A physical quantity is any property of a material or phenomenon that can be quantified and measured using a standard unit. Physical quantities are classified into two categories based on their dependence on other quantities: Fundamental Quantities and Derived Quantities.
Fundamental Quantities
Fundamental quantities (also known as base quantities) are those physical quantities that are completely independent of each other and cannot be defined or expressed in terms of any other physical quantities.
The International System of Units (SI)
The General Conference on Weights and Measures (CGPM) established the Système International d’Unités (SI) as the international standard for measurement. The SI system recognizes exactly seven fundamental quantities and two supplementary quantities.
| Fundamental Quantity | SI Base Unit | Symbol | Definition & Physical Standard |
| Length | Meter | m | The distance traveled by light in a vacuum during a specific time interval (1/299,792,458 of a second). |
| Mass | Kilogram | kg | Defined by taking the fixed numerical value of the Planck constant (h = 6.62607015 × 10-34 J s). |
| Time | Second | s | Defined by the fixed numerical value of the caesium frequency (Δ νCs) of the unperturbed ground-state hyperfine transition of the caesium-133 atom. |
| Electric Current | Ampere | A | Defined by taking the fixed numerical value of the elementary charge (e = 1.602176634 × 10-19 C). |
| Thermodynamic Temperature | Kelvin | K | Defined by taking the fixed numerical value of the Boltzmann constant (k = 1.380649 × 10-23 J/K). |
| Amount of Substance | Mole | mol | Contains exactly 6.02214076 × 1023 elementary entities (Avogadro’s number). |
| Luminous Intensity | Candela | cd | The luminous intensity of a source that emits monochromatic radiation of frequency 540 × 1012 Hz. |
Supplementary Quantities
Apart from the seven fundamental quantities, there are two purely geometrical quantities called supplementary quantities. They are dimensionless but possess specific units.
- Plane Angle: Measured in Radian (rad). It is the ratio of the arc length to the radius of the circle (dθ = ds / r).
- Solid Angle: Measured in Steradian (sr). It is the three-dimensional equivalent of a plane angle, defined as the ratio of the intercepted area of a spherical surface to the square of its radius (dΩ = dA / r2).
Derived Quantities
Derived quantities are those physical quantities that depend on one or more fundamental quantities for their definition and measurement. They are mathematically derived through multiplication, division, or a combination of operations on fundamental quantities.
Common Derived Quantities and Their SI Units
The following table outlines key derived quantities frequently tested in competitive examinations, tracking how they break down into base fundamental units.
| Derived Quantity | Mathematical Formula | Derived SI Unit | Breakdown in Fundamental SI Units |
| Area | Length × Breadth | m2 | m2 |
| Volume | Length × Breadth × Height | m3 | m3 |
| Density | Mass / Volume | kg/m3 | kg·m-3 |
| Speed / Velocity | Distance / Time | m/s | m· s-1 |
| Acceleration | Change in Velocity / Time | m/s2 | m· s-2 |
| Force | Mass × Acceleration | Newton (N) | kg·m· s-2 |
| Work / Energy | Force × Displacement | Joule (J) | kg·m2· s-2 |
| Power | Work / Time | Watt (W) | kg·m2· s-3 |
| Pressure / Stress | Force / Area | Pascal (Pa) | kg·m-1· s-2 |
| Electric Charge | Current × Time | Coulomb (C) | A⋯ |
| Electric Potential | Work / Charge | Volt (V) | kg·m2· s-3·A-1 |
| Electrical Resistance | Potential Difference / Current | Ohm (Ω) | kg·m2· s-3·A-2 |
| Frequency | 1 / Time Period | Hertz (Hz) | s-1 |
Systems of Units (Historical Context)
Before the worldwide adoption of the SI system, different countries utilized alternative coherent systems of units. Understanding these is important for tracking historical scientific literature.
CGS System (Gaussian System)
Introduced in France, it uses Centimeter for length, Gram for mass, and Second for time. It is still used in certain specialized fields of advanced electrodynamics and theoretical physics.
MKS System
A precursor to the modern SI system, it uses Meter for length, Kilogram for mass, and Second for time.
FPS System (British Engineering System)
Historically used across the British Empire, it relies on Foot for length, Pound for mass, and Second for time. It remains a non-metric system used colloquially in specific nations.
Characteristics of an Ideal Standard Unit
For any measurement unit to be accepted globally as a standard (whether fundamental or derived), it must meet specific physical and practical criteria.
- Invariability: The unit must not change with variations in environmental conditions like temperature, pressure, time, or location.
- Accessibility: The standard setup for verifying or replicating the unit must be easily accessible to scientists and standard laboratories worldwide.
- Indestructibility: The physical or quantum definition must be permanent and immune to physical decay or accidental destruction.
- Reproducibility: It should be capable of being reproduced precisely anywhere without ambiguity.
- International Acceptability: It must be recognized by global scientific accords and bodies.
UPSC Prelims High-Yield Facts and Trivia
Dimensionless Quantities with Units
Not all dimensionless quantities are without units. Supplementary quantities like Plane Angle (radian) and Solid Angle (steradian) have specific units despite having no physical dimensions ([M0L0T0]). Conversely, quantities like Relative Density, Refractive Index, and Strain have neither dimensions nor units.
The 2019 SI Base Unit Redefinition
In May 2019, the International Bureau of Weights and Measures (BIPM) redefined the kilogram, ampere, kelvin, and mole. They are no longer linked to physical artifacts (like the old platinum-iridium cylinder for the kilogram kept in France). Instead, they are now strictly tied to immutable constants of nature, such as the Planck constant (h), the elementary charge (e), the Boltzmann constant (k), and the Avogadro constant (NA). This ensures absolute stability in measurements over cosmological timescales.
Coherent System of Units
The SI system is classified as a “coherent” system because all derived units can be obtained directly by multiplying or dividing fundamental units without introducing any numerical conversion factors other than unity (one).
Last Modified: May 27, 2026