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All Dimensional Formula List PDF Details



PDF Name 
All Dimensional Formula List

No. of Pages  05 
PDF Size  96.4KB 
Language  English 
Category  Education & Job 
Source  cuemath.com 
Dimensional Formula
In mathematics, a dimension is a measurement of length, width, or height extended in a certain direction. It is a measure of a point or line extended in one direction, according to dimension definition. Every shape we see has a set of dimensions. In mathematics, there is no specific dimensional formula for the idea of dimension. The power to which the fundamental units are elevated to obtain one unit of any physical quantity is called its dimension.
What Is the Dimensional Formula?
The dimensional formula of any quantity is the expression showing the powers to which the fundamental units are to be raised to obtain one unit of a derived quantity. If Q is any physical quantity, the expression representing its dimensional formula is given by,
Dimensional Formula:
Q = M^{a}L^{b}T^{c}
where, M, L, T are base dimensions mass, length, and time respectively and a, b and, c are their respective exponents.
All Dimensional Formula List
Dimensional formulas for several physical quantities are shown in the table below:
Physical quantity  Unit  Dimensional formula 
Length  m  L 
Mass  kg  M 
Time  s  T 
Acceleration or acceleration due to gravity  ms^{–2}  LT^{–2} 
Angle (arc/radius)  rad  M^{o}L^{o}T^{o} 
Angular displacement  rad  M^{o}L^{o}T^{o} 
Angular frequency (angular displacement/time)  rads^{–1}  T^{–1} 
Angular impulse (torque × time)  Nms  ML^{2}T^{–1} 
Angular momentum (Iω)  kgm^{2}s^{–1}  ML^{2}T^{–1} 
Angular velocity (angle/time)  rads^{–1}  T^{–1} 
Area (length × breadth)  m^{2}  L^{2} 
Boltzmann’s constant  JK^{–1}  ML^{2}T^{–2}θ^{–1} 
Bulk modulus (ΔP × (V/ΔV))  Nm^{–2}, Pa  M^{1}L^{–1}T^{–2} 
Calorific value  Jkg^{–1}  L^{2}T^{–2} 
Coefficient of linear or areal or volume expansion  ^{o}C^{–1} or K^{–1}  θ^{–1} 
Coefficient of surface tension (force/length)  Nm^{–1} or Jm^{–2}  MT^{–2} 
Coefficient of thermal conductivity  Wm^{–1}K^{–1}  MLT^{–3}θ^{–1} 
Coefficient of viscosity (F = η × A × (dv/dx))  poise  ML^{–1}T^{–1} 
Compressibility (1/bulk modulus)  Pa^{–1}, m^{2}N^{–2}  M^{–1}LT^{2} 
Density (mass / volume)  kgm^{–3}  ML^{–3} 
Displacement, wavelength, focal length  m  L 
Electric capacitance (charge/potential)  CV^{–1}, farad  M^{–1}L^{–2}T^{4}I^{2} 
Electric conductance (1/resistance)  Ohm^{–1} or mho or siemen  M^{–1}L^{–2}T^{3}I^{2} 
Electric conductivity (1/resistivity)  siemen/metre or Sm^{–1}  M^{–1}L^{–3}T^{3}I^{2} 
Electric charge or quantity of electric charge (current × time)  coulomb  IT 
Electric current  ampere  I 
Electric dipole moment (charge × distance)  Cm  LTI 
Electric field strength or Intensity of electric field (force/charge)  NC^{–1}, Vm^{–1}  MLT^{–3}I^{–1} 
Electric resistance (potential difference/current)  ohm  ML^{2}T^{–3}I^{–2} 
Emf (or) electric potential (work/charge)  volt  ML^{2}T^{–3}I^{–1} 
Energy (capacity to do work)  joule  ML^{2}T^{–2} 
Energy density (energy/volume)  Jm^{–3}  ML^{–1}T^{–2} 
Entropy (ΔS = ΔQ/T)  Jθ^{–1}  ML^{2}T^{–2}θ^{–1} 
Force (mass x acceleration)  newton (N)  MLT^{–2} 
Force constant or spring constant (force/extension)  Nm^{–1}  MT^{–2} 
Frequency (1/period)  Hz  T^{–1} 
Gravitational potential (work/mass)  Jkg^{–1}  L^{2}T^{–2} 
Heat (energy)  J or calorie  ML^{2}T^{–2} 
Illumination (Illuminance)  lux (lumen/metre^{2})  MT^{–3} 
