The International System of Units (Système International d’Unités or SI) is the modern metric system of measurement used universally in science, technology, and commerce. Maintained by the International Bureau of Weights and Measures (BIPM), it ensures global uniformity and precision. The SI system is structured into two primary classes of units: Base Units and Derived Units.
Seven SI Base Units
The core of the SI system comprises seven base units, which are frictionally independent and serve as the foundation from which all other units are derived. In 2019, the BIPM redefined these base units in terms of invariant natural constants rather than physical artifacts.
| Physical Quantity | Symbol of Quantity | SI Base Unit | Unit Symbol | Defining Natural Constant / Anchor |
| Length | l, x, r | meter | m | Speed of light in vacuum (c) |
| Mass | m | kilogram | kg | Planck constant (h) |
| Time | t | second | s | Hyperfine transition frequency of Caesium-133 (Δ νCs) |
| Electric Current | I, i | ampere | A | Elementary charge (e) |
| Thermodynamic Temperature | T | kelvin | K | Boltzmann constant (k) |
| Amount of Substance | n | mole | mol | Avogadro constant (NA) |
| Luminous Intensity | Iv | candela | cd | Luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz (Kcd) |
Scientific Definitions of Base Units
Meter (m)
The meter is defined by taking the fixed numerical value of the speed of light in vacuum, c, to be $299,792,458$ when expressed in the unit m s-1.
Kilogram (kg)
The kilogram is defined by taking the fixed numerical value of the Planck constant, h, to be 6.62607015 × 10-34 when expressed in the unit J s (which is equal to kg m2 s-1).
Second (s)
The second is defined by taking the fixed numerical value of the caesium frequency, Δ νCs, the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom, to be $9,192,631,770$ when expressed in the unit Hz (equal to s-1).
Ampere (A)
The ampere is defined by taking the fixed numerical value of the elementary charge, e, to be 1.602176634 × 10-19 when expressed in the unit C (equal to A s).
Kelvin (K)
The kelvin is defined by taking the fixed numerical value of the Boltzmann constant, k, to be 1.380649 × 10-23 when expressed in the unit J K-1 (equal to kg m2 s-2 K-1).
Mole (mol)
One mole contains exactly 6.02214076 × 1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol-1.
Candela (cd)
The candela is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, Kcd, to be $683$ when expressed in the unit lm W-1 (equal to cd sr W-1 or cd sr kg-1 m-2 s3).
SI Derived Units with Special Names
Derived units are formed by combining base units according to the algebraic relations linking the corresponding quantities. Several derived units have been assigned special names and symbols for convenience.
| Derived Quantity | Special Name | Symbol | Expression in Base Units | Expression in other SI Units |
| Frequency | hertz | Hz | s-1 | — |
| Force | newton | N | kg m s-2 | — |
| Pressure, Stress | pascal | Pa | kg m-1 s-2 | N m-2 |
| Energy, Work, Heat | joule | J | kg m2 s-2 | N m |
| Power, Radiant Flux | watt | W | kg m2 s-3 | J s-1 |
| Electric Charge | coulomb | C | A s | — |
| Electric Potential, EMF | volt | V | kg m2 s-3 A-1 | W A-1 or J C-1 |
| Capacitance | farad | F | kg-1 m-2 s4 A2 | C V-1 |
| Electric Resistance | ohm | Ω | kg m2 s-3 A-2 | V A-1 |
| Electric Conductance | siemens | S | kg-1 m-2 s3 A2 | A V-1 or Ω-1 |
| Magnetic Flux | weber | Wb | kg m2 s-2 A-1 | V s |
| Magnetic Flux Density | tesla | T | kg s-2 A-1 | Wb m-2 |
| Inductance | henry | H | kg m2 s-2 A-2 | Wb A-1 |
| Celsius Temperature | degree Celsius | °C | K | — |
| Luminous Flux | lumen | lm | cd | cd sr |
| Illuminance | lux | lx | cd m-2 | lm m-2 |
| Radioactivity | becquerel | Bq | s-1 | — |
| Absorbed Dose (Radiation) | gray | Gy | m2 s-2 | J kg-1 |
| Equivalent Dose (Radiation) | sievert | Sv | m2 s-2 | J kg-1 |
| Catalytic Activity | katal | kat | mol s-1 | — |
Supplementary Units (Dimensionless Derived Units)
The SI system previously classified two units as supplementary units, which are now categorized as dimensionless derived units.
- Plane Angle: Measured in radian (rad). It is the plane angle between two radii of a circle which cut off on the circumference an arc equal in length to the radius. (rad = m m-1 = 1).
- Solid Angle: Measured in steradian (sr). It is the solid angle which, having its vertex in the center of a sphere, cuts off an area of the surface of the sphere equal to that of a square with sides of length equal to the radius of the sphere. (sr = m2 m-2 = 1).
