# Table of Units and Dimensions of Physical quantities.

Units & Dimensions of Physical quantities in S.I system.

Fundamental Physical Quantities:

 S.No Fundamental Physical Quantity Formula Dimensional Formula S.I Unit of physical quantity 1. Mass Amount of matter in the object M kg 2. Length L meter 3. Time T sec 4. Electric current I or A ampere 5. Amount of substance N mole(mol 6. Luminous intensity J candela(cd) 7. Temperature K or $\theta$ Kelvin

Derived Physical Quantities:

 S.No Derived Physical Quantity Formula Dimensional Formula S.I Unit of physical quantity 1. Area $l\times b$ [$M^0L^2T^o$] $m^2$ 2. Volume $l\times b\times h$ [$M^0L^3T^o$] $m^3$ 3. Density $\frac{M}{V}$ [$M^1L^{-3}T^0$] $kg/m^3$ 4. Specific Gravity $\frac{Density of Substance}{Density of Water}$ [$M^0L^0T^0$] No units 5. Frequency $\frac{no of vibrations}{Time}$ [$M^0L^0T^{-1}$] hertz 6. Angle $\frac{Arc}{radius}$ $M^0L^oT^o$ No units 7. Velocity $\frac{Displacement}{time}$ $M^0L^1T^{-1}$ m/sec 8. Speed $\frac{Distance}{time}$ $M^0L^1T^{-1}$ m/sec 9. Areal velocity $\frac{Area}{time}$ $M^0L^2T^{-1}$ $m^2sec^{-1}$ 10. Acceleration $\frac{Change in velocity }{time}$ $M^0L^1T^{-2}$ $m/sec^2$ 11. Linear momentum $M\times V$ $M^1L^1T^{-1}$ kg m/sec 12. Force $mass\times acceleration$ $M^1L^1T^{-2}$ kg-m/$sec^2$ or Newton 13. Weight w=mg $M^1L^1T^{-2}$ kg-m/$sec^2$ or Newton 14. Moment of force/Torque/Couple $Force\times arm$ $M^1L^2T^{-2}$ kg$m^2sec^{-2}$ 15. Impulse $Force\times time$ $M^1L^1T^{-1}$ kg m/sec or Ns 16. Pressure $\frac{Force}{Area}$ $M^1L^{-1}T^{-2}$ N/$m^2$ or Pa 17. Work $Force\times Distance$ $M^1L^2T^{-2}$ Nm or Joule 18. Kinetic Energy $\frac{1}{2} mv^2$ $M^1L^2T^{-2}$ joule 19. Potential Energy mgh $M^1L^2T^{-2}$ joule 20. Gravitational constant $\frac{Force\times (Length)^2}{(mass)^2}$ $M^{-1}L^3T^{-2}$ $kg^{-1}m^3sec^{-2}$ 21. Gravitational field strength $\frac{Force}{mass}$ $M^0L^1T^{-2}$ $N kg^{-1}$ 22. Gravitational Potential $\frac{Work}{mass}$ $M^0L^2T^{-2}$ $J kg^{-1}$ 23. Force constant (k) $\frac{F}{L}$ $M^1L^0T^{-2}$ $N m^{-1}$ 24. Power $\frac{Work}{time}$ $M^1L^2T^{-3}$ W or J/sec 25. Moment of Inertia ( I ) $Mass\times Distance^2$ $M^1L^2T^{0}$ kg$m^2$ 26. Stress $\frac{Force}{Area}$ $M^1L^{-1}T^{-2}$ N/$m^2$ or Pa 27. Strain $\frac{Change in length}{Origional length}$ $M^0L^0T^0$ No units 28. Modulus of Elasticity $\frac{Stress}{Strain}$ $M^1L^{-1}T^{-2}$ N/$m^2$ or Pa 29. Poission’s Ratio σ =$\frac{Y}{2n}$-1 $M^0L^0T^0$ No units 30. Velocity gradient $\frac{Change in velocity}{Distance}$ $M^0L^0T^{-1}$ $sec^{-1}$ 31. Coefficient of dynamic viscosity $\frac{Tangential stress}{Velocity Gradient}$ $M^1L^{-1}T^{-1}$ kg$m^{-1}sec^{-1}$(or) N-sec/$latex \m^2$ (or)pascal-sec (or)poiseuille 32. Surface Tension $\frac{Force}{Length}$ $M^1L^0T^{-2}$ $kg sec^2$,N/m 33. Angular displacement ($\theta$) $\frac{Arc}{radius}$ $M^0L^oT^o$ no Units 34. Angular velocity(ω) $\frac{Angular displacement}{Time}$ $M^0L^oT^{-1}$ rad/sec 