one ten-millionth part of a meridional quadrant of the earth. The Meter of 

the Archives, the platinum length standard which was the standard for most of the 19th century, at first was supposed 

to be exactly this fractional part of the quadrant. More refined measurements over the earth’s surface showed that 

this supposition was not correct. In 1889, a new international metric standard of length, the International Prototype 

Meter, a graduated line standard of platinum-iridium, was selected from a group of bars because precise 

measurements found it to have the same length as the Meter of the Archives. The meter was then defined as the 

distance, under specified conditions, between the lines on the International Prototype Meter without reference to any 

measurements of the earth or to the Meter of the Archives, which it superseded. Advances in science and technology 

have made it possible to improve the definition of the meter and reduce the uncertainties associated with artifacts. 

From 1960 to 1983, the meter was defined as the length equal to 1 650 763.73 wavelengths in a vacuum of the 

radiation corresponding to the transition between the specified energy levels of the krypton 86 atom. Since 1983 the 

meter has been defined as the length of the path traveled by light in a vacuum during an interval of 1

/299 792 458 of a 

second. 

The kilogram, originally defined as the mass of one cubic decimeter of water at the temperature of maximum density, 

was known as the Kilogram of the Archives. It was replaced after the International Metric Convention in 1875 by the 

International Prototype Kilogram which became the unit of mass without reference to the mass of a cubic decimeter 

of water or to the Kilogram of the Archives. Each country that subscribed to the International Metric Convention 

was assigned one or more copies of the international standards; these are known as National Prototype Meters and 

Kilograms. 

The liter is a unit of capacity or volume. In 1964, the 12th GCPM redefined the liter as being one cubic decimeter. 

By its previous definition – the volume occupied, under standard conditions, by a quantity of pure water having a 

mass of one kilogram – the liter was larger than the cubic decimeter by 28 parts per 1 000 000. Except for 

determinations of high precision, this difference is so small as to be of no consequence. 

The modern metric system (SI) includes two classes of units: 

(a) base units for length, mass, time, temperature, electric current, luminous intensity, and amount of 

substance; and 

(b) derived units for all other quantities (e.g., work, force, power) expressed in terms of the seven base 

units. 

For details, see NIST Special Publication 330 (2001), The International System of Units (SI) and NIST Special 

Publication 811 (1995), Guide for the Use of the International System of Units. 

2.2.4. International Bureau of Weights and Measures. – The International Bureau of Weights and Measures 

(BIPM) was established at Sèvres, a suburb of Paris, France, by the International Metric Convention of 

May 20, 1875. The BIPM maintains the International Prototype Kilogram, many secondary standards, and 

equipment for comparing standards and making precision measurements. The Bureau, funded by assessment of the 

signatory governments, is truly international. In recent years the scope of the work at the Bureau has been 

considerably broadened. It now carries on researches in the fields of electricity, photometry and radiometry, ionizing 

radiations, and time and frequency besides its work in mass, length, and thermometry. 

2.2.5. Status of the Metric System in the United States. – The use of the metric system in this country was 

legalized by Act of Congress in 1866, but was not made obligatory then or since. 

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Handbook 44 – 2009 Appendix B – Units and Systems of Measurement 

Following the signing of the Convention of the Meter in 1875, the United States acquired national prototype 

standards for the meter and the kilogram. U. S. Prototype Kilogram No. 20 continues to be the primary standard for 

mass in the United States. It is recalibrated from time to time at the BIPM. The prototype meter has been replaced 

by modern stabilized lasers following the most recent definition of the meter. 

From 1893 until 1959, the yard was defined as equal exactly to 3600/3937 meter. In 1959, a small change was made in 

the definition of the yard to resolve discrepancies both in this country and abroad. Since 1959, we define the yard as 

equal exactly to 0.9144 meter; the new yard is shorter than the old yard by exactly two parts in a million. At the 

same time, it was decided that any data expressed in feet derived from geodetic surveys within the United States 

would continue to bear the relationship as defined in 1893 (one foot equals 1200/3937 meter). We call this foot the U. S. 

