## Units of Measurement: Fundamental and Derived Units, Systems of Measurement

written by: Haresh Khemani • edited by: Lamar Stonecypher • updated: 2/23/2010

This article describe fundamental or basic and derived units of measurement and the desired requirement of these units. It also describes systems of units like CGS, MKS, FPS and SI.

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### Standard Units of Measurment

Units of measurement are vital parts of any physical quantity. Just as the person is known by his or her name, the physical quantities are known by the units of measurement. Let us suppose that the length of the iron rod is 5 meters. This means that 1 meter is the standard used for the measurement of the length and that measured length is 5 times greater than the length of 1 meter. The unit of measurement is defined as the standard used for the measurement of the physical quantity.

In the above example of the length of the rod, meter is the unit of measurement of length, while the number 5 which gives the amount of the length is called as magnitude of length. The magnitude gives the actual value of the measured quantity. Thus measurement of any physical quantity involves two parameters: unit of measurement and the magnitude. The unit of measurement of the physical quantity remains same, while its magnitude keeps on changing depending on the actual amount of the physical quantity.

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### Qualities of the Units of Measurement

The units of measurement should possess following qualities:

1) The unit of measurement of the physical quantity should be invariable. This means that the magnitude of the particular unit of measurement should remain the same irrespective of the time or place. In the above example, no matter in which part of the world and at what time the length of the rod is measured, it should remain the same.

2) The unit of measurement should be easily reproducible. This means the unit of measurement should be easy to copy and it is always readily available.

3) The units of measurement should be accepted universally in all the parts of the world and all the communities. There should not be any objections or the partiality towards the units of measurement. Though in the world there may be differences among the people due to their religious backgrounds, as far the as the acceptance of the units of measurement is concerned, all the people of the world are united.

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### Fundamental or Basic Units of Measurement

In our universe there are large numbers of human beings and majority of them have different names (though many have common names). Similarly, there are large numbers of the physical quantities, and each of them should have the units of measurement. However, it is not necessary to define separate unit for each and every physical quantity. Out of so many physical quantities, there are only seven that do not depend on any other physical quantity for their measurement. These are called as the fundamental quantities.

The seven fundamental quantities are: length, mass, time, temperature, electric current, luminous intensity, and the amount of substance. Since these are totally independent quantities, it is necessary to define the units of measurement for these units only. The units of measurement defined for the fundamental physical quantities are called as the fundamental or the basic units of measurement.

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There are four categories of systems of units: CGS (centimeter, gram, second) system, MKS (meter, kilogram, second) system, FPS (foot, pound, second) and SI systems of units of measurement. Other quantities are derived from the fundamental quantities, hence they are called as the derived physical quantities and the units of measurement of these quantities are called as the derived units.
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### Derived Units of Measurement

Apart from the seven fundamental quantities, all the other physical quantities depend on the fundamental quantities for their measurement. These quantities are derived from the fundamental quantities, hence they are called as the derived physical quantities and the units of measurement of these quantities are called as the derived units.

In our above example, the length of the rod is the fundamental physical quantity. The physical quantity, "length," does not depend on any other quantity. Now let is consider the example of the speed of the car, which is let us say 100 miles per hour. In this case the physical quantity speed depends on the miles (length) and hour (time). Thus speed is the unit derived from fundamental quantities length and time and its units of measurement is derived from the units of measurement of length and time.

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### Systems of Units of Measurement

Though the fundamental units are independent of all other units, there are different fundamental units accepted in different countries or the regions of the world. The group of fundamental units followed in different regions along with the derived units forms the systems of units. There are four categories of systems of units as described below:

1) The CGS (centimeter, gram, second) system: In the CGS system of measurement length is measured in centimeters, the mass of the body or substance is measured in grams and time is measured in seconds. Thus centimeter, gram and seconds are the fundamental units of measurement in the CGS system.

2) MKS (meter, kilogram, second) system: In MKS system or metric system, the unit of measurement for length is meter, for mass it is kilogram and for time it is seconds. Thus in this system meter, kilogram and seconds are fundamental units of measurement. This system was used in France and number of other European countries.

3) FPS (foot, pound, second) system: In this system the unit of measurement for length is foot, for mass it is pound and for time it is second. This system is used commonly in Britain and the countries that were under its rule.

4) SI system: The SI system or the International system of standards has now replaced all the systems of measurement. It is the improved metric system of measurement. In SI system length is measured in meter, mass in kilogram and time in seconds.

In the above systems we saw that different fundamental units are used in different systems. Since the derived units depend on the fundamental units, they also change in different systems of measurement. Let s consider the example of the speed or velocity of the body. In MKS system its unit of measurement is meter/second, in CGS system it is centimeter/second, in FPS system it is foot/second and in SI system it is meter/second.