35. Angular acceleration(α) $\frac{Change in angular velocity}{Time}$ $M^0L^oT^{-2}$ rad/$sec^{-2}$ 36. Angular momentum Iω $ML^2T^{-1}$ $kg-m^2 sec^{-1}$ 37. Angular Impulse Iω $ML^2T^{-1}$ $kg-m^2 sec^{-1}$ 38. Temperature $\theta$ or K kelvin or degree Celsius 39. Coefficient of linear expansion(α) $\frac{l_2-l_1}{l_1\times Temp(t_2-t_1)}$ $M^0L^0T^0K^{-1}$ /kelvin 40. Specific heat $\frac{Energy}{Mass\times Temp}$ $M^0L^2T^{-2}K^{-1}$ 41. Latent heat $\frac{Energy}{Mass}$ $M^0L^2T^{-2}$ $joule-kg^{-1}$ 42. Entropy $\frac{Q}\theta$ $M^1L^2T^{-2}K^{-1}$ $J K^{-1}$ 43. Thermal capacity $\frac{H}\theta$ $M^1L^2T^{-2}K^{-1}$ $J K^{-1}$ 44. Gas constant $\frac{PV}{m T}$ $M^0L^2T^{-2}K^{-1}$ $joule-K^{-1}$ 45. coefficient of thermal conductivity $\frac{Qd}{A(\theta_2-\Theta_1)t}$ $M^1L^1T^{-3}K^{-1}$ $W m^{-1}K^{-1}$ 46. Pole strength $Ampere\times meter$ $M^0L^1T^0I$ Am 47. Magnetic Moment $M^0L^2T^0I^1$ $Amp-m^2$ 48. Magnetic flux $\phi$ $ML^2T^{-2}I^{-1}$ weber ;$T-m^{2}$ ;J/Amp 49. Magnetic field,magnetic flux density (B) $MT^{-2}I^{-1}$ Tesla;$J/A-m^{2}$ 50. Permeability of free space $\frac{\mu}{\mu_r}$ $MLT^{-2}I^{-2}$ $NA^{-2}$ 51. Magnetic susceptibilty also called volumetric or bulk susceptibility χm χm = μr − 1 $M^0L^oT^o$ no units 52. Electric Charge $I\times T$ $M^0L^0T^1I^1$ Amp sec , coul 53. Electric potential $\frac{Work}{Charge}$ $M^1L^2T^{-3}I^{-1}$ Volt 54. E.M.F $\frac{Work}{Charge}$ $M^1L^2T^{-3}I^{-1}$ Volt 55. Electric Capacity $\frac{q}{V}$ $M^{-1}L^{-2}T^4I^2$ Farad 56. Electric Resistance $\frac{V}{i}$ $M^1L^2T^{-3}I^{-2}$ Ohm (Ω) or volt/amp 57. Resistivity $\rho$ $\frac{R A}{L}$ $M^1L^3T^{-3}I^{-1}$ Ohm mt (Ω-m) 58. Conductivity $\sigma$ 1/$\rho$ $M^{-1}L^{-3}T^3I$ Siemens/m 59. Permittivity $\varepsilon$ $M^{-1}L^{-3}T^4I^2$ farad/m 60. Electric conductance $\frac{1}{R}$ $M^{-1}L^{-2}T^3I^2$ Siemens (or) mhos 61. Electric power $V\times I$ $M^1L^2T^{-3}I^{-1}$ Watt 62. Electrical Impedance(Z) $\frac{V}{i}$ $M^1L^2T^{-3}I^{-2}$ Ohm (Ω) or volt/amp 63. Electrical admittance 1/Z(Reciprocal of electric impedance) $M^{-1}L^{-2}T^3I^3$ Siemens (or) mhos 64. Self Inductance(L) $\displaystyle v=L\frac{di}{dt}$ $ML^2T^{-2}I{-2}$ weber/amp or Henry 65. Boltzmann’s constant $\frac{Energy}{Temp}$ $M^1L^2T^{-2}K^{-1}$ J/kelvin 66. Stefan’s constant $\frac{E}{At \theta^4}$ $M^1L^0T^{-3}K^{-4}$ $W m^{-2}K^{-4}$ 67. Co-efficient of friction $\mu$ $\mu$=$\frac{F}{N}$,N=Normal reaction dimension less scalar no units 68. Dielectric constant $\varepsilon_r$ It is also called relative permittivity dimension less no units 69. Planck’s constant $E=h\nu$ $ML^2T^{-1}$ J.sec (or) eV.sec 70. Refractive index μ $M^0L^oT^o$ no units 71. Focal length(f) Distance between center of the lens(mirror) to its focus L meter 72. Power of a lens (P) The reciprocal of the focal length of a lens in meters is called power of a lens; p=1/f $L^{-1}$ diaptors 73. Wave number No.of waves/distance $L^{-1}$ $m^{-1}$ 74. Wave length Length of a wave L meter