Survey Foot, while the foot defined in 1959 is called the International Foot. Measurements expressed in U. S. statute 

miles, survey feet, rods, chains, links, or the squares thereof, and acres should be converted to the corresponding 

metric values by using pre-1959 conversion factors if more than five significant figure accuracy is required. 

Since 1970, actions have been taken to encourage the use of metric units of measurement in the United States. A 

brief summary of actions by Congress is provided below as reported in the Federal Register Notice dated 

July 28, 1998. 

Section 403 of Public Law 93-380, the Education Amendment of 1974, states that it is the policy of the United States 

to encourage educational agencies and institutions to prepare students to use the metric system of measurement as 

part of the regular education program. Under both this act and the Metric Conversion Act of 1975, the “metric 

system of measurement” is defined as the International System of Units as established in 1960 by the General 

Conference on Weights and Measures and interpreted or modified for the United States by the Secretary of 

Commerce (Section 4(4)- Public Law 94-168; Section 403(a)(3)- Public Law 93-380). The Secretary has delegated 

authority under these subsections to the Director of the National Institute of Standards and Technology. 

Section 5164 of Public Law 100-418, the Omnibus Trade and Competitiveness Act of 1988, amends Public 

Law 94-168, The Metric Conversion Act of 1975. In particular, Section 3, The Metric Conversion Act is amended to 

read as follows: 

“Sec. 3. It is therefore the declared policy of the United States– 

(1) to designate the metric system of measurement as the preferred system of weights and measures for United 

States trade and commerce; 

(2) to require that each federal agency, by a date certain and to the extent economically feasible by the end of 

the fiscal year 1992, use the metric system of measurement in its procurements, grants, and other businessrelated activities, except to the extent that such use is impractical or is likely to cause significant 

inefficiencies or loss of markets to U. S. firms, such as when foreign competitors are producing competing 

products in non-metric units; 

(3) to seek ways to increase understanding of the metric system of measurement through educational 

information and guidance and in government publications; and 

(4) to permit the continued use of traditional systems of weights and measures in nonbusiness activities.” 

The Code of Federal Regulations makes the use of metric units mandatory for agencies of the federal government. 

(Federal Register, Vol. 56, No. 23, page 160, January 2, 1991.) 

2.3. British and United States Systems of Measurement. – In the past, the customary system of weights and measures 

in the British Commonwealth countries and that in the United States were very similar; however, the SI metric system is 

now the official system of units in the United Kingdom, while the customary units are still predominantly used in the 

United States. Because references to the units of the old British customary system are still found, the following 

discussion describes the differences between the U. S. and British customary systems of units. 

After 1959, the U. S. and the British inches were defined identically for scientific work and were identical in commercial 

usage. A similar situation existed for the U. S. and the British pounds, and many relationships, such as 12 inches = 1 foot, 

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Appendix B – Units and Systems of Measurement Handbook 44 – 2009 

3 feet = 1 yard, and 1760 yards = 1 international mile, were the same in both countries; but there were some very 

important differences. 

In the first place, the U. S. customary bushel and the U. S. gallon, and their subdivisions differed from the corresponding 

British Imperial units. Also the British ton is 2240 pounds, whereas the ton generally used in the United States is the 

short ton of 2000 pounds. The American colonists adopted the English wine gallon of 231 cubic inches. The English of 

that period used this wine gallon and they also had another gallon, the ale gallon of 282 cubic inches. In 1824, the British 

abandoned these two gallons when they adopted the British Imperial gallon, which they defined as the volume of 

10 pounds of water, at a temperature of 62 °F, which, by calculation, is equivalent to 277.42 cubic inches. At the same 

time, they redefined the bushel as 8 gallons. 

In the customary British system, the units of dry measure are the same as those of liquid measure. In the United States 

these two are not the same; the gallon and its subdivisions are used in the measurement of liquids and the bushel, with its 

subdivisions, is used in the measurement of certain dry commodities. The U. S. gallon is divided into four liquid quarts 

and the U. S. bushel into 32 dry quarts. All the units of capacity or volume mentioned thus far are larger in the customary 

British system than in the U. S. system. But the British fluid ounce is smaller than the U. S. fluid ounce, because the 

British quart is divided into 40 fluid ounces whereas the U. S. quart is divided into 32 fluid ounces. 

