## Units and Dimensional Formulas of Physical Quantities

Physical quantity |
Unit |
Dimensional formula |

Acceleration or acceleration due to gravity | ms–2 | LT–2 |

Angle (arc/radius) | rad | MoLoTo |

Angular displacement | rad | MoloTo |

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.VΔVΔP.ΔVV.) |
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 =ηAdv/dx) | 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 differencecurrentcurrentpotential difference) |
ohm | ML2T–3I–2 |

Emf (or) electric potential (work/charge) | volt | ML2T–3I–1 |

Energy (capacity to do work) | joule | ML2T–2 |

Energy density (energyvolumevolumeenergy) |
Jm–3 | ML–1T–2 |

Entropy (ΔS=ΔQ/TΔS=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 =12LI221LI2) 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 | MoLoTo |

Latent heat (Q = mL) | Jkg–1 | MoL2T–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=4πFd2m1m2μo=m1m24πFd2) |
Hm–1 or NA–2 | MLT–2I–2 |

Permittivity of free space (εo=Q1Q24πFd2εo=4πFd2Q1Q2.) |
Fm–1 or C2N–1m–2 | M–1L–3T4I2 |

Planck’s constant (energy/frequency) | Js | ML2T–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 Pa | ML–1T–2 |

Pressure coefficient or volume coefficient | oC–1 or θ–1 | θ–1 |

Pressure head | m | MoLTo |

Radioactivity | disintegrations per second | MoLoT–1 |

Ratio of specific heats | –– | MoLoTo |

Refractive index | –– | MoLoTo |

Resistivity or specific resistance | ΩΩ–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) | –– | MoLoTo |

Specific heat (Q = mst) | Jkg–1θ–1 | MoL2T–2θ–1 |

Specific volume (1/density) | m3kg–1 | M–1L3 |

Speed (distance/time) | ms–1 | LT–1 |

Stefan’s constant(heat energyarea x time x temperature4)(area x time x temperature4heat energy). |
Wm–2θ–4 | MLoT–3θ–4 |

Strain (change in dimension/original dimension) | –– | MoLoTo |

Stress (restoring force/area) | Nm–2 or Pa | ML–1T–2 |

Surface energy density (energy/area) | Jm–2 | MT–2 |

Temperature | oC or θ | MoLoToθ |

Temperature gradient (change in temperaturedistancedistancechange in temperature) |
oCm–1 or θm–1 | MoL–1Toθ |

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. m1m2d2d2m1m2) |
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 | MLoTo |

Work (force x displacement) | J | ML2T–2 |