Dimensional Formulae and Dimensional Equations

Physical quantity

Unit

Dimensional formula

Acceleration or acceleration due to gravity

ms^–2

LT^–2

Angle (arc/radius)

rad

M^oL^oT^o

Angular displacement

rad

M^ol^oT^o

Angular frequency (angular displacement/time)

rads^–1

T^–1

Angular impulse (torque x time)

Nms

ML²T^–1

Angular momentum (Iω)

kgm²s^–1

ML²T^–1

Angular velocity (angle/time)

rads^–1

T^–1

Area (length x breadth)

m²

L²

Boltzmann’s constant

JK^–1

ML²T^–2θ^–1

Bulk modulus (ΔP.VΔV.)

Nm^–2, Pa

M¹L^–1T^–2

Calorific value

Jkg^–1

L²T^–2

Coefficient of linear or areal or volume expansion

OC^–1 or K^–1

θ^–1

Coefficient of surface tension (force/length)

Nm^–1 or Jm^–2

MT^–2

Coefficient of thermal conductivity

Wm^–1K^–1

MLT^–3θ^–1

Coefficient of viscosity (F =ηAdvdx)

poise

ML^–1T^–1

Compressibility (1/bulk modulus)

Pa^–1, m²N^–2

M^–1LT²

Density (mass / volume)

kgm^–3

ML^–3

Displacement, wavelength, focal length

m

L

Electric capacitance (charge/potential)

CV^–1, farad

M^–1L^–2T⁴I²

Electric conductance (1/resistance)

Ohm^–1 or mho or siemen

M^–1L^–2T³I²

Electric conductivity (1/resistivity)

siemen/metre or Sm^–1

M^–1L^–3T³I²

Electric charge or quantity of electric charge (current x time)

coulomb

IT

Electric current

ampere

I

Electric dipole moment (charge x distance)

Cm

LTI

Electric field strength or Intensity of electric field (force/charge)

NC^–1, Vm^–1

MLT^–3I^–1

Electric resistance (potential difference current)

ohm

ML²T^–3I^–2

Emf (or) electric potential (work/charge)

volt

ML²T^–3I^–1

Energy (capacity to do work)

joule

ML²T^–2

Energy density (energyvolume)

Jm^–3

ML^–1T^–2

Entropy (ΔS=ΔQ/T)

Jθ^–1

ML²T^–2θ^–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

L²T^–2

Heat (energy)

J or calorie

ML²T^–2

Illumination (Illuminance)

lux (lumen/metre2)

MT^–3

Impulse (force x time)

Ns or kgms^–1

MLT^–1

Inductance (L) (energy =12LI2) or

coefficient of self-induction

henry (H)

ML²T^–2I^–2

Intensity of gravitational field (F/m)

Nkg^–1

L¹T^–2

Intensity of magnetization (I)

Am^–1

L^–1I

Joule’s constant or mechanical equivalent of heat

Jcal^–1

M^oL^oT^o

Latent heat (Q = mL)

Jkg^–1

M^oL²T^–2

Linear density (mass per unit length)

kgm^–1

ML^–1

Luminous flux

lumen or (Js^–1)

ML²T^–3

Magnetic dipole moment

Am²

L²I

Magnetic flux (magnetic induction x area)

weber (Wb)

ML²T^–2I^–1

Magnetic induction (F = Bil)

NI^–1m^–1 or T

MT^–2I^–1

Magnetic pole strength (unit: ampere–meter)

Am

LI

Modulus of ^elasticity (stress/strain)

Nm^–2, Pa

ML^–1T^–2

Moment of inertia (mass x radius2)

kgm²

ML²

Momentum (mass x velocity)

kgms^–1

MLT^–1

Permeability of free space (μo=4πFd2m1m2)

Hm^–1 or NA^–2

MLT^–2I^–2

Permittivity of free space (εo=Q1Q24πFd2.)

Fm^–1 or C²N^–1m^–2

M^–1L^–3T⁴I²

Planck’s constant (energy/frequency)

Js

ML²T^–1

Poisson’s ratio (lateral strain/longitudinal strain)

––

M^oL^oT^o

Power (work/time)

Js^–1 or watt (W)

ML²T^–3

Pressure (force/area)

Nm^–2 or Pa

ML^–1T^–2

Pressure coefficient or volume coefficient

OC^–1 or θ^–1

θ^–1

Pressure head

m

M^oLT^o

Radioactivity

disintegrations per second

M^oL^oT^–1

Ratio of specific heats

––

M^oL^oT^o

Refractive index

––

M^oL^oT^o

Resistivity or specific resistance

Ω–m

ML³T^–3I^–2

Specific conductance or conductivity (1/specific resistance)

siemen/metre or Sm^–1

M^–1L^–3T³I²

Specific entropy (1/entropy)

KJ^–1

M^–1L^–2T²θ

Specific gravity (density of the substance/density of water)

––

M^oL^oT^o

Specific heat (Q = mst)

Jkg^–1θ^–1

M^oL²T^–2θ^–1

Specific volume (1/density)

m³kg^–1

M^–1L³

Speed (distance/time)

ms^–1

LT^–1

Stefan’s constant(heat energy /area x time x temperature4).

Wm^–2θ^–4

ML^oT^–3θ^–4

Strain (change in dimension/original dimension)

––

M^oL^oT^o

Stress (restoring force/area)

Nm^–2 or Pa

ML^–1T^–2

Surface energy density (energy/area)

Jm^–2

MT^–2

Temperature

oC or θ

M^oL^oT^oθ

Temperature gradient (change in temperaturedistance)

OCm^–1 or θm^–1

M^oL^–1T^oθ

Thermal capacity (mass x specific heat)

Jθ^–1

ML²T^–2θ–1

Time period

second

T

Torque or moment of force (force x distance)

Nm

ML²T^–2

Universal gas constant (work/temperature)

Jmol^–1θ^–1

ML²T^–2θ^–1

Universal gravitational constant (F = G. m1m2d2)

Nm²kg^–2

M^–1L³T^–2

Velocity (displacement/time)

ms^–1

LT^–1

Velocity gradient (dv/dx)

s^–1

T^–1

Volume (length x breadth x height)

m³

L³

Water equivalent

kg

ML^oT^o

Work (force x displacement)

J

ML²T^–2