Si derived units

1. SI DERIVED UNITS
A 6.1 Some SI Derived Units expressed in SI Base Unita
SI Unit
Physical quantity
Symbol1
Name
square metre
cubic metre
m2
Area
Volumee
m
Speed, velocity
Angular velocity i
Acceleration
metre per second
radian per second
metre per second
m/s o m s-l
rad/s or rad s-1
m/s2 or ms-2
square
radian per second rad/s2 or rad s-2
Angular acceleration
Square
per metre
kilogram per cubic
m-1
Wave number
Density, mass density kg/m3 or kg m-3
metre
A/m2 or A m2
Current density ampere per square
metre
Magnetic field strength, magnetic ampere per metre
intensity, magnetic moment
density
Concentration (of amount of
substance)
Specific volume
A/m or A m-1
mole per cubic metre mol/m3 or mol mn3
m3/kg or m3 kg
cubic metre per
kilogram
candela per square
Luminance, intensity of
illumination
cd/m2 or cd m2
metre
Kinematic viscosity square metre per m2/s or m2 s-
second
Momentum kilogram metre per kg m s
secondd
Moment of inertia
Radius of gyration
Linear/superficial/volume
expansivitles
Flow rate
kilogram square metre kg m
metre m
per kelvin K-1
cubic metre per m3 s-l
second

2. ENDICES
A 6.2 SI Derived Units with special names
Physical quantity SI Unit
Expression in
terms of other
Expression in
terms of SI
base Units
Name Symbol
units
s1
Frequency hertz Hz
kg m s2 or
kg m/s2
Force newtona N
kg m-l s2 or
kg /s2 mn
kg m2 s-2 or
kg m2/s2
kg m2 s-3or
kg m2/s3
Pressure, stressS pascal N/m2 or N m-2
Pa
N m
Energy, work, quantity of
heat
joule J
Power, radiant flux W J/s or J s-l
watt
As
Quantity of electricity,
electric charge
Electric potential,
potential difference,
electromotive force
coulomb C
kg m2s 3 A-l or
kg m2/s3 A
volt V W/A or WA-1
Capacitance
Electric resistance
A2 s4 kg1 m2
C/V
/A
4/
Vs orJ/A
Wb/m2
farad
kgm2 s-3 A-2
m-2 kg-1 s3 A2
kg m2 s2 A-1
kg s-2 A-1
ohm
Conductance siemens S
Magnetic flux
Magnetic field, magnetiC
flux density, magnetic
induction
weber Wb
tesla T
Inductance
henry kg m2 s-2 A2
cd /sr
H Wb/A
Luminous flux, luminouss lumen Im
power
Tiluminance
Activity(of a radioo
nuclide/radioactive
source)
lux lm/m2 m2 cd sr-1
becquerel Bq S-1
Absorbed dose, absorbed
dose index
gray Gy J/kg m2/s2 or m2 s-2
A6.3 Some SI Derived Units expressed by means of SI Units with special n a
SI Unit
Physical quantity Name Symbol Expression in
terms of SI
base units
m A
Magnetic moment
Dipole moment
Dynamic viscosity
Joule per tesla
coulomb metre
JT
C m sAm
poiseiulles or pascal
second or newton
Pl or Pa s or m kg s
N s m
second per square
metre
Torque, couple, moment
offorce
Surface tension
Power density,
iradiance, heat flux
density
newton metre N m m kgs
newton permetre
watt per squaremetre
N/m
W/m
kg s
kg s

3. Joule per kelvin
joule per kilogram
kelvin
J/K
J/kg K
m kg s K
m s K
Heat capacity, entropy
Specific heat capacity,
specific entropy
Specific energy, latent
heat
J/kg ms
joule per kilogramn
Radiant intensity
Thermal conductivity
Energy density
Electric field strength
Electric charge density
watt per steradian
watt per
metre kelvin
joule per cubic nmetre
volt per metre
coulomb per cubic
metre
W sr
Wm' K
J/m
V/m
C/m
kgm s sr
m kgs' K
kg m* s*
m kg s' A
m As
coulomb per square C/m m As
Electric flux density
metre
Permittivity
Permeability
Molar energy
Angular momentum,
Planck's constant
farad per metre
henry per metre
joule per mole
joule second
F/m
H/m
J/mol
m kg' s'A
m kgs* A
m kgs'mol
kg m' s
Js
J/mol K m kgs*K
mol
joule per mole kelvin
Molar entropy, molar
heat capacity
coulomb per kilogram C/kg kg' s A
Exposure (x-rays and
rays
Absorbed dose rate gray per second Gy/s m's
Pa
newton per square N/m or Nm kgm' s
Compressibility per pascal m kg' s
Elastic moduli
metre
Pressure gradienat pascal per metre Pa/m or Nm* kg m* s
Surface potential
joule per kilogramn m s*
J/kg orr
Nm/kg
Pressure energy
Impulse
Angular impulse
Specificresistance
Surface energy
kg m s
kgms
kg m's
kg m s A
kg s
pascal cubic metre Pa m or N m
newton second Ns
newton metre second Nms
ohm metre Qm
joule per square metre J/m or N/m

