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Physical Quantities and Units

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Physical Quantities and Units

Physical Quantities and Units

shape Introduction

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity“. Example: A Length is a physical quantity. The metre is a unit of length that represents a definite predetermined length. 20 metres (or 20 m), we means 20 times the definite predetermined length called “metre”. International System of Units (SI), the modern form of the metric system is now the global standard for Units of Measurement.The article Physical Quantities and Units presents the list of Base Quantities and Derived Quantities and their Units.


shape Quantities

The International System of Units (abbreviated as SI Units from its French name, System International units) is an internationally agreed metric system of units of measurement. SI system has been in existence since 1960. The history of the meter and the kilogram, two of the fundamental units, goes back to the French Revolution. The SI system is based on the concept of seven fundamental base units of quantity, from which all other units of quantity can be derived. By the end of the Second World War, it was increasingly evident that a worldwide system of measurement was required. In 1954, the 10th General Conference on Weights and Measures, proposed a system based on six base quantities. The quantities recommended were the meter, kilogram, second, ampere, kelvin and candela.


Base quantities are those quantities which are distinct in nature and cannot be defined by other quantities. Base quantities are those quantities on the basis of which other quantities can be expressed. The seven base quantities of the International System of Quantities (ISQ) and their corresponding SI units and dimensions are listed in the following table.

Based Quantity Symbol SI Unit Dimension
Amount of substance n mole (mol) N
Electric current I ampere (A) I
Length l metre (m) L
Luminous intensity L candela (cd) J
Mass m kilogram (kg) M
Temperature T kelvin (K) Θ
Time t second (s) T

A derived quantity is a quantity in a system of quantities that is a defined in terms of the base quantities of that system.

Based Quantity Symbol SI Unit Dimension
Absement A m s L T
Absorbed dose rate Gy s−1 L2 T−3
Acceleration a→ m s−2 L T−2
Angular acceleration α rad s−2 T−2
Angular momentum L kg m2 s−1 M L2 T−1
Angular speed ω rad s−1 T−1
Area A m2 L2
Area density ρA kg m−2 M L−2
Capacitance C farad (F = A2 s4 kg−1 m−2) M−1 L−2 T4 I2
Catalytic activity katal (kat = mol s−1) T−1 N
Catalytic activity concentration kat m−3 L−3 T−1 N
Chemical potential μ J mol−1 M L2 T−2 N−1
Crackle c→ m s−5 L T−5
Current density J→ A m−2 L−2 I
Dose equivalent H sievert (Sv = m2 s−2) L2 T−2
Dynamic viscosity η Pa s M L−1 T−1
Electric charge Q coulomb (C = A s) T I
Electric charge density ρQ C m−3 L−3 T I
Electric displacement D C m−2 L−2 T I
Electric field strength E→ V m−1 M L T−3 I−1
Electrical conductance G siemens (S = A2 s3 kg−1 m−2) M−1 L−2 T3 I2
Electrical conductivity σ S m−1 M−1 L−3 T3 I2
Electric potential V volt (V = kg m2 A−1 s−3) M L2 T−3 I−1
Electrical resistance R ohm (Ω = kg m2 A−2 s−3) M L2 T−3 I−2
Electrical resistivity ρ ohm metre (Ω⋅m = kg m3 A−2 s−3) M L3 T−3 I−2
Energy E joule (J = kg m2 s−2) M L2 T−2
Energy Density ρE J m−3 M L−1 T−2
Entropy S J K−1 M L2 T−2 Θ−1
Force F→ newton (N = kg m s−2) M L T−2
Frequency f hertz (Hz = s−1) T−1
Fuel efficiency L−2
Half-life t1/2 s T
Heat Q joule (J) M L2 T−2
Heat capacity Cp J K−1 M L2 T−2 Θ−1
Heat flux density ϕQ W m−2 M T−3
Illuminance Ev lux (lx = cd sr m−2) L−2 J
Impedance Z ohm (Ω = kg m2 A−2 s−3) M L2 T−3 I−2
Impulse J newton second (N⋅s = kg m s−1) M L T−1
Inductance L henry (H = kg m2 A−2 s−2) M L2 T−2 I−2
Irradiance E W m−2 M T−3
Intensity I W m−2 M T−3
Jerk j→ m s−3 L T−3
Jounce (or snap) s→ m s−4 L T−4
Linear density ρl M L−1
Luminous flux (or luminous power) F lumen (lm = cd sr) J
Mach number (or mach) M unitless 1
Magnetic field strength H A m−1 L−1 I
Magnetic flux Φ weber (Wb = kg m2 A−1 s−2) M L2 T−2 I−1
Magnetic flux density B tesla (T = kg A−1 s−2) M T−2 I−1
Magnetization M A m−1 L−1 I
Mass fraction x kg/kg 1
(Mass) Density (or volume density) ρ kg m−3 M L−3
Mean lifetime τ s T
Molar concentration C mol m−3 L−3 N
Molar energy J mol−1 M L2 T−2 N−1
Molar entropy J K−1 mol−1 M L2 T−2 Θ−1 N−1
Molar heat capacity c J K−1 mol−1 M L2 T−2 Θ−1 N−1
Moment of inertia I kg m2 M L2
Momentum p→ N s M L T−1
Permeability μ H m−1 M L T−2 I−2
Permittivity ε F m−1 M−1 L−3 T4 I2
Plane angle θ radian (rad) 1
Power P watt (W) M L2 T−3
Pressure p pascal (Pa = kg m−1 s−2) M L−1 T−2
Pop p→ m s−6 L T−6
(Radioactive) Activity A becquerel (Bq = s−1) T−1
(Radioactive) Dose D gray (Gy = m2 s−2) L2 T−2
Radiance L W m−2 sr−1 M T−3
Radiant intensity I W sr−1 M L2 T−3
Reaction rate r mol m−3 s−1 N L−3 T−1
Refractive index n unitless 1
Solid angle Ω steradian (sr) 1
Speed v m s−1 L T−1
Specific energy J kg−1 L2 T−2
Specific heat capacity c J kg−1 K−1 L2 T−2 Θ−1
Specific volume v m3 kg−1 M−1 L3
Spin S kg m2 s−1 M L2 T−1
Strain ε unitless 1
Stress σ Pa M L−1 T−2
Surface tension γ N m−1 or J m−2 M T−2
Thermal conductivity k W m−1 K−1 M L T−3 Θ−1
Torque τ newton metre (N m) M L2 T−2
Velocity v→ m s−1 L T−1
Volume V m3 L3
Wavelength λ m L
Wavenumber k m−1 L−1
Wavevector k→ m−1 with direction L−1
Weight w newton (N = kg m s−2) M L T−2
Work W joule (J = kg m2 s−2) M L2 T−2
Young’s modulus E pascal (Pa = kg m−1 s−2) M L−1 T−2