Metric system is a group of units used to make measurements in science and engineering, in commerce, and in everyday life. The original metric system was adopted by France in 1795. The modern system, called the International System of Units, is a modified version of that system. People commonly refer to the modern system by the initials SI, which stand for its name in French—Système International d’Unités. Representatives from throughout the world meet every four years at a General Conference on Weights and Measures (CGPM) to deal with matters concerning SI.
SI is the main system of measurement in all the technologically advanced nations of the world except the United States. Scientists and many engineers in the United States use SI. For most commercial and everyday measurements, however, Americans use the inch-pound system. Inch-pound units entered what is now the United States in the 1600’s, when the English began to settle along the Atlantic coast of North America.
Kinds of metric units
SI is a comprehensive system of measurement, one that has units for all measurable properties of physical objects and processes. An example of a measurable property of an object is the length of a city block: A block might be 200 meters long. The velocity (speed) of a moving object is an example of a measurable property of a process: A baseball pitched by a major-league professional might travel at a velocity of 40 meters per second. Scientists refer to measurable properties as physical quantities, or simply quantities.
SI units are related to one another in a simple, logical way that makes the metric system easy to use. Seven base units serve as the “building blocks” from which all the other units are constructed. For example, the meter is the base unit used to measure length, and the second is the base unit to measure time. Derived units are built up from base units. Meter per second is an example of a derived unit. Base units and derived units together are known as SI units.
Multiples and submultiples, in turn, are built from SI units. A multiple is larger than the SI unit from which it is built. For example, the kilometer, a multiple of the meter, is 1,000 times as large as the meter. A submultiple is smaller than its SI unit. The millimeter, a submultiple of the meter, is 1/1,000 the size of the meter.
Every unit in SI has a symbol. For example, the symbol for meter is m. The SI symbols are not ordinary abbreviations. They are not written with a period, except at the end of a sentence; they are the same in singular and plural; and they are the same in all languages.
Advantages of the metric system
Four features help make SI easy to use and give it an advantage over the inch-pound system: (1) Only one “family” of units—one SI unit and its multiples and submultiples—is needed for all measurements of any one quantity, (2) SI uses the decimal system for building multiples and submultiples, (3) SI uses standard prefixes for naming multiples and submultiples, and (4) units used to measure different quantities are related in a simple way. The inch-pound system has none of these features.
Use of one “family” of units per quantity.
An example of the first feature is the use of the “meter family” to measure length. People use the meter to measure large distances, such as the lengths of athletic fields and the heights of mountains. To measure the distance between cities, people use the kilometer. The centimeter, which is 1/100 the size of the meter, is used to measure such quantities as the length of a pencil and the height of a person. The millimeter is useful for measuring such small objects as coins and computer chips.
Use of decimal multiples.
An SI unit is related to its multiples and submultiples by factors of 10. For example, the kilometer differs from the meter by three factors of 10: It is 10 X 10 X 10 = 1,000 times as long as the meter. The centimeter differs from the meter by two factors of 10: A centimeter is 1/10 X 1/10 = 1/100 of a meter.
This use of decimal multiples makes it easy to convert from one unit to another unit in the same “family” of units. For example, to convert meters to kilometers, you would divide by 1,000, merely shifting the decimal point three places to the left. Thus, 4,356 meters would convert to 4.356 kilometers.
Use of standard prefixes.
The third helpful feature of SI appears in the use of the prefixes kilo, centi, and milli in our examples. These are standard SI prefixes. Attaching them to any SI unit multiplies the value of that unit by 1,000, 1/100, and 1/1,000, respectively. For example, attaching kilo to the watt, the SI unit for power, creates the kilowatt, which equals 1,000 watts. Attaching milli creates the milliwatt, equal to 1/1,000 watt.
Use of related units.
The simple relationships between the “families” of units for length, area, and volume illustrate the fourth helpful feature. The meter is the base unit for all three families. The “meter family” is for measuring length. To measure area, you can use the square meter, square kilometer, square millimeter, and other members of the “square meter family.” The cubic meter, cubic kilometer, cubic millimeter, and other members of the “cubic meter family” are for measuring volume.
The inch-pound system
has no decimally related multiples and submultiples. In most cases, that system offers a choice of different-sized units for measuring a single quantity. To measure length, for example, you can choose, in order of increasing size, the inch, the foot, the yard, or the mile. But the factors relating these units to one another are difficult to use in making conversions. There are 12 inches in a foot, 3 feet or 36 inches in a yard, and 1,760 yards or 5,280 feet in a mile. Furthermore, the names of the units provide no clue to their numerical relationships.
