Fundamental and Derived Units of Measurement

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History of Measurement

Before humans created a standardized system of measurement, many cultures utilized local traditions for measuring objects. These are as follows:

  1. The Cubit - This measurement originated in Egypt about 3000 B.C. It was used to build pyramids.

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  1. The Fathom - It is a unit of length in the imperial and the U.S. customary systems equal to 6 feet (1.8288 m).  

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3. The Hand-Span - It is the distance between the tip of the smallest finger and the tip of the thumb. We still use this to measure the height of horses.  

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Need for Measurement

We all know that physics is a branch of science which deals with the study of nature and natural phenomena. 

Let’s say I drop a ball from a certain height; it falls freely on the ground. 

Being a physics enthusiast to understand this natural phenomenon; I will search for answers to the following questions:

  1. Why did this ball fall on the ground?

  2. At what speed does an object fall?

  3. Is the velocity of a ball constant?

  4. How much will it take for a ball to reach the ground?

  5. Is the velocity of a body directly related to its mass?

To get a precise answer to these questions, measuring the quantities like distance, velocity, and time becomes essential.

A System of Units

The system of units is the complete set of units, both fundamental units, and derived units, for all kinds of physical quantities. Each system is named with reference to fundamental units on which it is based. The common system of units utilized in mechanics are as follows:

  1. The f.p.s or Foot-Pound System: A British engineering system of units that uses the foot as the unit of measurement of length, and pound as the unit of mass and second as the unit of time.

  2. The c.g.s or Centimeter-Gram-Second System: A Gaussian system that uses centimeter, gram, and second as the three basic units for length, mass, and time respectively.

  3. The M.K.S or Meter-Kilogram-Second System: The fundamental units of length, mass, and time are meter, kilogram, and second respectively.

Fundamental and Derived Units

The quantities which we can measure directly or indirectly are known as physical quantities. 

For example, distance, displacement, momentum, etc.

The Physical Quantities are Divided into Two Categories:

  1. Fundamental quantities, and

  2. Derived quantities

Fundamental Quantities

The physical quantities that do not depend upon the other quantities are the fundamental quantities.

There are Seven Fundamental Quantities


Base Quantity

SI Basic Unit











Luminous Intensity



Amount of substance



Plane angle



Solid angle


Row 8, and 9: Two supplementary units on the SI system are:

  1. The Radian - It is the unit of a plane angle. One radian is the angle subtended by the center of a circle by an arc and is equal in length to the radius of a circle.

  2. The Steradian - It is the unit of solid angle. One steradian is the solid angle subtended at the center of a sphere, by the surface of a sphere which is equal in area to the square of its radius.

Derived Quantities

The physical quantities that depend upon the fundamental quantities are known as the derived quantities.

Let’s take examples of derived units:

Derived Units Table: The Table Shows the List of Derived Units




SI Derived Unit



Kgm -1





Change in velocity/Time



Side x Side



Mass x Acceleration

  1. Work

  2. Energy

Force x Displacement


Kg. m.s-2


Pressure, Stress




Current density

J = I/A


Some Important Practical Units

1.  In macrocosm measurements, i.e., measurement of very large distances:

  1. Astronomical units (A.U.)

     It is the average distance of the center of the sun from the center of the earth.

1 A.U. = 1.496 x 1011m ≃ 1.5 x 1011m

  1. A light-year (ly) 

     One light-year is the distance traveled by light in a vacuum in one Earth year. 

     As the speed of light in a vacuum is 3 x 108 m/s, and 

    1 year = 365 x 24 x 60 x 60 seconds.

   Therefore, one light-year = 3 x 108 x 365 x 24 x 60 x 60 meter

      1 ly = 9.46 x 1015meter 

  1. Parsec

     It is the unit of long distances and represents the parallactic seconds.

    Parsec is the distance at which 1 A.U. long arc subtends an angle of 1”.

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 As 1 A.U. = 1.496 x 1011m, and

Ө = 1/60 min  = 1/60 x 60 degree = 1/60 x 60 x π/180 radian

Since the radius of an arc, r = length of an arc (l)/angle subtended (Ө)

Therefore, 1 parsec = 1 A.U./1 sec = (1.496 x 1011) x (60 x 60 x 180)/(π)


1 parsec = 3.1 x 1016m

FAQ (Frequently Asked Questions)

Q1: Calculate the Number of Astronomical Units in Two Meters.

Solution: We know 1 A.U.= 1.5 x 1011m 

If 1 m = 1/1.5 x 1011A.U.

Then,  2 m = 2/1.5 x 1011

So, the number of astronomical units in 2 meters is 1.333 x 10-11A.U.

Q2: What are the Advantages of the SI System?

Ans: The main advantages of the SI are:

It is:

  1. A coherent system of units

  2. A rational system of units

  3. An absolute system of units

  4. A metric system

Q3: Why is a Parsec 3.26 Light-Years?

Ans: As 1 ly = 9.46 x 1015m, and 1 parsec = 3.1 x 1016m

Now, 1 parsec/1 ly = 3.1 x 1016/ 9.46 x 1015

On solving, we get,

1 parsec = 3.26 ly

Q4: What System of Measurement is Used in the US?

Ans: The US uses two major systems of measurement, they are:

  1. Metric systems (International system of units or SI), and

  2. The U.S. Customary Units (The U.S. standard, British Imperial Units, or English standard).