Units, Measurements & Scientific Instruments Module

SI Base & Derived Units

The International System of Units (SI), maintained by the General Conference on Weights and Measures (CGPM), standardizes scientific measurement across seven base physical quantities: meter (length), kilogram (mass), second (time), ampere (electric current), kelvin (thermodynamic temperature), mole (amount of substance), and candela (luminous intensity). The historic 2019 redefinition grounded these units entirely in fundamental invariants, including the Planck constant ( $h$ ), speed of light ( $c$ ), and elementary charge ( $e$ ). Derived units quantify complex physical interactions, expressing force in Newtons ( $kg\\\\cdot m/s^2$ ), pressure in Pascals ( $N/m^2$ ), electrical potential in Volts ( $W/A$ ), and capacitance in Farads ( $C/V$ ). Competitive examinations regularly assess base dimensions, prefix multiples from pico- to tera-, and dimensional consistency in physical equations.

Practice Topic MCQs All Category Topics

Key Concepts & Examination Highlights

The seven SI base units are meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), and candela (cd).
The 2019 CGPM redefinition fixed the numerical value of Planck's constant at exactly $6.62607015 \times 10^{-34} J\cdot s$ to define the kilogram.
Pressure is measured in Pascals ( $Pa$ ), where $1 Pa = 1 N/m^2 = 1 kg\cdot m^{-1}\cdot s^{-2}$ .
Electrical capacitance is expressed in Farads (F), defined as one Coulomb of charge per Volt of potential difference.
Magnetic flux density (magnetic field strength) is measured in Tesla (T), where one Tesla equals one Weber per square meter ( $1\ ext{ T} = 1\ ext{ Wb/m}^2 = 1\ ext{ N}/(\ ext{A}\cdot\ ext{m})$ ).
Luminous flux is measured in lumens (lm), while illuminance (luminous flux incident on a surface per unit area) is measured in lux (lx, where $1\ ext{ lx} = 1\ ext{ lm/m}^2$ ).
Radioactive decay activity is measured in Becquerels (Bq), defined as one nuclear disintegration per second, whereas absorbed radiation dose is measured in Grays (Gy).
The SI derived unit of electrical conductance is the Siemens (S), defined as the reciprocal of electrical resistance ( $1\ ext{ S} = 1\ ext{ }\Omega^{-1} = 1\ ext{ A/V}$ ).
Frequency is measured in Hertz (Hz), representing one cycle per second ( $1\ ext{ Hz} = 1\ ext{ s}^{-1}$ ), named after German physicist Heinrich Hertz.
The mole is defined by fixing Avogadro's constant at exactly $6.02214076 \times 10^{23}$ elementary entities per mole.
Plane angle is measured in radians (rad) and solid angle is measured in steradians (sr), both classified as dimensionless SI derived units.
Work and energy are measured in Joules ( $J$ ), where $1\ ext{ J} = 1\ ext{ N}\cdot\ ext{m} = 1\ ext{ kg}\cdot\ ext{m}^2\cdot\ ext{s}^{-2}$ .
Power is measured in Watts ( $W$ ), defined as one Joule per second ( $1\ ext{ W} = 1\ ext{ J/s} = 1\ ext{ kg}\cdot\ ext{m}^2\cdot\ ext{s}^{-3}$ ).
Electric charge is measured in Coulombs ( $C$ ), defined as the amount of charge transported by a constant current of one Ampere in one second ( $1\ ext{ C} = 1\ ext{ A}\cdot\ ext{s}$ ).
Electrical potential difference and electromotive force are measured in Volts ( $V$ ), where $1\ ext{ V} = 1\ ext{ W/A} = 1\ ext{ kg}\cdot\ ext{m}^2\cdot\ ext{s}^{-3}\cdot\ ext{A}^{-1}$ .