Structure of the metric system
SI extends the systematic approach of the early metric system. Over the years, the CGPM has chosen certain physical quantities as base quantities. For each base quantity, the CGPM has defined an SI base unit. It has then derived other quantities using multiplication and division, leading to the creation of corresponding SI derived units. The CGPM has given special names to some important derived units.
SI base units are (1) the meter; (2) the kilogram, which is the unit for mass (amount of matter); (3) the second, for time; (4) the ampere, for electric current; (5) the kelvin, for temperature; (6) the candela, << kan DEHL uh >> , for the brightness of light; (7) and the mole, for amount of substance, a term with a special meaning in chemistry.
The remainder of this section discusses the structure of SI as the system is applied in six areas: (1) space and time, (2) mechanics, (3) heat, (4) electricity, (5) light, and (6) chemistry.
Space and time.
Length is the base quantity for space measurement, and the meter is the base unit. The area of a rectangle is its length times its width. So the derived unit of area is the product of the unit of length and the unit of width. This product is meter times meter, or square meter—in algebraic notation, m2. Thus, the area of a floor that measures 3 m X 5 m is 15 m2.
When a prefix is used in an area measurement, the prefix is squared also. Thus, a square centimeter (cm2) is a square that is 1 cm on a side. The area of this square in square meters is 0.01 m X 0.01 m, or 0.0001 m2.
The volume of a rectangular object is the product length times width times height—three length quantities. Thus, the SI derived unit for volume is the cubic meter, m3. The volumes of everyday objects, such as a refrigerator or a gasoline tank, are measured in cubic decimeters. A cubic decimeter (dm3) is equivalent to a cube that is 1 dm on a side, and 1 dm equals 0.1 m. Therefore, the volume of a cubic decimeter is 0.1 m X 0.1 m X 0.1 m, or 0.001 m3.
For the measurement of time, the second (s) is the base unit. Races in a track meet are sometimes won by milliseconds. Calculations in a personal computer are performed in microseconds (millionths of a second).
Because velocity or speed is distance traveled divided by the time required, the derived unit for velocity is meter per second (m/s). A sprinter can achieve a speed of 10 m/s over a short distance.
Acceleration is a change in velocity during a period of time. The SI derived unit for acceleration is therefore the unit of velocity divided by the unit of time—meter per second squared (m/s2).
Frequency measures how often a regularly repeating event occurs over time. Frequency is measured in cycles (repetitions) per second, a unit that has been given the special name hertz (Hz). Many computers run at 500 megahertz or higher, which means that the electronic clock that is timing the computer’s operations is “ticking” 500 million times a second.
Mechanics
deals with such questions as why moving objects move as they do, and how buildings and bridges support weight. These kinds of questions involve mass and force.
Mass is an SI base quantity, and its unit is the kilogram (kg). One kilogram is almost exactly the mass of 1 liter of water. In everyday language, mass is usually called weight, as in the statement, “My weight is 80 kilograms.” Most adults weigh between 50 and 100 kg. Groceries are measured in grams and kilograms, while most medicines are measured in milligrams.
The kilogram is the only base unit whose name includes a standard prefix. The CGPM had the option of choosing the gram, equal to 1/1000 kilogram, as a base unit. It chose the kilogram instead because the gram is such a small unit—a dollar bill has a mass of about 1 gram. When units larger or smaller than the kilogram are needed, one must attach prefixes to gram.
Force is a push or a pull. A force tends to cause a body to move, or a body that is in motion to change its motion. A force is equal to the product of the mass that it accelerates and the acceleration. The derived unit for force is therefore the unit of mass times the unit of acceleration, kilogram meter per second squared. This SI unit has the special name newton (N). To feel a newton, lift a small apple or a lemon. The force of gravity on the fruit will be roughly 1 newton.
Pressure is force per unit area. The SI derived unit is the newton per square meter, which has the special name pascal (Pa). Atmospheric pressure at sea level is about 100 kilopascals.
Work occurs when a force acts through a distance, and it is the product of force and distance. The SI derived unit for work is the newton meter, given the special name joule (J). Energy, which is the capacity for doing work, is measured in the same unit.
A closely related quantity is power, which is energy divided by time. The SI derived unit is joule per second, which has the special name watt (W). As a unit of electric power, the watt is one of the most familiar SI units. It is also the proper unit to use in expressing mechanical power. The horsepower, an inch-pound unit of mechanical power, equals about 750 watts.
Heat
is a form of energy, and so it is measured in joules. Temperature is the base quantity needed to study heat, and its SI base unit is the kelvin (K). A more familiar name given to the same unit is degree Celsius (°C). The Celsius scale is used for everyday measurements in the metric system.
