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 (centimetergramsecond), m.k.s (meterkilogram second), and f.p.s (feetpoundsecond) 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)} 
 
m^{2}·m^{2 }= 1 ^{(b)} 
frequency 
Hertz 
Hz 
 
s^{1} 
force 
Newton 
N 
 
m·kg·s^{2} 
pressure, stress 
Pascal 
Pa 
N/m^{2} 
m^{1}·kg·s^{2} 
energy, work, quantity of heat 
Joule 
J 
N·m 
m^{2}·kg·s^{2} 
power, radiant flux 
Watt 
W 
J/s 
m^{2}·kg·s^{3} 
electric charge, quantity of electricity 
Coulomb 
C 
 
A·s 
electric potential difference, 
Volt 
V 
W/A 
m^{2}·kg·s^{3}·A^{1} 
capacitance 
Farad 
F 
C/V 
m^{2}·kg^{1}·s^{4}·A^{2} 
electric resistance 
Ohm 
V/A 
m^{2}·kg·s^{3}·A^{2} 

electric conductance 
Siemens 
S 
A/V 
m^{2}·kg^{1}·s^{3}·A^{2} 
magnetic flux 
Weber 
Wb 
V·s 
m^{2}·kg·s^{2}·A^{1} 
magnetic flux density 
Tesla 
T 
Wb/m^{2} 
kg·s^{2}·A^{1} 
inductance 
Henry 
H 
Wb/A 
m^{2}·kg·s^{2}·A^{2} 
Celsius temperature 
Degree Celsius 
°C 
 
K 
luminous flux 
Lumen 
lm 
cd·sr ^{(c)} 
m^{2}·m^{2}·cd = cd 
illuminance 
Lux 
lx 
lm/m^{2} 
m^{2}·m^{4}·cd = m^{2}·cd 
activity (of a radionuclide) 
Becquerel 
Bq 
 
s^{1} 
absorbed dose, specific energy (imparted), kerma 
Gray 
Gy 
J/kg 
m^{2}·s^{2} 
dose equivalent ^{(d)} 
Sievert 
Sv 
J/kg 
m^{2}·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.
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