The International System of Units (SI): 7 Base Units, Derived Units & More

You have landed on the right page to learn about the International System of Units. We come across a variety of measurements in our daily lives. We buy vegetables in kilogrammes, milk in litres, fabric in metres etc., However, in scientific studies, we come across the measurement of a variety of other values in addition to mass, volume, and lengths, such as temperature, pressure, concentration, force, work, density, and so on.

In this article, we will study the International System of Units (SI), the meaning of SI units, base units, International System of Units, derived units, Prefixes of SI units, etc. Continue reading to know more.

What is the International System of Units?

A unit is defined as the standard of reference chosen to measure any physical quantity. Since early times, different types of units of measurement have been very popular in different parts of the world. 

For example, sers, pounds for mass, and miles, yards, furlongs for distance. However, because the conversion factors are not regular, these units are rather inconvenient. For example,
\({\rm{1}}\,{\mkern 1mu} {\rm{mile}}{\mkern 1mu} \,{\rm{ = }}{\mkern 1mu} \,{\rm{1760}}{\mkern 1mu} \,{\rm{yards}},{\mkern 1mu} \,{\rm{1}}{\mkern 1mu} \,{\rm{yard}}\,{\mkern 1mu} {\rm{ = }}\,{\mkern 1mu} {\rm{3}}\,{\mkern 1mu} {\rm{feet}},{\mkern 1mu} \,{\rm{1}}{\mkern 1mu} {\rm{foot}}{\mkern 1mu} \,{\rm{ = }}\,{\mkern 1mu} {\rm{12}}{\mkern 1mu} \,{\rm{inches}}\)

To overcome this problem, the metric system was introduced by the French Academy of science in \(1791.\) In this method, different units of a physical quantity are related to each other as multiples of powers of \(10.\) For example, \({\rm{1}}\,{\rm{km}}\,{\rm{ = }}\,{\rm{1}}{{\rm{0}}^{\rm{3}}}\,{\rm{m,}}\,{\rm{1}}\,{\rm{cm}}\,{\rm{ = }}\,{\rm{1}}{{\rm{0}}^{\rm{3}}}\,{\rm{m,}}\) etc.

The General Conference of Weights and Measures in October \(1960\) in France revised the metric system that had been proposed previously. The International System of Units, or SI units, is the revised system of units that has gained international acceptance (for System International in French).

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Base SI Units 

The International System of Units (SI) has 7 base units, i.e., metre, kilogram, second, kelvin, ampere, candela, and mole. These base units pertain to seven fundamental scientific quantities, i.e., length, mass, time, temperature, electric current, luminous intensity, and amount of substance, respectively. From these base units, all other units can be derived.

Example:  Velocity is defined as the distance travelled in unit time. Its derived unit is \({\rm{m}}{{\rm{s}}^{ – 1}}.\)

\({\rm{Velocity}}\,{\mkern 1mu} = \,{\mkern 1mu} \frac{{{\rm{Distance}}}}{{{\rm{Time}}}}\,{\mkern 1mu} = {\mkern 1mu} \,\frac{{{\rm{metre}}}}{{{\rm{second}}}}\, = \,\frac{{\rm{m}}}{{\rm{s}}}\, = \,{\rm{m}}{{\rm{s}}^{ – 1}}\)

International System of Units: \({\rm{m}},{\mkern 1mu} {\rm{kg}},{\mkern 1mu} {\rm{s}},{\rm{A}},{\mkern 1mu} {\rm{K}},{\mkern 1mu} {\rm{Cd}},{\rm{mol}}\)

Metre

Metre is the SI unit of length. It is represented as ‘\({\rm{m}}\)’. Length is defined as the distance of the path travelled by light in a vacuum during a time interval of \(\frac{1}{{299,792,458}}\) second. But the metre was originally defined as the length between two marks on a Pt-Ir bar kept at a temperature of \(0\,^\circ {\rm{C}}\left( {273\,{\rm{K}}} \right).\)

Kilogram

Kilogram is the SI unit of mass. It is represented as ‘\({\rm{kg}}\)’ It is defined as the mass of a platinum-iridium (Pt-Ir) cylinder that is stored in an air-tight jar at the International Bureau of Weights and Measures in France. 