Although the kelvin and the degree Celsius are the same size, the scales in which they are used have different zero points. Zero kelvin is the is the coldest possible temperature, a point that is called absolute zero. The zero point of the Celsius scale is the freezing point of water. The size of the temperature unit is such that 0 K = –273.15 °C, and 0 °C = 273.15 K. At sea level, water boils at a temperature of 100 °C. Normal body temperature for human beings is about 37 °C.
Electricity.
Electric current, motion of electric charge, is the base quantity for electricity. The corresponding base unit is the ampere (A). When 1 ampere flows for 1 second, the amount of charge moved is equal to 1 ampere second. The SI derived unit ampere second has the special name coulomb (C). The electromotive force that is required to move charges is known as voltage, and it is measured in a derived unit called the volt (V).
The ampere, the coulomb, and the volt have direct relationships to the SI units for work and power. If 1 coulomb of charge moves through a voltage difference of 1 volt, 1 joule of work is done on the charge. If a current of 1 ampere is flowing, then work is occurring at a rate of 1 joule per second, which is a power of 1 watt.
Electric power is the product of voltage and current. In homes in the United States, the voltage at ordinary electrical outlets is about 110 volts. For this voltage, the power equation “volts times amperes equals watts” shows that the current in a 100-watt light bulb will be a little less than 1 ampere.
Light.
The base quantity for the measurement of illumination is luminous intensity, the brightness of light. The corresponding SI base unit is the candela (cd). The candela is defined in terms of the rate at which light energy flows from the source of the light. An ordinary candle has an intensity of roughly 1 candela.
The derived quantity luminous flux is the rate at which light energy falls on a surface. The derived unit for this quantity is the lumen (lm). A surface that is 1 square meter in area, placed 1 meter away from a source of 1 candela, receives 1 lumen. Light bulbs are rated in terms of the number of lumens they produce.
Chemistry
is the study of the interactions of the atoms and molecules that make up material substances. Chemists use a base quantity called amount of substance that enables them to relate the number of individual atoms or molecules in one system to that in another. In this case, the word system refers to a set of elementary objects that are to be studied in an experiment or used in a reaction. The objects may be atoms, molecules, electrons, or other subatomic particles.
The SI unit for amount of substance is the mole (mol), and it is defined so that 1 mole of the most common form of carbon atoms weighs exactly 12 grams. One mole of any other substance will contain the same number of elementary objects as 1 mole of such carbon atoms. For example, 1 mole of atoms of carbon (chemical symbol C) combines with 1 mole of oxygen molecules (O2) to form 1 mole of carbon dioxide (CO2).
Chemical engineers determine the number of moles in a system by measuring its mass—that is, by weighing it—because it is not practical for them to count atoms or molecules. The masses of different atoms and molecules have been measured, and they may be compared by using a number called the relative atomic mass or the relative molecular mass. By international agreement, the relative atomic mass of the most common form of carbon is exactly 12, so 1 mole of it weighs 12 grams. The relative molecular mass of O2 is very close to 32, and therefore 1 mole of O2 would weigh very close to 32 grams.
Non-SI metric units.
People still use many old metric units that are not a part of SI. The international authorities that set standards for the use of SI consider only a few such units to be acceptable for general use. These units include the liter, the metric ton, and the hectare.
The liter is a unit of volume equal to a cubic decimeter. Its symbol is L or l. Metric authorities in the United States prefer the use of the capital “L” because the lower-case letter closely resembles the number “1” in many kinds of type.
According to international agreement, most other non-SI metric units should be avoided. These include the calorie for energy (use joules), the millimeter of mercury for pressure (use pascals), and the kilogram-force or the kilogram used as a unit of force (use newtons). Also to be avoided are derived units from older metric systems that use the centimeter, gram, and second as base units. Among these derived units are a force unit called the dyne and a unit of acceleration known as the gal.
Selection of SI prefixes.
Although any SI prefix may be attached to any SI unit, the prefixes centi, deci, deka, and hecto find limited use. An important exception is the centi in centimeter, which is a useful unit for many purposes. The deciliter, dekaliter, and hectoliter are all of practical size and are used in household and commercial measurements. The decimeter, dekameter, and hectometer appear in some special places, such as maps and nautical charts. The square decimeter, square dekameter, and square hectometer are useful for measuring areas; the cubic decimeter, cubic dekameter, and cubic hectometer, for measuring volumes.
