Handbook 44 – 2020 Appendix B – Units and Systems of Measurement

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Table of Contents

Page

Appendix B. Units and Systems of Measurement Their Origin, Development, and 

Present Status...................................................................................................B-3

1. Introduction ..................................................................................................................................................B-3

2. Units and Systems of Measurement ............................................................................................................B-3

2.1. Origin and Early History of Units and Standards. ..............................................................................B-3

2.1.1. General Survey of Early History of Measurement Systems. ................................................B-3

2.1.2. Origin and Development of Some Common Customary Units. ...........................................B-4

2.2. The Metric System..............................................................................................................................B-5

2.2.1. Definition, Origin, and Development. ..................................................................................B-5

2.2.2. International System of Units...............................................................................................B-6

2.2.3. Units and Standards of the Metric System. ..........................................................................B-6

2.2.4. International Bureau of Weights and Measures....................................................................B-7

2.2.5. Status of the Metric System in the United States..................................................................B-7

2.3. British and United States Systems of Measurement. ..........................................................................B-8

2.4. Subdivision of Units. ..........................................................................................................................B-9

2.5. Arithmetical Systems of Numbers....................................................................................................B-10

3. Standards of Length, Mass, and Capacity or Volume.............................................................................B-10

3.1. Standards of Length..........................................................................................................................B-10

3.1.1. Calibration of Length Standards.........................................................................................B-10

3.2. Standards of Mass.............................................................................................................................B-10

3.2.1. Mass and Weight. ...............................................................................................................B-11

3.2.2. Effect of Air Buoyancy. .....................................................................................................B-11

3.2.3. Calibrations of Standards of Mass......................................................................................B-11

3.3. Standards of Capacity. ......................................................................................................................B-12

3.3.1. Calibrations of Standards of Capacity. ...............................................................................B-12

3.4. Maintenance and Preservation of Fundamental Standard of Mass. ..................................................B-12

4. Specialized Use of the Terms “Ton” and “Tonnage” ..............................................................................B-12
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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 humans. Primitive societies needed rudimentary measures for many tasks: 

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

Humans 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, 
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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.

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 
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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 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 units centimeter, gram, and second (cgs) for the quantities 

of length, mass, and time. 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 uses the historical base 

units of the meter, kilogram and second as well as additional base units for the quantities thermodynamic 

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.
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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 U.S. customary 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 CGPM, in 1948, 

asked the CIPM 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 CGPM 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 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 CGPM 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. In 1971, the 14th CGPM adopted 

the mole for the quantity of substance as the seventh base unit. The SI metric system is now either obligatory 

or permissible throughout the world.

In 2018, the 26th CGPM approved the most significant change to the SI since its establishment in 1960, which 

is documented in NIST Special Publication 330 (2019). SP 330 itself is based on the definitive 

international reference known as the BIPM SI Brochure (available at https://www.bipm.org/en/

publications/si-brochure/). The SI is now established in terms of seven defining constants, some of which 

are fundamental constants of nature such as the Planck constant and the speed of light in a vacuum. The 

seven SI base units can be derived from the defining constants. 

The definitions for the SI no longer make reference to any artifact standard, material property, or measurement 

description. These changes enable the realization of all units with an accuracy that is ultimately limited only 

by the quantum structure of nature and our technical abilities, but not by the definitions themselves. 

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

/299792458 of a second. With the decision of the 26th CGPM in 2018, 

the wording of the meter definition was revised to include the fixed numerical value of the speed of light and 

the definition of the second in terms of the hyperfine transition frequency of the cesium 133 atom.

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. After the International Metric Convention in 1875,in

1889 the definition of the kilogram was simply the mass of the International Prototype Kilogram (IPK), an
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artifact made of platinum-iridium (it took from 1875 until 1889 to fabricate the IPK). Each country that 

subscribed to the International Metric Convention was assigned one or more copies of the international 

standard, known as National Prototype Kilogram. That IPK artifact was the definition of the kilogram from 

1889 until the decision of the 26th CGPM in 2018 noted earlier that redefines the SI. The fundamental revision 

to the SI now defines the kilogram from the fixed value of the Planck constant, along with definitions of the 

meter and second. The numerical value of the Planck constant is such that at the time of its adoption, the 

kilogram was equal to the mass of the IPK of 1 kg. Going forward, primary realizations of mass can occur with 

any experimental method that provides the uncertainty desired, such as with a Kibble balance or using the xray crystal density method. 

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. 

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 (2019), The International System of Units (SI) and NIST Special 

Publication 811 (2008), 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 former 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. Following the signing of 

the Convention of the Meter in 1875, the United States acquired national prototype standards for the meter and 

the kilogram Up to 2019, mass measurements in the US were traceable to US national prototype kilograms 

which were in turn traceable to the IKP. From 2019 onward, mass measurements in the US are traceable to 

Planck’s constant through the US national prototype kilograms, 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.
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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 business-related 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, 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 
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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 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 
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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

1 inch = 25.4 millimeters exactly.

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 Mass measurements in the US are traceable to Planck’s constant through the US 

national prototype kilograms.

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 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.

 1 See Federal Register for July 1, 1959. Also see next-to-last paragraph of 2.2.5. 2 See Federal Register for July 1, 1959.
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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)].

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.
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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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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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