Do you ever wonder how tall Mount Everest is? Or how far is San Francisco from New Delhi? Well, Mount Everest is 8,849 meters tall, and San Francisco is 12,349 kilometers away from New Delhi. But to derive a precise answer to such a question, we need to find a way to measure physical quantities.

But before understanding the measurement of physical quantities, let us define physical quantities, fundamental quantities, and derived quantities.

## Physical Quantities

‘Quantities which can be measured either directly or indirectly’ are defined as physical quantities. We can express the laws of physics in terms of physical quantities. Some examples of physical quantities include length, mass, speed, force, current, temperature, etc.

Further, physical quantities are divided into fundamental quantities and derived quantities.

### Fundamental Quantities

The fundamental quantities are defined as physical quantities that don’t depend upon other quantities for measurement. The fundamental quantities are length, mass, time, current, temperature, luminous intensity, and amount of substance.

### Derived quantities

The derived quantities are physical quantities that depend upon fundamental quantities for measurement. E.g. Velocity = distance/time, where distance(length) and time are fundamental quantities.

## How to measure physical quantities?

The measurement of a physical quantity is the process of comparing this measured quantity with a standard amount of physical quantity of the same kind called its unit. In ancient times humans measured physical quantities in various units such as Cubit, Fathom, and Hand-Span.

Presently, the following four systems are in use:-

- Foot-Pound-Second system (FPS)
- Centimeter-Gram-Second system (CGS)
- Meter-Kilogram-Second (MKS)
- International system of units (SI)

### SI System (Système International)

The SI system of measurement was published in 1960 based on the MKS system. It was devised to be used in technical & scientific research to avoid confusion. The SI system is based on seven basic units which can be used to generate an unlimited number of additional units called derived units.

## What Base units?

Units that measure fundamental quantities and are mutually independent are known as Base units. These base or fundamental units can neither be derived from one another nor can be further resolved into simpler units.

There are seven base units as mentioned in the table given below.

**Table 1. Examples of SI base units**

Base Quantity | Base Unit | Symbol |

Length | meter | m |

Mass | kilogram | kg |

Time | second | s |

Electric Current | ampere | A |

Thermodynamic Temperature | kelvin | K |

Amount of Substance | mole | mol |

Luminosity | candela | Cd |

Apart from these 7 base units we also have two supplementary units namely radial and steradian used for plane angle and solid angle respectively.

Know more about What are the units of measurement in the metric system?

## What are Derived Units?

Units that measure derived quantities and are dependent on the base units for their measurement are known as derived units. So, these are the physical units that can be expressed in terms of fundamental or base units.

**Table 2. Examples of SI derived units**

Derived Quantity | Basic Unit Name | Symbol |

Area | Square meter | $[m^2]$ |

Volume | Cubic meter | $[m^3]$ |

Speed | Meter per second | $[m^1s^{-1}]$ |

Acceleration | Meter per second squared | $[m^1s^{-2}]$ |

Wave Number | Reciprocal of meter | $[m^{-1}]$ |

Mass Density | Kilogram per cubic meter | $[Kg^1m^{-3}]$ |

Specific Volume | Cubic meter per kilogram | $[m^3Kg^{-1}]$ |

Force | Kilogram meter per second squared | $[Kg^1m^1s^{-1}]$ |

Pressure | Kilogram per meter second squared | $[Kg^1m^{-1}s^{-2}]$ |

Energy | Kilogram meter squared per second squared | $[Kg^1m^2s^{-2}]$ |

Power | Kilogram meter squared per second cube | $[Kg^1m^2s^{-3}]$ |

## How are base units & derived units related?

From our previous discussion, we know that every derived unit can be expressed in terms of its base units.

For example, one newton is defined as the force that is required to accelerate a mass of 1kg by 1m.s^{-2} in the direction of applied force

Therefore, $1N = 1 kg \times 1 m / s^2$

$1N = m^1Kg^1s^{-2}$

Similarly, 1 pascal is defined as the 1 Newton force applied on an area of 1 meter square.

Therefore, $1Pa=1N/1m^2$

$1Pa=1Kg\times \frac{1m}{s^2} \times 1m^{-2}$

$1Pa=1Kg/(s^2\times m^1)$

$1Pa= [Kg^1 s^{-2}m^{-1}]$

Thus, in this way, every derived unit is related to the base unit.

## Difference between a base unit and a derived unit

The table below shows the difference between base unit and derived unit

Base Unit | Derived Unit |

all units that are not dependant on any other unit, including themselves | are calculated by multiplying or dividing one or more base units with or without the addition of any other numerical factor |

Because they are elementary units, they cannot be further reduced to other elementary units. | Because they are made up of basic or fundamental units, they can be reduced to their most basic form. |

In the metric or SI system, only seven base units and two supplementary units exist. | In the SI system of units, there are a vast number of derived units. |

## Conclusion

A measurement method is needed in any system of units to define the units for these physical quantities. The algebraic combinations of the base quantities can then be used to represent all other physical quantities. All of these physical quantities is then referred to as a derived quantity, with each unit being referred to as a derived unit.

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