Electrical resistance is measured in Ohms ( $\Omega$ ), where $1\ ext{ }\Omega = 1\ ext{ V/A} = 1\ ext{ kg}\cdot\ ext{m}^2\cdot\ ext{s}^{-3}\cdot\ ext{A}^{-2}$ .
Magnetic flux is measured in Webers ( $Wb$ ), where $1\ ext{ Wb} = 1\ ext{ V}\cdot\ ext{s} = 1\ ext{ T}\cdot\ ext{m}^2$ .
Inductance is measured in Henrys ( $H$ ), defined as the magnetic flux per unit electric current ( $1\ ext{ H} = 1\ ext{ Wb/A} = 1\ ext{ V}\cdot\ ext{s/A}$ ).
Dynamic viscosity is measured in Pascal-seconds ( $\ ext{Pa}\cdot\ ext{s}$ or $\ ext{kg}\cdot\ ext{m}^{-1}\cdot\ ext{s}^{-1}$ ), while the CGS unit is poise ( $1\ ext{ Pa}\cdot\ ext{s} = 10\ ext{ poise}$ ).
Kinematic viscosity is measured in square meters per second ( $\ ext{m}^2/\ ext{s}$ ), with the corresponding CGS unit being the stokes ( $1\ ext{ stokes} = 10^{-4}\ ext{ m}^2/\ ext{s}$ ).
The speed of light in vacuum is an exact SI defining constant fixed at $c = 299,792,458\ ext{ m/s}$ , defining the length of the meter.
The unperturbed ground-state hyperfine transition frequency of the Caesium-133 atom is fixed at $\Delta\nu_{\ ext{Cs}} = 9,192,631,770\ ext{ Hz}$ to define the second.
The Boltzmann constant is fixed at exactly $k = 1.380649 \times 10^{-23}\ ext{ J}\cdot\ ext{K}^{-1}$ to define the kelvin.
The elementary charge is fixed at exactly $e = 1.602176634 \times 10^{-19}\ ext{ C}$ to define the ampere.
Surface tension is measured in Newtons per meter ( $\ ext{N/m}$ ) or Joules per square meter ( $\ ext{J/m}^2$ ), having dimensions $[M T^{-2}]$ .
The International System of Units (SI) defines seven fundamental base units: meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), and candela (cd).
The 2019 SI redefinition anchored all base units to seven invariant fundamental constants, including the Planck constant ( $h$ ) and elementary charge ( $e$ ).
The derived SI unit of force is the Newton (N), defined dimensionally as $1\ ext{ N} = 1\ ext{ kg}\cdot\ ext{m}/\ ext{s}^2$ ( $[M L T^{-2}]$ ).
The derived SI unit of energy, work, and quantity of heat is the Joule (J), equal to one Newton-meter ( $1\ ext{ J} = 1\ ext{ N}\cdot\ ext{m} = 1\ ext{ kg}\cdot\ ext{m}^2/\ ext{s}^2$ ).
The derived SI unit of power is the Watt (W), equal to one Joule per second ( $1\ ext{ W} = 1\ ext{ J}/\ ext{s} = 1\ ext{ kg}\cdot\ ext{m}^2/\ ext{s}^3$ ).
The derived SI unit of pressure and mechanical stress is the Pascal (Pa), defined as one Newton per square meter ( $1\ ext{ Pa} = 1\ ext{ N}/\ ext{m}^2$ ).
The derived SI unit of electrical potential difference and electromotive force is the Volt (V), equal to one Joule per Coulomb ( $1\ ext{ V} = 1\ ext{ W}/\ ext{A}$ ).
The derived SI unit of electrical resistance is the Ohm ( $\Omega$ ), defined as one Volt per Ampere ( $1\,\Omega = 1\ ext{ V}/\ ext{A}$ ).
The derived SI unit of electrical conductance is the Siemens (S), equal to the reciprocal of resistance ( $1\ ext{ S} = 1/\Omega$ ).
The derived SI unit of electrical capacitance is the Farad (F), defined as one Coulomb per Volt ( $1\ ext{ F} = 1\ ext{ C}/\ ext{V}$ ).
The derived SI unit of magnetic flux is the Weber (Wb), equal to one Volt-second ( $1\ ext{ Wb} = 1\ ext{ V}\cdot\ ext{s}$ ).