4. D I M E N S I O N A L F O R M U L A
Relationship with other
physical quantities
UANTITTES
Dimensions
imensional
Physical quantity
formula
S. No
Length x breadth
M 1T
Area
Length x breadth x height L' M°L T
Volume
Mass/volume [MV[L'] or[ML') ML'T
Mass density
1/timeperiod VIT [M° LT'
Frequency
Displacement/time [LIT M°LT'
Velocity, speed
Velocity /time Lr V[T] MLT
Acceleration
Mass x acceleration [M]LT' [M LT'
Force
Forcex time [M LT IT] [M LT'
Impulse
Forcexdistance MLT'1 L MLTT
Work, Energy
Work/time [MLTV [T [MLT]
10. Power
Mass xvelocity [M [LT' MLT
11
Momentum
Force/area [M LT VL [MLT
12.
Pressure, stress
Change in dimension L]/[L] or[L'j/[Lj M°LT
13 Strain
Oringinal dimension
MLT
[MLT
IM°L°T°]
14 Modulus ofelasticity Stress/strain
Surface tension Force/length [MLT VLI [MLT
15
Surface enerEy Energy/area [MLTVL MLT
16.
Velocity Velocity/distance [LTVL) MLT
17.
gradient
18 Pressure gradient Pressure/distance [MLT*V [MLT
19. Pressure energy Pressure x volume [MLT][L [MLT
20 Coefficient of
MLT
Force/area x velocityY
gradient
[MLT
LLT/LI
viscosity
21 Angle, Angular
displacement
[M'LTI
Arc/radius [L[LI
22 M'LT
Trigonometric ratio
(sine, cos0, tan6, etc.)
Length/length [LVILI
23 Angular velocity Angle/time L"VT] [M'L'TT

5. P P E N D I C E S
Angular acceleration Angular velocity/time TVT (M°LT'I
Radius of gyration L) [M'LT
Distance
Moment ofinertia Mass x (radius ofgyration [M][L'] [MI T
26
IMI T'
Moment of inertia x angular [ML'JIT'I
velocity
27 Angular momentum
Moment of force, Force x distance (MLT'J[LJ ML T'
28,
moment ofcouple
Torque Angular momentum/time, [ML'T']/[T] IML T'
Or or
Force x distance
[MLT' JL
30 Angular frequency 21t Frequency [T'] MLT
Wavelength Distance [L MLT
31.
Hubble constant Recession speed/distance LT'VLI MLT
Intensity ofwave Energy/timeyarea MIL' TTVLL'1 ML'T
Radiation pressure Intensityof wave
Speedoflight
[MTVLT' MLT1
34.
35 Energy density Energy/volume [MILTy L1 MLT
36. Critical velocity Reynold's umber x coefficient of viscocity
M°1T°MLT
[MLILI
[MLT'
Mass density x radius
37 Escape velocity (2 acceleration due to
gravity xearth'sradius) 2
[LTx[L MLT']
Heat energy, internal Work (Force x distance)
[MLT ]L] ML T
38.
energy
Kinetic energy (1/2) mass x (velocity) [M] [LT'} [MLT
40 Potential energy Mass x acceleration
due to gravity x height
[M LTIL [ML T
41 Rotational kinetic 4* moment ofinertia x
(angular velocityy
[ML'T][M }x[T"f ML'T
energy
42.
Efficiency [MLT*
Output work orenerg8y
Input work or energy
ML'T
[ML'T* 1
49 Angular impulse Torque x time [ML'T'1(T MLTI
44
Gravitational IMLT 1LC
M IM
Forcex(distance M'LT)
constant mass mass
Planck constant Energy/trequency [ML'T)/T [ML'T'1