Second

Second is the SI unit of time. It is represented as ‘s’. The duration of \({\rm{9192631770}}\) periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom is called the second.

Kelvin

The SI unit of temperature is kelvin. It is represented as ‘\({\rm{K}}\)’ It is defined as the unit of thermodynamic temperature and is equal to \(\frac{1}{{273.16}}\) of the thermodynamic temperature of the triple point of water.

Temperature in degree kelvin \(\left( {\rm{K}} \right){\rm{ = }}{\mkern 1mu} ^\circ {\rm{C}}\,{\rm{ + }}\,{\mkern 1mu} {\rm{273}}.{\rm{15}}\)

Temperature is also measured in degrees Fahrenheit \({(^ \circ }{\rm{F)}}\) It is related to degree Celsius \({(^ \circ }{\rm{C)}}\)

\(^\circ {\rm{F}}\,{\rm{ = }}\,{\mkern 1mu} \frac{9}{5}\,\left( {^\circ {\rm{C}}} \right){\rm{ + 32}}\)

Ampere

The SI unit of electric current is the ampere. It is represented as ‘\({\rm{A}}\)’. The ampere is that constant current which is maintained in two straight parallel conductors of the infinite length of negligible circular cross-section and placed 1 metre apart in vacuum, would produce between these conductors a force equal to \(2\, \times \,10{\,^{ – 7}}\) newton per metre of length.

Mole

A mole is the SI unit for measuring the quantity of a substance. The symbol for it is ‘mol.’ A mole is the amount of substance that includes the same number of elementary entities as there are atoms in \(0.012\) kilos of carbon-\(12.\) Atoms, molecules, ions, electrons, and other particles are examples of elementary entities.

Candela

The SI unit of luminous intensity is candela. It is represented as ‘\({\rm{cd}}\)’. The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency \(540{\mkern 1mu} \,{\mkern 1mu} \times \,{\mkern 1mu} {10^{12}}\) hertz and that has a radiant intensity in that direction of \(\frac{1}{{683}}\) watt per steradian is called candela.

Derived Units

Derived units are those that are derived from the seven basic units. The following are some of the most regularly used derived units.

