The International System of Units

Why an international system exists

Before the 1960s, scientists ran three different systems side by side. CGS used centimetre, gram, second; FPS (the British system) used foot, pound, second; MKS used metre, kilogram, second. NCERT records all three in §1.2. Each was internally consistent, but conversions between them were tedious and error-prone — the kind of friction that turns reproducible science into folklore.

The resolution came in 1971, when the 14th General Conference on Weights and Measures (CGPM) finalised the Système International d'Unités — French for "International System of Units", abbreviated SI in every language — with seven base units. The system was substantially revised in November 2018 (effective May 2019), redefining every base unit through fixed numerical values of fundamental physical constants. The 2019 revision retired the last physical artefact — the platinum-iridium kilogram cylinder kept at the BIPM in Sèvres, France, with India's National Physical Laboratory historically holding prototype no. 57.

SI's advantages are practical: it is coherent (derived units factorise cleanly into base units), decimal (every multiple is a power of ten), and universal. The parent Units and Measurement chapter introduces the broader idea that a measurement equals a number multiplied by a unit; this article goes deeper into the unit half of that equation.

"SI units used the decimal system, conversions within the system are quite simple and convenient. We shall follow the SI units in this book."

NCERT Class 11 Physics, §1.2

The seven SI base units

The SI rests on seven base quantities — length, mass, time, electric current, thermodynamic temperature, amount of substance and luminous intensity — each assigned a base unit. After the 2019 revision, each base unit is defined by fixing the numerical value of a chosen fundamental constant. NCERT records the constant in Table 1.1; the table below collates them for NEET-fast revision.

Three things to internalise. First, the numerical values are exact by definition — they have no uncertainty, because the SI now chooses them. Second, the seven definitions are linked: the metre uses the second; the kilogram uses the metre and second; the ampere uses the second. A coherent chain runs outward from the caesium frequency. Third — and this is what NEET examiners exploit — the constants themselves need not be memorised numerically, but their roles in fixing the base units do. A question like "the kilogram is defined through which constant?" expects "Planck constant", not the digits.

Supplementary units — radian and steradian

Two further units sit alongside the seven base units. The radian (symbol rad) is the SI unit of plane angle, defined as the ratio of the arc length $ds$ to the radius $r$:

The steradian (symbol sr) is the SI unit of solid angle, defined as the ratio of the intercepted area $dA$ on a spherical surface to the square of the radius $r$:

Because both definitions are ratios of like quantities, the dimensions cancel completely. Yet the unit names and symbols are perfectly valid. This is the source of one of the most-tested traps in the chapter — quantities can have units but no dimensions.

Derived units — building everything from seven

Every other physical unit you will meet in NEET physics is a derived unit — a product or quotient of base units, sometimes with a special name. Derived units inherit their dimensions directly from the definition of the quantity. The list below covers the eight derived quantities NEET tests most often.

How to factorise a derived unit — a worked example

The same procedure works for any derived unit: energy $1$ J $= 1$ kg m$^2$ s$^{-2}$; power $1$ W $= 1$ kg m$^2$ s$^{-3}$; charge $1$ C $= 1$ A s; voltage $1$ V $= 1$ kg m$^2$ s$^{-3}$ A$^{-1}$. The skill is mechanical once you trust the definitions; the trap is mis-remembering which quantity factors into which.

SI prefixes — yocto to yotta

The SI is decimal, so any base or derived unit can be scaled by a prefix representing a power of ten. The full BIPM-recognised range runs from $10^{-24}$ (yocto) to $10^{24}$ (yotta) — twenty-four orders of magnitude on each side of unity. NEET will not ask the obscure ones, but you must recognise everything from pico ($10^{-12}$) through tera ($10^{12}$) on sight.

Three NEET-friendly conversions. Wavelength $500$ nm $= 5 \times 10^{-7}$ m. Radio frequency $1370$ kHz $= 1.370 \times 10^{-3}$ GHz (NIOS §1.2.1). A $4.7$ μF capacitor stores $4.7 \times 10^{-6}$ F. Prefixes attach directly to the unit symbol — no space, no dot: nm, not "n m".

Writing SI units — the conventions NEET examines

Beyond getting the unit right, NEET tests whether you can write it right. The conventions look picky, but they reflect a single principle: a unit symbol is a mathematical object that must be unambiguous in every printed context. NCERT records them through Appendix A8; NIOS lays them out in its "Nomenclature and Symbols" sidebar. The six rules that come up in question papers are:

1. No plural "s" on unit symbols. Write $10$ kg, not "10 kgs". Write $7$ cm, not "7 cms". The symbol is invariable; only the unit's full name takes a plural in running prose (seven centimetres).
2. No full stop after a unit symbol unless the symbol ends a sentence. "The pencil is 7 cm long" — not "7 cm. long".
3. Single space between number and symbol. Write $25$ m, not "25m" and not "25 m". The only exception is for percent (%) and the degree (°): $30°$, $80\%$.
4. Lowercase unit names; uppercase symbols only when named after a person. Newton (the unit) is written in lower case in prose; its symbol N is capital because Newton (the person) is. So: 7 newtons, 7 N. Likewise: pascal/Pa, hertz/Hz, kelvin/K, ampere/A. But: metre/m, second/s, kilogram/kg — common nouns stay lowercase in both name and symbol.
5. Avoid double prefixes. One nanosecond is $1$ ns, not "$1$ mμs". One picofarad is $1$ pF, not "$1$ μμF". Combine the powers and pick the single prefix that matches.
6. A prefix-plus-symbol is one symbol. So $\mu\text{s}^{-1} = (10^{-6}\text{ s})^{-1} = 10^6 \text{ s}^{-1}$, not $10^{-6} \text{ s}^{-1}$. The entire combination raises to the exponent.

NIOS gives a sharp illustration of why rule 6 matters: $1$ poise $= 1$ g s$^{-1}$ cm$^{-1}$. The negative-exponent notation forces clarity that "g/s/cm" hides.

Non-SI units NEET students still need

The SI is the official system, but several non-SI units are accepted alongside it because they are entrenched in particular domains. NEET physics — especially modern physics, astronomy and atomic-scale questions — uses these regularly. Master the conversion factors; do not memorise more than the table.