SI Prefixes for Multiples and Submultiples
SI prefixes are used to form decimal multiples and submultiples of SI units. They strictly follow factors of $10$.
| Prefix | Symbol | Factor | Prefix | Symbol | Factor |
| quetta | Q | 1030 | quecto | q | 10-30 |
| ronna | R | 1027 | ronto | r | 10-27 |
| yotta | Y | 1024 | yocto | y | 10-24 |
| zetta | Z | 1021 | zepto | z | 10-21 |
| exa | E | 1018 | atto | a | 10-18 |
| peta | P | 1015 | femto | f | 10-15 |
| tera | T | 1012 | pico | p | 10-12 |
| giga | G | 109 | nano | n | 10-9 |
| mega | M | 106 | micro | μ | 10-6 |
| kilo | k | 103 | milli | m | 10-3 |
| hecto | h | 102 | centi | c | 10-2 |
| deca | da | 101 | deci | d | 10-1 |
Non-SI Units Accepted for Use with SI
Certain non-SI units are widely used in specialized scientific fields and day-to-day governance, making them critical for UPSC analytical questions.
| Non-SI Unit | Symbol | Value in SI Units | Physical Quantity |
| Minute | min | 60 s | Time |
| Hour | h | 3600 s | Time |
| Day | d | 86400 s | Time |
| Astronomical Unit | au | 1.495978707 × 1011 m | Distance (Earth-Sun) |
| Light-year | ly | 9.4607 × 1015 m | Interstellar Distance |
| Parsec | pc | 3.0857 × 1016 m ≈ 3.26 ly | Astronomical Distance |
| Angstrom | Å | 10-10 m | Atomic Length |
| Litre | L / l | 1 dm3 = 10-3 m3 | Volume |
| Tonne | t | 1000 kg = 1 Mg | Mass |
| Dalton / AMU | Da / u | 1.660539066 × 10-27 kg | Atomic/Molecular Mass |
| Electronvolt | eV | 1.602176634 × 10-19 J | Energy |
| Bar | bar | 105 Pa | Atmospheric Pressure |
Mandatory Rules for Writing SI Units and Symbols
The General Conference on Weights and Measures (CGPM) enforces specific grammatical protocols to avoid ambiguity in technical documentation.
- Case Sensitivity of Symbols: Unit symbols are printed in lower case (e.g., m, s, kg) unless the name of the unit is derived from a proper name of a scientist, in which case the first letter of the symbol is capitalized (e.g., N for Newton, Pa for Pascal, W for Watt, J for Joule). Note that the unit litre is an exception where upper case ‘L’ or lower case ‘l’ are both allowed to prevent confusion with the number 1.
- Full Unit Names: When printed in full, unit names always start with a lower case letter (e.g., newton, pascal, joule, meter), even if named after a scientist. The only exception is Celsius, which retains its capital letter.
- Plurals: Unit symbols do not change in the plural form (e.g., 50 kg is correct; 50 kgs is incorrect). Full unit names take regular plurals (e.g., 50 kilograms, 20 henries).
- Punctuation and Spacing: Unit symbols are mathematical entities, not abbreviations. Therefore, they are never followed by a full stop or period unless they appear at the end of a sentence. A space must separate the numerical value and the unit symbol (e.g., 25 kg is correct; 25kg is incorrect).
- Prefix Application: Combined prefix and unit symbols form a new inseparable symbol. Double prefixes are strictly prohibited (e.g., use nanometer (nm), never millimicrometer (mμm)).
UPSC Prelims High-Yield Facts and Trivia
- The 2019 Historic Redefinition: The General Conference on Weights and Measures redefined the Kilogram, Ampere, Kelvin, and Mole in May 2019. The physical artifact called the International Prototype of the Kilogram (IPK)—a cylinder of platinum-iridium kept in Sèvres, France—was retired. Mass is now universally calibrated using a Kibble Balance via the Planck Constant.
- The Newest Prefixes: In November 2022, the 27th CGPM introduced four new prefixes to account for data sciences and extreme measurements: quetta (1030), ronna (1027), ronto (10-27), and quecto (10-30).
- Curie vs. Becquerel: Both are units of radioactivity. However, the Becquerel (Bq) is the official SI unit (one disintegration per second), whereas the Curie (Ci) is a non-SI unit based on the activity of 1 gram of Radium-226 (1 Ci = 3.7 × 1010 Bq).
- Tesla vs. Gauss: Tesla (T) is the SI unit of magnetic flux density. Gauss (G) belongs to the old CGS system (1 T = 104 G).
- Identical Dimensions: In physics, certain quantities share identical SI derived expressions. For instance, Impulse and Linear Momentum share the base unit expression kg m s-1 (or N s). Similarly, Work, Energy, and Torque share the base unit expression kg m2 s-2 (or N m).