Difference Between Fundamental and Derived Quantities

Fundamental vs Derived Quantities
 

Experimentation is a core aspect of physics and other physical sciences. Theories and other hypothesis are verified and established as scientific truth by means of experiments conducted. Measurements are an integral part of experiments, where the magnitudes of and the relations amongst different physical quantities are used to verify the truth of the theory or hypothesis tested.

There are very common set of physical quantities that are often measured in physics. These quantities are considered as fundamental quantities by convention. Using the measurements for these quantities and the relations amongst them, other physical quantities can be derived. These quantities are known as derived physical quantities.

Fundamental Quantities

A set of fundamental units are defined in every units system, and the corresponding physical quantities are called the fundamental quantities. Fundamental units are independently defined, and often the quantities are directly measurable in a physical system.

In general, a system of units requires three mechanical units (mass, length, and time). One electrical unit is also required. Even though above set of units may suffice, for convenience few other physical units are considered fundamental. c.g.s (centimeter-gram-second), m.k.s (meter-kilogram second), and f.p.s (feet-pound-second) are formerly used systems with fundamental units.

SI unit system has replaced much of the older units systems. In the SI system of units, by definition, following seven physical quantities are considered as fundamental physical quantities and their units as fundamental physical units. 

    Quantity

    Unit

    Symbol

    Dimensions

    Length

    Meter

m

L

    Mass

    Kilogram

kg

M

    Time

    Seconds

s

T

    Electric Current

    Ampère

A

 

    Thermodynamic Temp.

    Kelvin

K

 

    Amount of Substance

    Mole

mol

 

    Luminous intensity

    Candela

cd

 

Derived Quantities

Derived quantities are formed by product of powers of fundamental units. In other words, these quantities can be derived using fundamental units. These units are not defined independently; they depend on the definition of other units. Quantities attached to derived units are called derived quantities.

For example, consider the vector quantity of speed. By measuring the distance traveled by an object and the time taken, the average speed of the object can be determined. Therefore, speed is a derived quantity. Electric charge is also a derived quantity where it is given by the product of current flow and time taken. Each derived quantity has derived units. Derived quantities can be formed. 

    Physical Quantity

    Unit

Symbol

    plane angle

    Radian (a)

rad

  -

m·m-1 = 1 (b)

    solid angle

    Steradian (a)

sr (c)

  -

m2·m-2 = 1 (b)

    frequency

    Hertz

Hz

  -

s-1

    force

    Newton

N

  -

m·kg·s-2

    pressure, stress

    Pascal

Pa

N/m2

m-1·kg·s-2

    energy, work, quantity of heat  

    Joule

J

N·m

m2·kg·s-2

    power, radiant flux

    Watt

W

J/s

m2·kg·s-3

    electric charge, quantity of electricity

    Coulomb

C

  -

A·s

    electric potential difference,
    electromotive force

    Volt

V

W/A

m2·kg·s-3·A-1

    capacitance

    Farad

F

C/V

m-2·kg-1·s4·A2

    electric resistance

    Ohm

 

V/A

m2·kg·s-3·A-2

    electric conductance

    Siemens

S

A/V

m-2·kg-1·s3·A2

    magnetic flux

    Weber

Wb

V·s

m2·kg·s-2·A-1

    magnetic flux density

    Tesla

T

Wb/m2

kg·s-2·A-1

    inductance

    Henry

H

Wb/A

m2·kg·s-2·A-2

    Celsius temperature

    Degree Celsius

°C

  -

K

    luminous flux

    Lumen

lm

cd·sr (c)

m2·m-2·cd = cd

    illuminance

    Lux

lx

lm/m2

m2·m-4·cd = m-2·cd

    activity (of a radionuclide)

    Becquerel

Bq

  -

s-1

    absorbed dose,

    specific energy (imparted), kerma

    Gray

Gy

J/kg

m2·s-2

    dose equivalent (d)

    Sievert

Sv

J/kg

m2·s-2

    catalytic activity

    Katal

kat

 

s-1·mol

What is the difference between Fundamental and Derived Quantities?

• Fundamental quantities are the base quantities of a unit system, and they are defined independent of the other quantities.

• Derived quantities are based on fundamental quantities, and they can be given in terms of fundamental quantities.

• In SI units, derived units are often given names of people such as Newton and Joule.