PHYSICS | Fundamental SI Units of Measurement, SI Derived Units, Names and Symbols

Si units

SI Units

Standards and Units (abbreviated as SI Units): Laws of physics are expressed in terms of physical quantities such as time, force, temperature, density and numerous other parameters. Physical quantities are often divided into fundamental and derived quantities. Derived quantities arc those whose definitions are based on other physical quantities, e.g., speed, area, density, etc. Fundamental quantities are not defined of other physical quantities, e.g., length, mass and time.

The International System of Units, inspired by the metric system, is the most widely used system of units in the world; but it is not officially used in the United States, Liberia, and Burma.

Fundamental SI Units

Base quantityNameSymbol
Electric currentAmpereA
Amount of substanceMolemol
Luminous intensityCandelacd

Derived SI Units

Other quantities, called derived quantities, are defined in terms of the seven base quantities via a system of quantity equations. The SI derived units for these derived quantities are obtained from these equations and the seven SI base units. Examples of such SI derived units are given in the following table, where it should be noted that the symbol 1 for quantities of dimension 1 such as mass fraction is generally omitted.

Examples of SI Derived Units

SI derived unit
Derived quantityNameSymbol
AreaSquare meterm2
VolumeCubic meterm3
Speed, velocityMeter per secondm/s
AccelerationMeter per second squaredm/s2
Wave numberReciprocal meterm-1
Mass densityKilogram per cubic meterKg/m3
Specific volumeCubic meter per kilogramm3/kg
Current densityAmpere per square meterA/m2
Magnetic field strengthAmpere per meterA/m
Amount-of-substance concentrationMole per cubic metermol/m3
LuminanceCandela per square metercd/m2
Mass fractionKilogram per kilogram, which may be represented by the number 1kg/kg=1

For ease of understanding and convenience, 22 SI derived units have been given special names and symbols, as shown in the following table.

SI derived units with special names and symbols

Derived quantityNameSymbolExpression in terms of other SI units
Plane angleradianrad
Solid anglesteradiansr
Pressure, stresspascalPaN/m2
Energy, work, quantity of heatjouleJN.M
Power, radiant fluxwattWJ/s
Electric charge, quantity of electricitycoulombC
Electric potential difference, electromotive forceVoltVW/A
Electric resistanceohmV/A
Electric conductancesiemensSA/V
Magnetic fluxweberWbV.s
Magnetic flux densityteslaTWb/m2
Celsius temperaturedegree CelsiusoC
Activity (of a radionuclide)becquerelBq
Absorbed dose, specific energy (imparted), kermagrayGyJ/kh
Dose equivalentsievertSvJ/kg

Some commonly used units other than SI units

  • Light years: the light year is a unit of length and is equal to the distance travelled by light in one year. It is used to express large astronomical distance like the distance between the sun and earth etc. 1 light year = 9.46 x 1015m
  • An Astronomical Unit (A.U) is the mean distance from the centre of the earth to centre of the sun. 1 A. U = 1.495 x 1011 m.
  • F. P. S system is used in Britain, where length is measured in Foots, mass in pounds and time in Seconds.
  • In C.G.S system, length is measured in Centimeter, mass in Grams and time in Seconds.
  • Barrel is the internationally used unit for measuring the volume of crude oil. 1 Barrel = 159 Litres.

Base Units

The SI base units are the building blocks of the system and all the other units are derived from them.

The base units of the International System are the seven independent units of measurement (or fundamental units) of the International System from which all other units, called derived units, are obtained by dimensional analysis.

These units are assumed to be independent insofar as they make it possible to measure independent physical quantities. However, the definition of a unit may involve that of other units.

SI base unit

sTtimeThe duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
metremLlengthThe distance travelled by light in vacuum in 1/299792458 second.
kgMmassThe kilogram is defined by setting the Planck constant h exactly to 6.62607015×10−34 J⋅s (J = kg⋅m2⋅s−2), given the definitions of the metre and the second.
ampereAIelectric currentThe flow of exactly 1/1.602176634×10−19 times the elementary charge e per second.Equalling approximately 6.2415090744×1018 elementary charges per second.
The kelvin is defined by setting the fixed numerical value of the Boltzmann constant k to 1.380649×10−23 J⋅K−1, (J = kg⋅m2⋅s−2), given the definition of the kilogram, the metre, and the second.
molemolNamount of
The amount of substance of exactly 6.02214076×1023 elementary entities.[n 3] This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol−1.
The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 5.4×1014 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.
  1. ^ Within the context of the SI, the second is the coherent base unit of time, and is used in the definitions of derived units. The name “second” historically arose as being the 2nd-level sexagesimal division (​1602) of some quantity, the hour in this case, which the SI classifies as an “accepted” unit along with its first-level sexagesimal division the minute.
  2. ^ Despite the prefix “kilo-“, the kilogram is the coherent base unit of mass, and is used in the definitions of derived units. Nonetheless, prefixes for the unit of mass are determined as if the gram were the base unit.
  3. ^ When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