History
During the 1600’s and 1700’s, many people recognized the need for a measurement system that would be widely agreed upon and easy to use. At that time, different countries used their own systems, and there were many differences in units of measure within a single nation. Merchants found the lack of a universal system of measure inconvenient, especially as their markets expanded. A cloth merchant, for example, might deal with suppliers and customers who used several units of length measurement. The pace of scientific discovery was increasing as well. Scientists needed a universal system to help them share theories and experimental data with colleagues in other countries.
The creation of the metric system.
In 1790, the National Assembly, the parliament of France, took action. The Assembly asked the French Academy of Sciences to work out a system of units suitable for adoption by the entire world. The next year, the Academy submitted a proposal for such a system. The proposed system would be based on a single unit of length measurement. This length unit would be based in nature. It would be one ten-millionth of the distance from the North Pole to the equator.
The designers of the system defined the fundamental unit of mass in terms of the length unit, which they named the meter. The new unit of mass, which they named the gram, would be equal to the mass of 1 cubic centimeter of water at a specified temperature. It followed from the definition that a liter of water, which contains 1,000 cubic centimeters, would weigh 1 kilogram. This meant that anybody, anywhere, who had a meter measuring stick could also develop a practical standard for weighing objects. Thus, the early metric system used one unit, the meter, to tie together in a simple, systematic way the units for length, area, volume or capacity, and mass.
France adopted the metric system in 1795. A survey carried out in France established the length of the meter. Physical models of the meter were needed for comparison with the measuring sticks that would used to make actual measurements, and so several bars of platinum were cast. One was chosen as the standard meter and was stored in Paris.
Evolution of the metric system.
Formal international standardization of the metric system began in 1875, when 17 nations, including the United States, signed a document called the Treaty of the Meter. This document established an international framework for maintaining the metric system.
At that time, the metric system had no units for electricity or magnetism. But the British Association for the Advancement of Science (BAAS) had proposed such units a year earlier. These units were derived from the CGS system, which has the centimeter, gram, and second as base units. In the 1880’s, the BAAS and an organization called the International Electrical Congress approved a set of practical units for electricity and magnetism. These included the ampere and the volt.
In 1889, the CGPM selected a physical standard for the kilogram. The kilogram became the mass of a particular weight, made of platinum and iridium, known as the international prototype kilogram. All standard weights in the world, including those for pounds and ounces, were related to this standard. At the same time, the CGPM selected one standard bar, also made of platinum and iridium, to define the meter.
In 1939, the International Electrotechnical Commission, successor to the International Electrical Congress, recommended that the CGPM bring electrical units into its metric system. The resulting system would have four base units—the meter, the kilogram, the second, and the ampere. In 1954, the CGPM approved this recommendation. The CGPM also adopted two additional base units—the candela and the degree Kelvin ( °K), which became known as simply the kelvin in 1967.
The CGPM named the “official” metric system the International System of Units in 1960. Also in 1960, the CGPM defined the meter in terms of the wavelength of light. The CGPM added the mole as a base unit in 1971, bringing the number of base units to the present seven. In 2018, the CGPM voted to redefine the kilogram based on a universal fundamental value known as Planck’s constant.
Acceptance of the metric system.
Although France officially adopted the metric system in 1795, the French government did not require its people to use the system until 1840. Other nations then began to adopt it. By 1850, the metric system was also the official system of measurement in Greece, the Netherlands, Spain, and parts of Italy. By 1900, most of the commercially advanced countries of the world had adopted it. The main holdouts were the United States and nations of the British Empire.
But by the early 1960’s, the United Kingdom had drawn close to mainland Europe commercially. In 1965, the United Kingdom began a changeover to the metric system. New Zealand began to convert in 1969, Australia in 1970, and Canada in 1975.
In the United States, pharmacists had begun to use metric units to fill prescriptions in the 1950’s. The Department of Defense and the National Aeronautics and Space Administration (NASA) began to use metric measurements. Major U.S. makers of automobiles and farm machinery changed to the metric system in the 1970’s.
In 1975, the U.S. Congress passed a law establishing a policy of voluntary conversion to the metric system. Congress amended this law in 1988, naming the metric system the preferred system of weights and measures for U.S. trade and commerce. The amendment also called for federal agencies to use the metric system for purchases, grants, and other business-related activities.
By the early 2000’s, almost all scientific work and an increasing amount of engineering work in the United States was done using metric units. Contractors designed and built most major highways and many federal buildings in metric units. Major industrial firms had converted their U.S. facilities to metric. Packaged groceries were labeled in metric units as well as inch-pound units. Many beverages and other consumer products were sold in metric-sized containers.