## 142 thoughts on “Table of Units and Dimensions of Physical quantities.”

1. Its very good.But more dimensional formulae required like Tension and many more…

2. very very good

3. all the dimensional formulas are available in the columns and it is very easy to accomodate them

4. it is very good but i need de dimensional formula of permeability of free space

5. Basheer Bhai

but i also needed that of tension

6. rujuta satta

more dm should b there!!!!!!!!!!!!!

7. lina

dimensional formulas like planck’s constant etc are not available

8. well i expected man more dimensional formulas!

9. Yoz

Good work yaar..
but we need more dimensional formulas….

11. JAsHAn MAan

Gud1,,, BT MOre D.Fs SHud BE Dea,,, Sm r MissINg,, Tnx

12. very good but need more dimensional formulas (umer sn)

13. hum kya chahatay aazadi jis kashmir ko khoon se sencha wo kashmir hamara hai.

14. its really a very good table.

15. mariya maleka

it was very helpful to us but not up 2 the mark

16. aqsa

its nice

17. chand

I am with an I.Com background and now is studing IT Physics and facing a lot of problems in first semester.I was in need of Dimentions of SI units for average learning but reading the table above I have knewed extra ordinary information about dimentions.Thank you very much for this help!!!

18. Milan

I m now studing in class 11 & i m facing lots of problem in physics.

19. haleemah shehu

Wow!!,it really helped with my homework.

20. vivek

sir plz check about the dimensional formula of angular momentum and angular impulse, i hav a doubt wid d gvn infrmtn.

21. Ashish

This is osem. This table help me lot.i

mashALLAH
very very good excelent

23. gyaunnrraje

Name few physical quantities whose dimensional formula’s you want to know.

24. nitesh

here the dimensional formula of density is incorrect as it should be l-3……………..kindly make the changes …..

25. Sudha

It was really very helpful, but i don’t understand the Planck’s constant, can you tell the derivation, I always end up with [M L^2 T^-3]… how does it become T^-1 ? I have a test on monday, please help ! Also I have the same problem with Coefficient of Viscocity, I get M^1 L^-1 T^-3 ! instead of T^-1. Is there some specific reason for this ? :(

26. gyaunnrraje

We can derive dimensional formulas of physical quantities from their units also.Hence, the unit of plank’s constant is Joule-sec ,Joule(Unit of Energy) – D.F is ML^2T^-2 and sec(Unit of time) – D.F is T . If we multiply these two (ML^2T^-2)(T)= ML^2T^-1.Similarly Coefficient of viscosity = . D.F of Stress is M L ^-1 T^-2 and D.F of Velocity is reciprocal of time i.e T^-1.Therefore D.F Of Coefficient of viscosity=(M L ^-1 T^-2)/( T^-1)=M L ^-1 T^-1.Hope this clarifies your doubt.