Derived units

SI derived units with special names and symbols
NameSymbolQuantityIn SI base unitsIn other SI units
radianradplane anglem/m1
steradiansrsolid anglem2/m21
newtonNforce, weightkg⋅m⋅s−2
pascalPapressure, stresskg⋅m−1⋅s−2N/m2
jouleJenergy, work, heatkg⋅m2⋅s−2N⋅m = Pa⋅m3
wattWpower, radiant fluxkg⋅m2⋅s−3J/s
coulombCelectric charges⋅A
voltVelectrical potential difference (voltage), emfkg⋅m2⋅s−3⋅A−1W/A = J/C
ohmΩresistance, impedance, reactancekg⋅m2⋅s−3⋅A−2V/A
siemensSelectrical conductancekg−1⋅m−2⋅s3⋅A2Ω−1
weberWbmagnetic fluxkg⋅m2⋅s−2⋅A−1V⋅s
teslaTmagnetic flux densitykg⋅s−2⋅A−1Wb/m2
degree Celsius°Ctemperature relative to 273.15 KK
lumenlmluminous fluxcd⋅srcd⋅sr
becquerelBqradioactivity (decays per unit time)s−1
grayGyabsorbed dose (of ionising radiation)m2⋅s−2J/kg
sievertSvequivalent dose (of ionising radiation)m2⋅s−2J/kg
katalkatcatalytic activitymol⋅s−1

  1. Jump up to:a b The radian and steradian are defined as dimensionless derived units.
Examples of coherent derived units in terms of base units
NameSymbolDerived quantityTypical symbol
square metrem2areaA
cubic metrem3volumeV
metre per secondm/sspeed, velocityv
metre per second squaredm/s2accelerationa
reciprocal metrem−1wavenumberσ
vergence (optics)V, 1/f
kilogram per cubic metrekg/m3densityρ
kilogram per square metrekg/m2surface densityρA
cubic metre per kilogramm3/kgspecific volumev
ampere per square metreA/m2current densityj
ampere per metreA/mmagnetic field strengthH
mole per cubic metremol/m3concentrationc
kilogram per cubic metrekg/m3mass concentrationργ
candela per square metrecd/m2luminanceLv
Examples of derived units that include units with special names
NameSymbolQuantityIn SI base units
pascal-secondPa⋅sdynamic viscositym−1⋅kg⋅s−1
newton-metreN⋅mmoment of forcem2⋅kg⋅s−2
newton per metreN/msurface tensionkg⋅s−2
radian per secondrad/sangular velocity, angular frequencys−1
radian per second squaredrad/s2angular accelerations−2
watt per square metreW/m2heat flux density, irradiancekg⋅s−3
joule per kelvinJ/Kentropy, heat capacitym2⋅kg⋅s−2⋅K−1
joule per kilogram-kelvinJ/(kg⋅K)specific heat capacity, specific entropym2⋅s−2⋅K−1
joule per kilogramJ/kgspecific energym2⋅s−2
watt per metre-kelvinW/(m⋅K)thermal conductivitym⋅kg⋅s−3⋅K−1
joule per cubic metreJ/m3energy densitym−1⋅kg⋅s−2
volt per metreV/melectric field strengthm⋅kg⋅s−3⋅A−1
coulomb per cubic metreC/m3electric charge densitym−3⋅s⋅A
coulomb per square metreC/m2surface charge density, electric flux density, electric displacementm−2⋅s⋅A
farad per metreF/mpermittivitym−3⋅kg−1⋅s4⋅A2
henry per metreH/mpermeabilitym⋅kg⋅s−2⋅A−2
joule per moleJ/molmolar energym2⋅kg⋅s−2⋅mol−1
joule per mole-kelvinJ/(mol⋅K)molar entropy, molar heat capacitym2⋅kg⋅s−2⋅K−1⋅mol−1
coulomb per kilogramC/kgexposure (x- and γ-rays)kg−1⋅s⋅A
gray per secondGy/sabsorbed dose ratem2⋅s−3
watt per steradianW/srradiant intensitym2⋅kg⋅s−3
watt per square metre-steradianW/(m2⋅sr)radiancekg⋅s−3
katal per cubic metrekat/m3catalytic activity concentrationm−3⋅s−1⋅mol


A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The prefix kilo-, for example, may be added to gram to indicate multiplication by one thousand: one kilogram is equal to one thousand grams. The prefix milli-, likewise, may be added to metre to indicate division by one thousand; one millimetre is equal to one thousandth of a metre.