From this we see that in the customary British system an avoirdupois ounce of water at 62 °F has a volume of one fluid 

ounce, because 10 pounds is equivalent to 160 avoirdupois ounces, and 1 gallon is equivalent to 4 quarts, or 160 fluid 

ounces. This convenient relation does not exist in the U. S. system because a U. S. gallon of water at 62 °F weighs about 

81⁄3 pounds, or 1331⁄3 avoirdupois ounces, and the U. S. gallon is equivalent to 4 x 32, or 128 fluid ounces. 

1 U. S. fluid ounce = 1.041 British fluid ounces 

1 British fluid ounce = 0.961 U. S. fluid ounce 

1 U. S. gallon = 0.833 British Imperial gallon 

1 British Imperial gallon = 1.201 U. S. gallons 

Among other differences between the customary British and the United States measurement systems, we should note that 

they abolished the use of the troy pound in England January 6, 1879; they retained only the troy ounce and its 

subdivisions, whereas the troy pound is still legal in the United States, although it is not now greatly used. We can 

mention again the common use, for body weight, in England of the stone of 14 pounds, this being a unit now unused in 

the United States, although its influence was shown in the practice until World War II of selling flour by the barrel of 

196 pounds (14 stone). In the apothecary system of liquid measure the British add a unit, the fluid scruple, equal to one 

third of a fluid drachm (spelled dram in the United States) between their minim and their fluid drachm. In the United 

States, the general practice now is to sell dry commodities, such as fruits and vegetables, by their mass. 

2.4. Subdivision of Units. – In general, units are subdivided by one of three methods: (a) decimal, into tenths; 

(b) duodecimal, into twelfths; or (c) binary, into halves (twos). Usually the subdivision is continued by using the same 

method. Each method has its advantages for certain purposes, and it cannot properly be said that any one method is 

“best” unless the use to which the unit and its subdivisions are to be put is known. 

For example, if we are concerned only with measurements of length to moderate precision, it is convenient to measure 

and to express these lengths in feet, inches, and binary fractions of an inch, thus 9 feet, 43

/8 inches. However, if these 

lengths are to be subsequently used to calculate area or volume, that method of subdivision at once becomes extremely 

inconvenient. For that reason, civil engineers, who are concerned with areas of land, volumes of cuts, fills, excavations, 

etc., instead of dividing the foot into inches and binary subdivisions of the inch, divide it decimally; that is, into tenths, 

hundredths, and thousandths of a foot. 

The method of subdivision of a unit is thus largely made based on convenience to the user. The fact that units have 

commonly been subdivided into certain subunits for centuries does not preclude their also having another mode of 

subdivision in some frequently used cases where convenience indicates the value of such other method. Thus, while we 

usually subdivide the gallon into quarts and pints, most gasoline-measuring pumps, of the price-computing type, are 

graduated to show tenths, hundredths, or thousandths of a gallon. 

Although the mile has for centuries been divided into rods, yards, feet, and inches, the odometer part of an automobile 

speedometer shows tenths of a mile. Although we divide our dollar into 100 parts, we habitually use and speak of halves 

and quarters. An illustration of rather complex subdividing is found on the scales used by draftsmen. These scales are of 

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Handbook 44 – 2009 Appendix B – Units and Systems of Measurement 

two types: (a) architects, which are commonly graduated with scales in which 3

/32, 3/16, 1/8, 1⁄4, 3/8, 1⁄2, 3⁄4, 1, 11⁄2, and 

3 inches, respectively, represent 1 foot full scale, and also having a scale graduated in the usual manner to 1

/16 inch; and 

(b) engineers, which are commonly subdivided to 10, 20, 30, 40, 50, and 60 parts to the inch. 

The dictum of convenience applies not only to subdivisions of a unit but also to multiples of a unit. Land elevations 

above sea level are given in feet although the height may be several miles; the height of aircraft above sea level as given 

by an altimeter is likewise given in feet, no matter how high it may be. 