27. Sudha

:) thank u soo much. i scored full marks in my test !

28. Gulnawaz

Nice they are very helpful thanks

29. jahnavichowdary

yeah its very helpful but i think explanation should be there……………..:-)

[L][M][T-2][A-2] IS DIMENSION FOR PERMEABILITY OF FREE SPACE
HERE
T-2 =PER TIME SQUARE AND SAME FOR A

31. gyaunnrraje

Sorry,I am unable to understand your question.

EXCELLENT CLLECTION OF UNITS ,,,,,,,,,,,,,,,,,,,,,,,,,,,AND THE GOOD THING IS THAT THE ORGANISER OF THIS TABLE LISTENS TO SHORTCOMINGS AND IMPROVES THIS TABLE

33. TUSHAR

it is nicely arranged but some of the formulaes are missing but these formulaes are enough for +1

34. It’s very good and I think it sufficiet to get more DF’s. (D.K.)

35. prayag

now that’s what i wanted . it is the most helpful one

36. Masood

still need alot of formulae to be added here like light intensity etc

37. ruksss

areee….kitni sari..formules hai……….adhi toh tappi bhi nai padti.any easy way 4 tis?2 rembr??????????????????????????????

38. shom

The Formula of “Electric Conductance” is wrong

39. Niket Chaudhary

Can you give me dimensional equations for magnetic quantities.

40. sushmitha

dimensional formula of viscocity?

41. gyaunnrraje

It is there in the table sno:30

42. tarandeep singh

i want the dimension formula of surface tension and citical velocity plz reply as earliar as possible….

43. amit

i love dimension ans uint

44. anku

yr its good but i want more dimensional formula , but i thanks to it becose with the help of table i done my home work ……… Thanks to the formulas

45. good but expected more!!!

46. Mohit Nandan

i m very happy because my problem is solve now. thankyou very much.

47. Helpful fun of knowledge,great work dude,keep going good….

48. karan tiwari

thanks for the formulas

49. i m really feling proud.this techneque i really liked it fantastic fabulous and fantabulous

50. Khawaja javid

Thanks to all who gives these physics material and helps to all in solving the problem:::::::fantastic miss u shaz:::

51. shoib wazir

i need the dimention of tesla and weber that are related to magnetism

52. gyaunnrraje

Mr.Shoib ,Tesla is the unit of flux density and weber is the unit of flux.As desired by you I added these physical quantities to the table as 49& 48 entries respectively.

53. no

54. there r only 72-74 written some more need to be written like ryderberg’s constant!!!!!

55. sarita sharma

its very help full…..
but i can’t understand dimension of stefan constant i think its [M^1L^0T^-3K^-4] not [M1^L^0T^3K^-4] Plz explain……

56. i really liked the table,becoz it is just like the book .thanks a lot .

57. when i lost my very important dimentional table for ,but when i saw this table i really got help from this thanksss…

58. naeem hussain

nice work done .i need some more dimrensions as i am preparing for entry test mcat

59. vinay singh

Can anyone explain me relationship between accleration,radius and velocity using dimensional formulaes?

60. swati

the information is presented in a good which has really helped me

61. yo yo yogesh dhiman

Lazy Way To Succes…..♥

62. srishti

hey nice…:p
aur kya comment karun….

63. varun

wat a table thank u to the 1 who did this

64. Gyanendra mohanty

This is very good and short and very help full for all student

GREAT , IT’S REALLY HELPFUL .THAT WAS MY NEED .WHICH I GET NOW.

66. tooba

what is the dimension of radioactivity

67. WHATS THE DIMENSION OF RESISTIVITY??????????/

68. Ranjeet Mahto

l like this but some thing is less comfortable and this dimention should also express in electrostatic system of unit . And also in eletromegnetic system of unit.

69. rida ramzan

this table helps me alot 4 my entry test preptn thank u so much…

70. k ho yar science ma force ko dimensional formulae k ho

71. Saurabh Chaudhari

Gud table bro. Keep it up!!

72. elizabethpriyangani

haaaaaaaaaaa so huge man……….!!!!!!!!!!!!