The BIPM specifies 20 prefixes for the International System of Units (SI):

SI prefixes

PrefixBase 10DecimalEnglish wordAdoption
NameSymbolShort scaleLong scale
yottaY 10241000000000000000000000000 septillion quadrillion1991
zettaZ 10211000000000000000000000 sextillion trilliard1991
exaE 10181000000000000000000 quintillion trillion1975
petaP 10151000000000000000 quadrillion billiard1975
teraT 10121000000000000 trillion billion1960
gigaG 1091000000000 billion milliard1960
megaM 1061000000 million1873
kilok 1031000 thousand1795
hectoh 102100 hundred1795
decada 10110 ten1795
 1001 one
decid 10−10.1 tenth1795
centic 10−20.01 hundredth1795
millim 10−30.001 thousandth1795
microμ 10−60.000001 millionth1873
nanon 10−90.000000001 billionth milliardth1960
picop 10−120.000000000001 trillionth billionth1960
femtof 10−150.000000000000001 quadrillionth billiardth1964
attoa 10−180.000000000000000001 quintillionth trillionth1964
zeptoz 10−210.000000000000000000001 sextillionth trilliardth1991
yoctoy 10−240.000000000000000000000001 septillionth quadrillionth1991
  1. ^ Prefixes adopted before 1960 already existed before SI. The introduction of the CGS system was in 1873.
  • 5 cm = 5×10−2 m = 5 × 0.01 m = 0.05 m.
  • 9 km2 = 9 × (103 m)2 = 9 × (103)2 × m2 = 9×106 m2 = 9 × 1000000 m2 = 9000000 m2.
  • 3 MW = 3×106 W = 3 × 1000000 W = 3000000 W.

Non-SI units accepted for use with SI

Many non-SI units continue to be used in the scientific, technical, and commercial literature. Some units are deeply embedded in history and culture, and their use has not been entirely replaced by their SI alternatives. The CIPM recognised and acknowledged such traditions by compiling a list of non-SI units accepted for use with SI:

While not an SI-unit, the litre may be used with SI units. It is equivalent to (10 cm)3 = (1 dm)3 = 10−3 m3.

Some units of time, angle, and legacy non-SI units have a long history of use. Most societies have used the solar day and its non-decimal subdivisions as a basis of time and, unlike the foot or the pound, these were the same regardless of where they were being measured. The radian, being 1/ of a revolution, has mathematical advantages but is rarely used for navigation. Further, the units used in navigation around the world are similar. The tonne, litre, and hectare were adopted by the CGPM in 1879 and have been retained as units that may be used alongside SI units, having been given unique symbols. The catalogued units are given below:

Non-SI units accepted for use with SI units

QuantityNameSymbolValue in SI units
timeminutemin1 min = 60 s
hourh1 h = 60 min = 3600 s
dayd1 d = 24 h = 86400 s
lengthastronomical unitau1 au = 149597870700 m
plane and
phase angle
degree°1° = (π/180) rad
minute1′ = (1/60)° = (π/10800) rad
second1″ = (1/60)′ = (π/648000) rad
areahectareha1 ha = 1 hm2 = 104 m2
volumelitrel, L1 l = 1 L = 1 dm3 = 103 cm3 = 10−3 m3
masstonne (metric ton)t1 t = 1 000 kg
daltonDa1 Da = 1.660539040(20)×10−27 kg
energyelectronvolteV1 eV = 1.602176634×10−19 J
ratio quantities
neperNpIn using these units it is important that the nature of the quantity be specified and that any reference value used be specified.

These units are used in combination with SI units in common units such as the kilowatt-hour (1 kW⋅h = 3.6 MJ).

Photon is Boson with γ (gamma) Symbol in Physics

Photo credit: International Bureau of Weights and Measures (BIPM) / Wikipedia

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