1. Area: The area of an object is obtained by multiplying its length and breadth, i.e., area is the product of its two lengths.
   \({\rm{Area}}\,{\rm{ = }}\,{\rm{Length}}\,{\rm{ \times }}\,{\rm{Length}}\,{\rm{ = }}\,{\rm{m}}\,{\rm{ \times }}\,{\rm{m}}\,{\rm{ = }}\,{{\rm{m}}^{\rm{2}}}{\rm{.}}\)
   Hence, the derived unit of area is \({{\rm{m}}^2}\,\)
2. Volume: The derived unit of volume is \({{\rm{m}}^3}\,\) It is obtained as follows:
   \({\rm{Volume}}\, = \,{\rm{Length}}\, \times \,{\rm{Breadth}}\, \times \,{\rm{Height}}\)
   \({\rm{Volume}}\, = \,{\rm{Lengt}}{{\rm{h}}^3}\, = \,{{\rm{m}}^3}\)
3. Velocity: The distance travelled in unit time is called velocity. Its derived unit is \({\rm{m}}{{\rm{s}}^{ – 1}}.\)
   \({\rm{Velocity}}\, = \,\frac{{{\rm{Distance}}\,{\rm{travelled}}}}{{{\rm{Time}}}} = \,\frac{{\rm{m}}}{{\rm{s}}} = {\rm{m}}{{\rm{s}}^{ – 1}}.\)
4. Acceleration: The rate of change of velocity with respect to time is called acceleration. The derived unit of acceleration is \({\rm{m}}{{\rm{s}}^{ – 2}}.\)
   \({\rm{Acceleration}}\,{\rm{ = }}\,\frac{{{\rm{Velocity}}}}{{{\rm{Time}}}}{\rm{ = }}\frac{{{\rm{m}}{{\rm{s}}^{ – 1}}}}{{\rm{s}}}\,{\rm{ = }}\,{\rm{m}}{{\rm{s}}^{ – 2}}.\)
5. Density: Density is defined as the mass per unit volume. \({\rm{kg}}{{\rm{m}}^{ – 3}}\) is the derived unit of it.
   \({\rm{Density}}\, = \,\frac{{{\rm{Mass}}}}{{{\rm{Volume}}}}\, = \,\frac{{{\rm{kg}}}}{{{{\rm{m}}^3}}}\, = \,{\rm{kg}}{{\rm{m}}^{ – 3}}.\)
6. Force: The product of mass and acceleration is called force. The derived unit of force is \({\rm{kgm}}{{\rm{s}}^{ – 2}}\)
   \({\rm{Force}}\, = \,{\rm{Mass}}\, \times \,{\rm{Acceleration}}\, = \,{\rm{kg}}\, \times \,{\rm{m}}{{\rm{s}}^{ – 2}} = {\rm{kgm}}{{\rm{s}}^{ – 2}}\)
   In the SI system, \({\rm{kgm}}{{\rm{s}}^{ – 2}}\) is referred to as Newton. It is represented as N. Thus,
   \({\rm{1}}\,{\rm{N}}\,{\rm{ = }}\,{\rm{kgm}}{{\rm{s}}^{ – 2}}\)
7. Pressure: The force per unit area is called pressure. The derived unit of pressure is \({\rm{kg}}{{\rm{m}}^{ – 1}}{{\rm{s}}^{ – 2}}.\)
   \({\rm{Pressure}}\,{\rm{ = }}\,\frac{{{\rm{Force}}}}{{{\rm{Area}}}}{\rm{ = }}\,\frac{{{\rm{kg}}\,{\rm{m}}{{\rm{s}}^{ – 1}}}}{{{{\rm{m}}^2}}}\,{\rm{ = }}\,{\rm{kg}}{{\rm{m}}^{ – 1}}{{\rm{s}}^{ – 2}}\)
   In the SI system, \(\,{\rm{kg}}{{\rm{m}}^{ – 1}}{{\rm{s}}^{ – 2}}\) is referred to as Pascal. It is represented as ‘\({\rm{P}}\)’
   One pascal is defined as the force of \(1\,{\rm{N}}\) applied to an area of \(1\,{{\rm{m}}^2}.\)

Some commonly used physical quantities and their derived units are as follows:

The Prefixes of SI Unit System

In order to write very large and very small quantities compactly, we use certain prefixes in the International System of Units. The commonly used prefixes, their symbol and  value expressed in terms of the power of \(10\) are given below.

For example, \(0.000004\) s can be expressed as \(4 \times 10^{-6} \mathrm{~s}\) or \(4{\rm{\mu s}}.\) Similarly, a distance of \(142000\) m can be represented as \(1.42 \times 10^{5} \mathrm{~m}\) or \(142 \mathrm{~km}.\)

Summary 

In the article, The International System of Units (SI) you have understood the meaning of SI units; what are seven base units, Their symbol, definition, etc. Using the SI system’s seven base units and prefixes, you can derive units for a variety of physical quantities. This page is extremely useful for measuring and converting all of the physical quantities needed in science.

FAQS

Q.1. What is the International System of Units called?
Ans: The International System of Units is called the metric system. It has seven base units, namely metre, kilogram, second, kelvin, ampere, candela, and mole.

Q.2. Where is the International System of Units used?
Ans: The International System of Units is used to measure seven basic physical qualities like length, mass, time, temperature, electric current, luminous intensity, and amount of substance and derived units like work, pressure, frequency, etc.

Q.3. What is the International System of Units, and why was it created?
Ans: The International System of Unit is a metric system of measurement to measure different physical quantities. 
The International System of Unit was created to remove  the ambiguity in the
measurement and to measure physical quantities in a uniform manner throughout the world.

Q.4. What is the principle of the International System of Units?
Ans: The principle of the International System of Units is a uniform measurement of all physical quantities throughout the world.

Q.5. What is the SI unit of mass?
Ans: The SI unit of the mass is the kilogram \(\left( {{\rm{kg}}} \right).\)

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