6. PHYSICS
[ML TV[K]
Heat energy/temperature
MIT K
Heat capacity,
46
entropy
HeatEnergy [MLTVIMIK]
[MLTK
Specific heat capacity
Mass x temperature
[ML TVM
Heat energy/mass
[ML T
Latent heat
LI/LIK]
Changeindimension
Original dimensionx temperature [MLK 1
9
Thermal expansion
coefficient or
Thermal expansivity
[MLTIIL)
HeatenegY *thickness
Area x temperature x time MLTK'
S0
Thermal conductivity
Volume x(changeinpressure)
(changein volume)
Lj[ML 'T*]
[L
[MLT)
Bulk modulus
or(compressibility)
(Velocity) lradius [LT' /[L] [M'LT
Centripetal
acceleration
(Energy/areaxtime))
(Temperature)
[MT
(T] K
M TK
Stefan constant
Wavelength x temperature L [K) M LT°K
Wien constant
Energy/temperature [MIL T*VK] LML' TK1
Boltzmann constant
[MLTL
mol) [K]
[MTK
Pressurexvolume
mole xtemperature
Universal gas
constant
mol ]
Charge Currentx time [A] [T [MLTA]
Current density Current/area [A]/[L' MLTA
Work/charge [ML'TV[AT] ML TA]
Voltage, electric
potential,
electromotive force
59
ML T A
IMLT A']
[A
60 Resistance Potential difference
Current
61 Capacitance Charge/potential difference
[ML'T A
[AT]
[ML T'A]
ML' T A
[ML' TA*]
LVLI
62 Electrical
resistivity
or (electrical
Resistance x area
length
conductivity'
Electric field IMLTA
Electrical force/charge [MLTV[AT]
64 Electric flux EML T A"]
Electric ficld xarea MLT AL']

7. [M LTA]
Electric dipole Torque/electric field [ML T
65
moment (MLT' A"]
[MLTA*
Electricfield strength
or electric intensity
[ML'TA)
L
66.
Potential difference
distance
[MLTV[A]L) MLTA
Magnetic field,
magnetic flux density,
magnetic induction
67. Force
Current length
[MTA) L MLTA1
68 Magnetic flux Magnetic field xarea
[MT AA
Magnetic fux
Current
[ML'TA"
[A]
69 Inductance
Torque/magneticfield [MLT]/[MT A*][M'LTA}
70 Magnetic dipole
moment
or Or
CuITentxarea
AJL
L'A]
'
MLTAJ
Magnetic moment
Magnetic field
strength, magnetic
intensity or magnetic
moment density
Volumee
MLTA
Permittivity constant Charge x charge
[AT][AT]
[MLTJLF
(offree space) 4T xelectricforcex (distance)
Permeability constant
(of free space)
[M°L'TIMLTIUMTA
[A][AJL]
27 forcexdistance
current currentxlength
LT LT] [M°LT]
Speedofightinvacuum
Speed oflightinmedium
Refractive index
[ATmol] M'LTAmol
Avogadro constantx
elementary charge
Faraday
constant
27t/wavelength [MLT|/[ [MLT
Wave number
[MLTV[T] MI'T
Radiant flux, RadiantBnergyemitted/time
power
[ML'T/ [M°LTI IML T
Luminosity ofradiant Radiant powerorradiantfhusofsource
flux or radiant
18
Solid angle
intensity
[ML TVIT [MLT
Luminous energy emited
Luminous power or
luminous flux of time
Source

8. [ML T']
[MLT
2 Luminousflux
ML T
Luminousintensityor
illuminatingpowerof
Soildangie
80.
[ML' TVL
[ML'T
S O u r c e
Luninous intensity
Intensityof
illumination or
81
(distance)
[ML'T]
[MILT']
luminance
Luminous fiux ofa source of
gvenwavelength
Juminous filx ofpeaksensitivityy
wavelength (555 nm) source of
same powver
MLT)
82
Relative luminosity
[ML' T/[MLT] MLT
Total luminous flux
83.
Luminous efficiency
Total radiant flux
Luminous flux incident
[MLTVL [ML'T)
Iluminance or
illumination
84 area
(sum ofmasses ofnucleons)-
(mass ofthe nucleus)
[M
[ML'T
85. Mass defect
Binding energy of
nucleus
Mass defect x (speed oflight [M[LTr
in vacuum
86. [ML' T']
Decay constant 0.693/halflife [T] [MLT
87.
88. Resonant frequency [M'L' A°T
(Inductance x capacitance) 2
[MLTA?
[MLTA?J
89 Quality factor or Q
factor of coil
Resonant frequency x inductance
[T]MLTA] [M'LT]
Resistance
[MLPTA
90 Power of lens (Focallength
[ML'T]
91.
Magnification Image distance
Object distance
[L]/L] [M'LT]
92 Fluid flow rate
(T/8) (pressure)x (radius
viscosity coefficient)x length
(ML T] M'L'T]
IML'T] li
93
Capacitive reactance (Angular frequency x
capacitance ITTM'L'T'AT' [MLT A
94
Inductive reactance
(Angular frequency x
inductance) ITIML T A) [MLT A