73. Really its very easy to learn but if some trics are given to find dimensional formula that’s much better

74. very great site

75. hai myself n.nithin from new delhi this was very nice but somemore amendments like adding more stuff like increasing formulae number but anyway itwas fabulous (nithin nagulakonda b.tech)

76. kisa

really gud dfs usefull thanx !!!

I needed it at the time.

78. zeeshanahmed

very good

79. Rohit wasnik

Dimensions are important.

80. anshul

wt ius meantr by derivation?? :/

81. afnan bangush

Thanks…………. with the help of this table i have done my asignment…………………….need more…….

82. ainee

hahahahahaha, but muje in sub ki zaroorat nahi hai, sab k sub nalayak ho. .bladdyyyy FOOLS. .lol

83. I like ur infos and i want to partner with you.

84. Manish kumar

It is good for student their are many d f

85. Animesh kumar

most table, this is a very good table

86. nice

87. neeruganti Raja sekhar

I like this way of formula seeing. i want it more in several branches scinces.

88. a.k

wwooowww i am so hhppy nw bcoz it very imp

89. manish kumar

i get the great help from here thanks

90. Kunal

What is the dimension of relative velocity?plz answer

91. MANIK GUJJAR

This is good but there is no option for downloadin. so put it in.

92. Ajay

Nice

93. kshithija yangala

itssame as in our +1 texts.needed more plzzzzzz

94. shyam kumar gulabbag

95. Prem vardhan

its nice,very nice

96. it is very good for us because it gave us more knowladge.

97. what is this sign (*) representing

98. Iram

99. yatin

good inst.

100. rahul

Its very help full for a student

101. Fazal ali bugti

And diminsion of e=mc^2 is [ML^2T^-2] and also energy diminsion is [ML^2T^-2]

102. alina

its gud

103. its go0d bt momentum is missing!!!!!!!!!!!!!! :(

104. omkar todewar

nice

105. Akot Mayen

Many thanks for the good work its help us a lot, but kindly elevate some of the dimensional quantities

106. Etim Antai

107. Reeha Malik

plz tell me dimension of g,G,T,K

108. burhan rashid

realy its very helpul

109. Iqra

110. Thankyou brother.

111. Mrunal

nice but something more was needed…..

112. junaid

hlpd me alot… tq :)

113. Ernest Lydia

It was very helpful but i also need that of strain, load and effort

114. sanawar

thanks u these dimensions are helpful for me

115. deepti

this table is osum.helped me a lot. superb
could get all the dimensional formulae needed

116. my a from alam

Nice

117. I am not satisfied…

118. confidence

rubbish!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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120. piyushdatta

Itsssss truly veery very useful

121. Utkrisht

I think electric power should be ML2T-3 and not ML2T-3I-1

122. Sunil

There is no formula for torque

123. veena

still more dimentional formulas are needed like capacitance,resistance e.t.c .

124. Hira

It’s useful but more dimensions should also be given

125. Raja Ravi.

dimensions formula of electrical admittance is incorrect.

126. Sowmya Neelam

It’s really very helpful, Thank you so much…. 😊

127. i want only dimensional formulas of physical quantities in mechanics only (separately)

128. biswajit Biswal

Very good but need more dimensional formulas .

129. gyaunnrraje

Sure,I will try to improve.

130. Rahul Rai

it is very helpful..it is a booklet of formulas…

131. shahid

very good…………….

132. unknown

133. love lorn kamu

not much helpful. ………simply it further. ……along with more derivations

134. shubham mittal

tell me the dimension formula for the SURFACE TENSION if the Velocity, time and energy are fundamental unit

135. Anjali

It is very helpful to me I really like it

136. Mona

It is very useful for me

137. Planck’s constant dimensions are MLT^-1 not ML^2T^-1

138. Emily Jane

not at all usefull just wasted my time

139. shanmugam

IT IS USEFUL TO REMEMBER EASILY BUT IT IS HAVING SO ,MANY THINGS THAT CAN’T BE PICKED UP IN MIND

140. shanmugam

vaanmukilan – useful

141. Gayathri

It was really helpful….thnx a lot

142. alok raj

it is very simple to learn and rember of this table