On the other hand, machinists, toolmakers, gauge makers, scientists, and others who are engaged in precision 

measurements of relatively small distances, even though concerned with measurements of length only, find it convenient 

to use the inch, instead of the tenth of a foot, but to divide the inch decimally to tenths, hundredths, thousandths, etc., 

even down to millionths of an inch. Verniers, micrometers, and other precision measuring instruments are usually 

graduated in this manner. Machinist scales are commonly graduated decimally along one edge and are also graduated 

along another edge to binary fractions as small as 1

/64 inch. The scales with binary fractions are used only for relatively 

rough measurements. 

It is seldom convenient or advisable to use binary subdivisions of the inch that are smaller than 1

/64. In fact, 1/32-, 1/16-, or 1

/8-inch subdivisions are usually preferable for use on a scale to be read with the unaided eye. 

2.5. Arithmetical Systems of Numbers. – The subdivision of units of measurement is closely associated with 

arithmetical systems of numbers. The systems of units used in this country for commercial and scientific work, having 

many origins as has already been shown, naturally show traces of the various number systems associated with their 

origins and developments. Thus, (a) the binary subdivision has come down to us from the Hindus, (b) the duodecimal 

system of fractions from the Romans, (c) the decimal system from the Chinese and Egyptians, some developments having 

been made by the Hindus, and (d) the sexagesimal system (division by 60) now illustrated in the subdivision of units of 

angle and of time, from the ancient Babylonians. The use of decimal numbers in measurements is becoming the standard 

practice. 

3. Standards of Length, Mass, and Capacity or Volume

3.1. Standards of Length. – The meter, which is defined in terms of the speed of light in a vacuum, is the unit on which 

all length measurements are based. 

The yard is defined1 as follows: 

 1 yard = 0.914 4 meter 

and the inch is exactly equal to 25.4 millimeters. 

3.1.1. Calibration of Length Standards. – NIST calibrates standards of length including meter bars, yard bars, 

miscellaneous precision line standards, steel tapes, invar geodetic tapes, precision gauge blocks, micrometers, and 

limit gauges. It also measures the linear dimensions of miscellaneous apparatus such as penetration needles, cement 

sieves, and hemacytometer chambers. In general, NIST accepts for calibration only apparatus of such material, 

design, and construction as to ensure accuracy and permanence sufficient to justify calibration by the Institute. NIST 

performs calibrations in accordance with fee schedules, copies of which may be obtained from NIST. 

NIST does not calibrate carpenters’ rules, machinist scales, draftsman scales, and the like. Such apparatus, if they 

require calibration, should be submitted to state or local weights and measures officials. 

3.2. Standards of Mass. – The primary standard of mass for this country is United States Prototype Kilogram 20, which 

is a platinum-iridium cylinder kept at NIST. We know the value of this mass standard in terms of the International 

Prototype Kilogram, a platinum-iridium standard which is kept at the International Bureau of Weights and Measures. 

In Colonial Times the British standards were considered the primary standards of the United States. Later, the U. S. 

avoirdupois pound was defined in terms of the Troy Pound of the Mint, which is a brass standard kept at the United States 

 

1

 See Federal Register for July 1, 1959. See also next-to-last paragraph of 2.2.5. 

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Appendix B – Units and Systems of Measurement Handbook 44 – 2009 

Mint in Philadelphia. In 1911, the Troy Pound of the Mint was superseded, for coinage purposes, by the Troy Pound of 

the Institute. 

The avoirdupois pound is defined in terms of the kilogram by the relation: 

1 avoirdupois pound = 0.453 592 37 kilogram.2

These changes in definition have not made any appreciable change in the value of the pound. 

The grain is 1

/7000 of the avoirdupois pound and is identical in the avoirdupois, troy, and apothecary systems. The troy 

ounce and the apothecary ounce differ from the avoirdupois ounce but are equal to each other, and equal to 480 grains. 

The avoirdupois ounce is equal to 437.5 grains. 

3.2.1. Mass and Weight. – The mass of a body is a measure of its inertial property or how much matter it contains. 

The weight of a body is a measure of the force exerted on it by gravity or the force needed to support it. Gravity on 

earth gives a body a downward acceleration of about 9.8 m/s2

. (In common parlance, weight is often used as a 

synonym for mass in weights and measures.) The incorrect use of weight in place of mass should be phased out, and 

the term mass used when mass is meant. 