The derived SI unit of magnetic flux density (magnetic field) is the Tesla (T), defined as one Weber per square meter ( $1\ ext{ T} = 1\ ext{ Wb}/\ ext{m}^2$ ).
The derived SI unit of electrical inductance is the Henry (H), defined as one Weber per Ampere ( $1\ ext{ H} = 1\ ext{ Wb}/\ ext{A}$ ).
The derived SI unit of frequency is the Hertz (Hz), representing one cycle or periodic event per second ( $1\ ext{ Hz} = 1\ ext{ s}^{-1}$ ).
The derived SI unit of luminous flux is the Lumen (lm), defined as candela times steradian ( $1\ ext{ lm} = 1\ ext{ cd}\cdot\ ext{sr}$ ).
The derived SI unit of illuminance is the Lux (lx), defined as one lumen per square meter ( $1\ ext{ lx} = 1\ ext{ lm}/\ ext{m}^2$ ).
The derived SI unit of radioactivity is the Becquerel (Bq), representing one radioactive disintegration per second ( $1\ ext{ Bq} = 1\ ext{ s}^{-1}$ ).
The derived SI unit of absorbed ionizing radiation dose is the Gray (Gy), defined as one Joule per kilogram ( $1\ ext{ Gy} = 1\ ext{ J}/\ ext{kg}$ ).
The derived SI unit of equivalent radiation dose and effective dose is the Sievert (Sv), dimensionally equal to $1\ ext{ J}/\ ext{kg}$ with biological weighting.
The derived SI unit of catalytic activity in biochemistry is the Katal (kat), defined as one mole of substrate converted per second ( $1\ ext{ kat} = 1\ ext{ mol}/\ ext{s}$ ).
The two dimensionless supplementary SI units are the Radian (rad) for plane angle and the Steradian (sr) for solid angle.
The universal gravitational constant ( $G$ ) has the SI derived unit of $\ ext{N}\cdot\ ext{m}^2/\ ext{kg}^2$ and dimensional formula $[M^{-1} L^3 T^{-2}]$ .
Planck's constant ( $h$ ) has the SI unit of Joule-second ( $\ ext{J}\cdot\ ext{s}$ ) and dimensional formula $[M L^2 T^{-1}]$ .
Surface tension has the SI derived unit of Newton per meter ( $\ ext{N}/\ ext{m}$ ) and dimensional formula $[M T^{-2}]$ .
Coefficient of dynamic viscosity has the SI derived unit of Pascal-second ( $\ ext{Pa}\cdot\ ext{s}$ ) or $\ ext{kg}/(\ ext{m}\cdot\ ext{s})$ ( $[M L^{-1} T^{-1}]$ ).

Curriculum & Reference Sources: International Bureau of Weights and Measures (BIPM), National Physical Laboratory (NPL India), IUPAC Green Book

Sample Solved Questions & Concept Explanations

8 Verified Concept Questions

Q1.EASY

What is the SI derived unit of catalytic activity used in biochemistry and enzymology?

Q2.EASY

What is the SI derived unit of illuminance, representing the luminous flux incident per unit area of a surface?

Q3.EASY

In the International System of Units (SI), what is the derived unit of frequency, defined as one cycle per second?

Q4.EASY

What is the SI derived unit of electric charge, defined as the quantity of electricity conveyed in one second by a current of one ampere?

Q5.EASY

What is the SI derived unit of magnetic flux density (or magnetic field strength), named after Nikola Tesla?

Q6.MEDIUM

What is the SI derived unit of magnetic flux, defined as one volt-second (V·s)?

Q7.MEDIUM

In the SI system, what is the derived unit of self and mutual electrical inductance?

Q8.MEDIUM

What is the SI derived unit of electrical conductance and admittance (the reciprocal of electrical resistance, Ω⁻¹)?