Impulse (force x time)  Ns or kgms^{–1}  MLT^{–1} 
Inductance (L) (energy = 1212 LI^{2} orCoefficient of selfinduction  henry (H)  ML^{2}T^{–2}I^{–2} 
Intensity of gravitational field (F/m)  Nkg^{–1}  L^{1}T^{–2} 
Intensity of magnetization (I)  Am^{–1}  L^{–1}I 
Joule’s constant or mechanical equivalent of heat  Jcal^{–1}  M^{o}L^{o}T^{o} 
Latent heat (Q = mL)  Jkg^{–1}  M^{o}L^{2}T^{–2} 
Linear density (mass per unit length)  kgm^{–1}  ML^{–1} 
Luminous flux  lumen or (Js^{–1})  ML^{2}T^{–3} 
Magnetic dipole moment  Am^{2}  L^{2}I 
Magnetic flux (magnetic induction x area)  weber (Wb)  ML^{2}T^{–2}I^{–1} 
Magnetic induction (F = Bil)  NI^{–1}m^{–1} or T  MT^{–2}I^{–1} 
Magnetic pole strength  Am (ampere–meter)  LI 
Modulus of elasticity (stress/strain)  Nm^{–2}, Pa  ML^{–1}T^{–2} 
Moment of inertia (mass × radius^{2})  kgm^{2}  ML^{2} 
Momentum (mass × velocity)  kgms^{–1}  MLT^{–1} 
Permeability of free space (μo=4πFd2m1m2)(μo=4πFd2m1m2)  Hm^{–1} or NA^{–2}  MLT^{–2}I^{–2} 
Permittivity of free space (εo=Q1Q24πFd2)(εo=Q1Q24πFd2)  Fm^{–1} or C^{2}N^{–1}m^{–2}  M^{–1}L^{–3}T^{4}I^{2} 
Planck’s constant (energy/frequency)  Js  ML^{2}T^{–1} 
Poisson’s ratio (lateral strain/longitudinal strain)  ––  M^{o}L^{o}T^{o} 
Power (work/time)  Js^{–1} or watt (W)  ML^{2}T^{–3} 
Pressure (force/area)  Nm^{–2} or Pa  ML^{–1}T^{–2} 
Pressure coefficient or volume coefficient  ^{o}C^{–1} or θ^{–1}  θ^{–1} 
Pressure head  m  M^{o}LT^{o} 
Radioactivity  disintegrations per second  M^{o}L^{o}T^{–1} 
Ratio of specific heats  ––  M^{o}L^{o}T^{o} 
Refractive index  ––  M^{o}L^{o}T^{o} 
Resistivity or specific resistance  Ω–m  ML^{3}T^{–3}I^{–2} 
Specific conductance or conductivity (1/specific resistance)  siemen/metre or Sm^{–1}  M^{–1}L^{–3}T^{3}I^{2} 
Specific entropy (1/entropy)  KJ^{–1}  M^{–1}L^{–2}T^{2}θ 
Specific gravity (density of the substance/density of water)  ––  M^{o}L^{o}T^{o} 
Specific heat (Q = mst)  Jkg^{–1}θ^{–1}  M^{o}L^{2}T^{–2}θ^{–1} 
Specific volume (1/density)  m^{3}kg^{–1}  M^{–1}L^{3} 
Speed (distance/time)  ms^{–1}  LT^{–1} 
Stefan’s constant (heat energyarea×time×temperature4)(heat energyarea×time×temperature4)  Wm^{–2}θ^{–4}  ML^{o}T^{–3}θ^{–4} 
Strain (change in dimension/original dimension)  ––  M^{o}L^{o}T^{o} 
Stress (restoring force/area)  Nm^{–2} or Pa  ML^{–1}T^{–2} 
Surface energy density (energy/area)  Jm^{–2}  MT^{–2} 
Temperature  ^{o}C or θ  M^{o}L^{o}T^{o}θ 
Temperature gradient (change in temperaturedistance)(change in temperaturedistance)  ^{o}Cm^{–1} or θm^{–1}  M^{o}L^{–1}T^{o}θ 
Thermal capacity (mass × specific heat)  Jθ^{–1}  ML^{2}T^{–2}θ^{–1} 
Time period  second  T 
Torque or moment of force (force × distance)  Nm  ML^{2}T^{–2} 
Universal gas constant (work/temperature)  Jmol^{–1}θ^{–1}  ML^{2}T^{–2}θ^{–1} 
Universal gravitational constant (F=G.m1m2d2)(F=G.m1m2d2)  Nm^{2}kg^{–2}  M^{–1}L^{3}T^{–2} 
Velocity (displacement/time)  ms^{–1}  LT^{–1} 
Velocity gradient (dv/dx)  s^{–1}  T^{–1} 
Volume (length × breadth × height)  m^{3}  L^{3} 
Water equivalent  kg  ML^{o}T^{o} 
Work (force × displacement)  J  ML^{2}T^{–2} 
Decay constant  s^{1}  M^{0}L^{0}T^{1 } 
Potential energy  J  M^{1}L^{2}T^{2} 
Kinetic energy  J  M^{1}L^{2}T^{2} 
Uses of Dimensional Formula
The dimensional formula is used to check an equation’s accuracy and to determine the relationship between various physical quantities. The dimensional analysis is used to convert one system of units into another for any given quantity.
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