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All Dimensional Formula List
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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 = MaLbTc

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 quantityUnitDimensional formula
Acceleration or acceleration due to gravityms–2LT–2
Angle (arc/radius)radMoLoTo
Angular displacementradMoLoTo
Angular frequency (angular displacement/time)rads–1T–1
Angular impulse (torque × time)NmsML2T–1
Angular momentum (Iω)kgm2s–1ML2T–1
Angular velocity (angle/time)rads–1T–1
Area (length × breadth)m2L2
Boltzmann’s constantJK–1ML2T–2θ–1
Bulk modulus (ΔP × (V/ΔV))Nm–2, PaM1L–1T–2
Calorific valueJkg–1L2T–2
Coefficient of linear or areal or volume expansionoC–1 or K–1θ–1
Coefficient of surface tension (force/length)Nm–1 or Jm–2MT–2
Coefficient of thermal conductivityWm–1K–1MLT–3θ–1
Coefficient of viscosity (F = η × A × (dv/dx))poiseML–1T–1
Compressibility (1/bulk modulus)Pa–1, m2N–2M–1LT2
Density (mass / volume)kgm–3ML–3
Displacement, wavelength, focal lengthmL
Electric capacitance (charge/potential)CV–1, faradM–1L–2T4I2
Electric conductance (1/resistance)Ohm–1 or mho or siemenM–1L–2T3I2
Electric conductivity (1/resistivity)siemen/metre or Sm–1M–1L–3T3I2
Electric charge or quantity of electric charge (current × time)coulombIT
Electric currentampereI
Electric dipole moment (charge × distance)CmLTI
Electric field strength or Intensity of electric field (force/charge)NC–1, Vm–1MLT–3I–1
Electric resistance (potential difference/current)ohmML2T–3I–2
Emf (or) electric potential (work/charge)voltML2T–3I–1
Energy (capacity to do work)jouleML2T–2
Energy density (energy/volume​)Jm–3ML–1T–2
Entropy (ΔS = ΔQ/T)–1ML2T–2θ–1
Force (mass x acceleration)newton (N)MLT–2
Force constant or spring constant (force/extension)Nm–1MT–2
Frequency (1/period)HzT–1
Gravitational potential (work/mass)Jkg–1L2T–2
Heat (energy)J or calorieML2T–2
Illumination (Illuminance)lux (lumen/metre2)MT–3
Impulse (force x time)Ns or kgms–1MLT–1
Inductance (L) (energy = 1212 LI2 orCoefficient of self-inductionhenry (H)ML2T–2I–2
Intensity of gravitational field (F/m)Nkg–1L1T–2
Intensity of magnetization (I)Am–1L–1I
Joule’s constant or mechanical equivalent of heatJcal–1MoLoTo
Latent heat (Q = mL)Jkg–1MoL2T–2
Linear density (mass per unit length)kgm–1ML–1
Luminous fluxlumen or (Js–1)ML2T–3
Magnetic dipole momentAm2L2I
Magnetic flux (magnetic induction x area)weber (Wb)ML2T–2I–1
Magnetic induction (F = Bil)NI–1m–1 or TMT–2I–1
Magnetic pole strengthAm (ampere–meter)LI
Modulus of elasticity (stress/strain)Nm–2, PaML–1T–2
Moment of inertia (mass × radius2)kgm2ML2
Momentum (mass × velocity)kgms–1MLT–1
Permeability of free space (μo=4πFd2m1m2)(μo=4πFd2m1m2)Hm–1 or NA–2MLT–2I–2
Permittivity of free space (εo=Q1Q24πFd2)(εo=Q1Q24πFd2)Fm–1 or C2N–1m–2M–1L–3T4I2
Planck’s constant (energy/frequency)JsML2T–1
Poisson’s ratio (lateral strain/longitudinal strain)––MoLoTo
Power (work/time)Js–1 or watt (W)ML2T–3
Pressure (force/area)Nm–2 or PaML–1T–2
Pressure coefficient or volume coefficientoC–1 or θ–1θ–1
Pressure headmMoLTo
Radioactivitydisintegrations per secondMoLoT–1
Ratio of specific heats––MoLoTo
Refractive index––MoLoTo
Resistivity or specific resistanceΩ–mML3T–3I–2
Specific conductance or conductivity (1/specific resistance)siemen/metre or Sm–1M–1L–3T3I2
Specific entropy (1/entropy)KJ–1M–1L–2T2θ
Specific gravity (density of the substance/density of water)––MoLoTo
Specific heat (Q = mst)Jkg–1θ–1MoL2T–2θ–1
Specific volume (1/density)m3kg–1M–1L3
Speed (distance/time)ms–1LT–1
Stefan’s constant (heat energyarea×time×temperature4)(heat energyarea×time×temperature4)Wm–2θ–4MLoT–3θ–4
Strain (change in dimension/original dimension)––MoLoTo
Stress (restoring force/area)Nm–2 or PaML–1T–2
Surface energy density (energy/area)Jm–2MT–2
TemperatureoC or θMoLoToθ
Temperature gradient (change in temperaturedistance)(change in temperaturedistance)oCm–1 or θm–1MoL–1Toθ
Thermal capacity (mass × specific heat)–1ML2T–2θ–1
Time periodsecondT
Torque or moment of force (force × distance)NmML2T–2
Universal gas constant (work/temperature)Jmol–1θ–1ML2T–2θ–1
Universal gravitational constant (F=G.m1m2d2)(F=G.m1m2d2)Nm2kg–2M–1L3T–2
Velocity (displacement/time)ms–1LT–1
Velocity gradient (dv/dx)s–1T–1
Volume (length × breadth × height)m3L3
Water equivalentkgMLoTo
Work (force × displacement)JML2T–2
Decay constants-1M0L0T-1 
Potential energyJM1L2T-2
Kinetic energyJM1L2T-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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