Standards of mass are ordinarily calibrated by comparison to a reference standard of mass. If two objects are 

compared on a balance and give the same balance indication, they have the same “mass” (excluding the effect of air 

buoyancy). The forces of gravity on the two objects are balanced. Even though the value of the acceleration of 

gravity, g, is different from location to location, because the two objects of equal mass in the same location (where 

both masses are acted upon by the same g) will be affected in the same manner and by the same amount by any 

change in the value of g, the two objects will balance each other under any value of g. 

However, on a spring balance the mass of a body is not balanced against the mass of another body. Instead, the 

gravitational force on the body is balanced by the restoring force of a spring. Therefore, if a very sensitive spring 

balance is used, the indicated mass of the body would be found to change if the spring balance and the body were 

moved from one locality to another locality with a different acceleration of gravity. But a spring balance is usually 

used in one locality and is adjusted or calibrated to indicate mass at that locality. 

3.2.2. Effect of Air Buoyancy. – Another point that must be taken into account in the calibration and use of 

standards of mass is the buoyancy or lifting effect of the air. A body immersed in any fluid is buoyed up by a force 

equal to the force of gravity on the displaced fluid. Two bodies of equal mass, if placed one on each pan of an 

equal-arm balance, will balance each other in a vacuum. A comparison in a vacuum against a known mass standard 

gives “true mass.” If compared in air, however, they will not balance each other unless they are of equal volume. If 

of unequal volume, the larger body will displace the greater volume of air and will be buoyed up by a greater force 

than will the smaller body, and the larger body will appear to be of less mass than the smaller body. 

The greater the difference in volume, and the greater the density of the air in which we make the comparison 

weighing, the greater will be the apparent difference in mass. For that reason, in assigning a precise numerical value 

of mass to a standard, it is necessary to base this value on definite values for the air density and the density of the 

mass standard of reference. 

The apparent mass of an object is equal to the mass of just enough reference material of a specified density (at 20 °C) 

that will produce a balance reading equal to that produced by the object if the measurements are done in air with a 

density of 1.2 mg/cm3

 at 20 °C. The original basis for reporting apparent mass is apparent mass versus brass. The 

apparent mass versus a density of 8.0 g/cm3

 is the more recent definition, and is used extensively throughout the 

world. The use of apparent mass versus 8.0 g/cm3

 is encouraged over apparent mass versus brass. The difference in 

these apparent mass systems is insignificant in most commercial weighing applications. 

A full discussion of this topic is given in NIST Monograph 133, Mass and Mass Values, by Paul E. Pontius [for sale 

by the National Technical Information Service, 5285 Port Royal Road, Springfield, VA 22161 (COM 7450309)]. 

 

2

 See Federal Register for July 1, 1959. 

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Handbook 44 – 2009 Appendix B – Units and Systems of Measurement 

3.2.3. Calibrations of Standards of Mass. – Standards of mass regularly used in ordinary trade should be tested by 

state or local weights and measures officials. NIST calibrates mass standards submitted, but it does not manufacture 

or sell them. Information regarding the mass calibration service of NIST and the regulations governing the 

submission of standards of mass to NIST for calibration are contained in NIST Special Publication 250, Calibration 

and Related Measurement Services of NIST, latest edition. 

3.3. Standards of Capacity. – Units of capacity or volume, being derived units, are in this country defined in terms of 

linear units. Laboratory standards have been constructed and are maintained at NIST. These have validity only by 

calibration with reference either directly or indirectly to the linear standards. Similarly, NIST has made and distributed 

standards of capacity to the several states. Other standards of capacity have been verified by calibration for a variety of 

uses in science, technology, and commerce. 

3.3.1. Calibrations of Standards of Capacity. – NIST makes calibrations on capacity or volume standards that are 

in the customary units of trade; that is, the gallon, its multiples, and submultiples, or in metric units. Further, NIST 

calibrates precision-grade volumetric glassware which is normally in metric units. NIST makes calibrations in 

accordance with fee schedules, copies of which may be obtained from NIST. 

