Physical Quantities, Units and Measurements

Before we measure anything in science, we need two things: a number and a unit.

You cannot say “the bridge is 500” — 500 what? Metres? Feet? Kilometres? The unit gives meaning to the number.

This is the foundational idea of the entire chapter. Physics is, at its core, the art of precise measurement, and Units & Measurements is the grammar of that language.

Physical Quantities

A physical quantity is any property of a material or system that can be measured or calculated and expressed as a numerical value paired with a unit.

Think of it this way: mass, length, time, temperature — all of these are physical quantities because each can be assigned a precise number with a standard unit.

Classification Based on Units

Physical quantities split into two broad families depending on whether they need other quantities to define them:

• Fundamental (Base) Quantities:  These are the building blocks — independent, self-sufficient, and irreducible. They do not depend on any other physical quantity.
• There are seven of them: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity. They are also called base quantities.
• Derived Quantities:  These are combinations of fundamental quantities tied together by mathematical relationships.
• For example, velocity = length ÷ time; force = mass × acceleration.
• They are derived from the base quantities — hence the name.

📌 Key Insight:  In the revised SI system, plane angles (radian) and solid angles (steradian) are now treated as dimensionless derived quantities — they no longer belong to a separate category.

Classification Based on Direction and Magnitude

Physics also classifies quantities by whether they carry information about direction:

• Scalar Quantities:  Have only magnitude — no direction.
• If I say my bag weighs 10 kg, I do not need to say “10 kg northwards.”
• Examples: mass, time, speed, temperature, energy.
• Vector Quantities:  Have both magnitude and direction.
• “The car moved 50 m towards the east” — here, 50 m is the magnitude and east is the direction.
• Examples: displacement, velocity, force, acceleration, electric field.

Units

A unit is the standard reference against which a physical quantity is measured. When you say “2 metres,” the metre is your reference — your benchmark. Without a standard unit, science becomes chaotic. Imagine if every country used its own definition of “one kilogram” — trade, medicine, and engineering would all collapse.

Characteristics of a Good Standard Unit

A standard unit must satisfy six essential criteria:

• Well-defined: Its definition must be clear and unambiguous, leaving no room for interpretation.
• Invariable: It must not change with time, location, temperature, or any physical condition.
• Reproducible: Any laboratory in the world should be able to reproduce the unit with the same precision.
• Accessible: The unit must be easily available to anyone who needs to use it.
• Convenient Size: The unit’s magnitude should be practical — not too large or too small for everyday use.
• Universally Accepted: It must be adopted and recognised internationally.

Types of Units

• Fundamental Units:  Units for fundamental quantities that stand on their own.
• Examples: metre (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (amount of substance), candela (luminous intensity).
• Derived Units:  Units formed by combining fundamental units using mathematical relationships. Examples: m/s (speed), N or kg·m/s² (force), J or kg·m²/s² (energy).

System of Units

A system of units is a complete, coherent set of base units and derived units. Think of it as an ecosystem — all units within a system are internally consistent and interrelated. The name of the system is based on the fundamental units it is built around.

The Major Systems at a Glance

System	Length	Mass	Time	Also Known As	Primary Use
CGS	Centimetre (cm)	Gram (g)	Second (s)	Gaussian System	Academic Physics
MKS	Metre (m)	Kilogram (kg)	Second (s)	Basis of SI	Engineering
FPS	Foot (ft)	Pound (lb)	Second (s)	British System	USA & Engineering
SI	Metre (m)	Kilogram (kg)	Second (s)	International System	Global Standard

The SI System — The Modern Gold Standard

The International System of Units (SI) is the modern, globally accepted system for measuring physical quantities. It was formally adopted in 1960 and has since been revised to tie every unit to fundamental physical constants — making it extraordinarily precise and stable. The SI system is built upon seven base units, from which all other units are derived.

Notice how the defining constants in the table below are universal physical constants — they do not change anywhere in the universe. This is what makes modern SI units “artefact-free” and more reliable than older physical standards.

Physical Quantity	SI Unit	Symbol	Defining Constant
Length	Metre	m	Speed of light in vacuum (c)
Mass	Kilogram	kg	Planck constant (h)
Time	Second	s	Hyperfine transition frequency of Caesium-133
Electric Current	Ampere	A	Elementary charge (e)
Thermodynamic Temperature	Kelvin	K	Boltzmann constant (k)
Amount of Substance	Mole	mol	Avogadro constant (Nₐ)
Luminous Intensity	Candela	cd	Luminous efficacy of 540 THz radiation

Important Derived Units of SI System

Derived Quantity	SI Unit	Symbol	Formula
Area	Square metre	m²	Length × Width
Volume	Cubic metre	m³	Length × Width × Height
Speed / Velocity	Metre per second	m/s	Distance / Time
Acceleration	Metre per second²	m/s²	Change in velocity / Time
Force	Newton	N (kg·m/s²)	Mass × Acceleration
Energy / Work	Joule	J (kg·m²/s²)	Force × Distance
Power	Watt	W (kg·m²/s³)	Work / Time
Pressure	Pascal	Pa (kg·m⁻¹·s⁻²)	Force / Area
Electric Charge	Coulomb	C (A·s)	Current × Time
Electric Potential	Volt	V	Work done / Electric Charge
Resistance	Ohm	Ω	Voltage / Current
Capacitance	Farad	F	Charge / Voltage
Frequency	Hertz	Hz (s⁻¹)	Cycles / Time

📌 Key Insight:  Always remember: the Newton is named after Isaac Newton, the Joule after James Prescott Joule, the Watt after James Watt, the Pascal after Blaise Pascal, and the Hertz after Heinrich Hertz. These names often appear in questions testing the history of science.