International System of Units (SI Units)

The International System of Units (Système International, SI) is the single language in which all JEE Main and NEET physics is examined. Building on the introduction to units and measurement, this page fixes the seven base units with their official definitions, the two supplementary units, the full prefix ladder from atto to exa, and the writing conventions whose violation NTA turns into questions. Standard constants used throughout this chapter are quoted here once: c = 2.998 × 10⁸ m s⁻¹ (≈ 3 × 10⁸), h = 6.63 × 10⁻³⁴ J s, e = 1.602 × 10⁻¹⁹ C, m_e = 9.11 × 10⁻³¹ kg, N_A = 6.022 × 10²³ mol⁻¹, G = 6.67 × 10⁻¹¹ N m² kg⁻², g = 9.8 m s⁻², k_B = 1.381 × 10⁻²³ J K⁻¹, R = 8.314 J mol⁻¹ K⁻¹, 1 u = 1.66 × 10⁻²⁷ kg.

What is the International System of Units? — Complete Theory

1. Origin and the 2019 revision

SI was adopted in 1960 by the General Conference on Weights and Measures (CGPM) to replace the competing CGS, FPS and MKS systems. In 2019 the definitions were re-anchored to exact values of universal constants: the kilogram is now defined by fixing h = 6.62607015 × 10⁻³⁴ J s exactly, the ampere by fixing e = 1.602176634 × 10⁻¹⁹ C, the kelvin by fixing k_B = 1.380649 × 10⁻²³ J K⁻¹, and the mole by fixing N_A = 6.02214076 × 10²³ mol⁻¹. The old artefact definitions (the platinum–iridium prototype kilogram stored near Paris; the triple-point-of-water kelvin) are now historical. NCERT's table follows the classical definitions; quote the artefact version for NCERT-based questions and add the 2019 constants-based version for one bonus line of sophistication.

2. The seven SI base units (NCERT Table 1.1)

3. Supplementary units: radian and steradian

Two purely geometric ratios complete the toolkit. The radian (rad) is the plane angle subtended at the centre of a circle by an arc whose length equals the radius: θ = arc/radius, so a full circle is 2π rad. The steradian (sr) is the solid angle subtended at the centre of a sphere by a spherical cap whose area equals r²: Ω = area/radius², so the full sphere is 4π sr. Both are ratios of like quantities — length/length and area/area — hence dimensionless, yet they carry special names. This is why angular velocity ω = dθ/dt has dimensions [T⁻¹] but unit rad s⁻¹, a pairing NTA tests directly.

4. Derived units with special names

Derived units are products/quotients of base units; the useful ones get special names for brevity: newton N = kg m s⁻² (force), joule J = N m (energy), watt W = J s⁻¹ (power), pascal Pa = N m⁻² (pressure), hertz Hz = s⁻¹ (frequency), coulomb C = A s (charge), volt V = J C⁻¹ (potential), ohm Ω = V A⁻¹ (resistance), tesla T = N A⁻¹ m⁻¹ (magnetic field), farad F = C V⁻¹ (capacitance), henry H = V s A⁻¹ (inductance). Unit names derived from scientists are written lowercase (newton, kelvin) but their symbols are capitalised (N, K). The full dimensional breakdown of each is on the Dimensional Formulae page.

5. SI prefixes (10⁻¹⁸ → 10¹⁸)

6. Rules for writing SI units (mark-earning conventions)

(i) Symbols are never pluralised and take no full stop: 5 kg, 10 s. (ii) A space separates the number and the symbol; the degree symbol is the exception (25 °C). (iii) Unit names are lowercase; symbols are lowercase unless named after a person (N, J, Hz, K). (iv) Products use a space or a raised dot: kg m s⁻¹ or kg·m·s⁻¹; quotients use one slash only: m s⁻¹ preferred over m/s² → write m s⁻² not m/s/s. (v) Prefixes attach to a single root unit: 10⁻⁶ kg is written 1 mg (never μkg); pF not μμF. (vi) "kilo" takes lowercase k. Each of these has appeared as a "spot the correct statement" MCQ.

Visualising International System of Units

Think of SI as a currency system: seven coins (base units) cannot be minted from each other, every other denomination (derived units) is an arithmetic combination of them, and prefixes are the lakh/crore-style notation that keeps numbers readable across 36 decades. When a derived unit appears in a question (say, pascal), mentally decompose it to base units — Pa = kg m⁻¹ s⁻² — because dimensional questions are always answered in base units, never in named units.

Solved Examples on International System of Units (Step-by-Step)

Solved Example 1 — Everyday speed into SI

Q. Express 72 km h⁻¹ in SI base units.

Step 1. Replace prefixes: 72 km h⁻¹ = 72 × 10³ m per 3600 s.

Step 2. Divide: 72 × 10³ ÷ 3600 = 72 × 1000/3600 = 72000/3600 = 20.

Step 3. Attach the base unit: 20 m s⁻¹. (Memorise: multiply km h⁻¹ by 5/18.)

Solved Example 2 — Density from CGS to SI

Q. Water has density 1 g cm⁻³. Express it in SI.

Step 1. 1 g = 10⁻³ kg; 1 cm³ = (10⁻² m)³ = 10⁻⁶ m³.

Step 2. ρ = 10⁻³ kg / 10⁻⁶ m³ = 10³ kg m⁻³.

Step 3. Sanity: metals reach 2–19 × 10³ kg m⁻³; water at 1000 is right. ✔

Practice Questions on International System of Units (With Solutions)

Practice Q1 (Numerical-value type)

Q. How many cubic centimetres make exactly 1 cubic metre?

Solution. 1 m = 10² cm → 1 m³ = (10²)³ cm³ = 10⁶ cm³. Volume conversions cube the length factor — the single most common slip.

Practice Q2 (Single-correct MCQ)

Q. Which pair lists SI supplementary units? (a) radian, steradian (b) radian, hertz (c) steradian, candela (d) mole, radian

Solution. Supplementary units are the two geometric ratios: radian and steradian. Candela is a base unit; hertz and mole are base/derived regulars.

Practice Q3 (Assertion–Reason)

Q. Assertion (A): "5 kgs" is an incorrect way to write 5 kilograms in SI. Reason (R): SI unit symbols are never pluralised.

Solution. The symbol kg is invariable; 5 kgs violates rule (i). R is precisely why A is wrong — R explains A.

Key Formulas & Takeaways

FAQs on International System of Units

What is the International System of Units (SI)?

SI is the modern metric system adopted in 1960 (and refined in 2019) with seven base units — metre, kilogram, second, ampere, kelvin, mole and candela — plus two dimensionless supplementary units (radian, steradian), from which all derived units are built.

Why is the kilogram the only base unit with a prefix?

Historically the gram was too small to serve as the base, so the kilogram (prototype mass) was chosen; multiples and sub-multiples are therefore written with gram as the root (mg, μg) and never as micro-kilogram.

What are the correct rules for writing SI symbols?

Unit symbols are never pluralised (5 kg, not 5 kgs), take no full stop, are lowercase except when named after a person (N, J, K), and a space is left between the number and the symbol (299792458 m s⁻¹).

Define the metre and the second in SI.

The metre is the distance light travels in vacuum in 1/299792458 of a second, and the second is the duration of 9192631770 periods of the radiation of the caesium-133 ground-state hyperfine transition.