3.4. Maintenance and Preservation of Fundamental Standard of Mass. – It is a statutory responsibility of NIST to 

maintain and preserve the national standard of mass at NIST and to realize all the other base units. The U. S. Prototype 

Kilogram maintained at NIST is fully protected by an alarm system. All measurements made with this standard are 

conducted in special air-conditioned laboratories to which the standard is taken a sufficiently long time before the 

observations to ensure that the standard will be in a state of equilibrium under standard conditions when the 

measurements or comparisons are made. Hence, it is not necessary to maintain the standard at standard conditions, but 

care is taken to prevent large changes of temperature. More important is the care to prevent any damage to the standard 

because of careless handling. 

4. Specialized Use of the Terms “Ton” and “Tonnage”

As weighing and measuring are important factors in our everyday lives, it is quite natural that questions arise about the 

use of various units and terms and about the magnitude of quantities involved. For example, the words “ton” and 

“tonnage” are used in widely different senses, and a great deal of confusion has arisen regarding the application of these 

terms. 

The ton is used as a unit of measure in two distinct senses: (1) as a unit of mass, and (2) as a unit of capacity or volume. 

In the first sense, the term has the following meanings: 

(a) The short, or net ton of 2000 pounds. 

(b) The long, gross, or shipper’s ton of 2240 pounds. 

(c) The metric ton of 1000 kilograms, or 2204.6 pounds. 

In the second sense (capacity), it is usually restricted to uses relating to ships and has the following meaning: 

(a) The register ton of 100 cubic feet. 

(b) The measurement ton of 40 cubic feet. 

(c) The English water ton of 224 British Imperial gallons. 

In the United States and Canada the ton (mass) most commonly used is the short ton. In Great Britain, it is the long ton, 

and in countries using the metric system, it is the metric ton. The register ton and the measurement ton are capacity or 

volume units used in expressing the tonnage of ships. The English water ton is used, chiefly in Great Britain, in statistics 

dealing with petroleum products. 

There have been many other uses of the term ton such as the timber ton of 40 cubic feet and the wheat ton of 20 bushels, 

but their uses have been local and the meanings have not been consistent from one place to another. 

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Appendix B – Units and Systems of Measurement Handbook 44 – 2009 

Properly, the word “tonnage” is used as a noun only in respect to the capacity or volume and dimensions of ships, and to 

the amount of the ship’s cargo. There are two distinct kinds of tonnage; namely, vessel tonnage and cargo tonnage and 

each of these is used in various meanings. The several kinds of vessel tonnage are as follows: 

Gross tonnage, or gross register tonnage, is the total cubical capacity or volume of a ship expressed in register tons of 

100 cubic feet, or 2.83 cubic meters, less such space as hatchways, bakeries, galleys, etc., as are exempted from 

measurement by different governments. There is some lack of uniformity in the gross tonnages as given by different 

nations due to lack of agreement on the spaces that are to be exempted. Official merchant marine statistics of most 

countries are published in terms of the gross register tonnage. Press references to ship tonnage are usually to the gross 

tonnage. 

The net tonnage, or net register tonnage, is the gross tonnage less the different spaces specified by maritime nations in 

their measurement rules and laws. The spaces deducted are those totally unavailable for carrying cargo, such as the 

engine room, coal bunkers, crew quarters, chart and instrument room, etc. The net tonnage is used in computing how 

much cargo that can be loaded on a ship. It is used as the basis for wharfage and other similar charges. 

The register under-deck tonnage is the cubical capacity of a ship under her tonnage deck expressed in register tons. In a 

vessel having more than one deck, the tonnage deck is the second from the keel. 

There are several variations of displacement tonnage. 

The dead weight tonnage is the difference between the “loaded” and “light” displacement tonnages of a vessel. It is 

expressed in terms of the long ton of 2240 pounds, or the metric ton of 2204.6 pounds, and is the weight of fuel, 

passengers, and cargo that a vessel can carry when loaded to its maximum draft. 

The second variety of tonnage, cargo tonnage, refers to the weight of the particular items making up the cargo. In 

overseas traffic it is usually expressed in long tons of 2240 pounds or metric tons of 2204.6 pounds. The short ton is only 

occasionally used. Therefore, the cargo tonnage is very distinct from vessel tonnage. 

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