โญโญโญโญ (4.4/5 from 348 reviews)
Learn the dimensional formulas for various physical quantities, including derived SI units with special names. Explore how different quantities have the same dimensional formula and understand their significance in physics and engineering. Perfect for students and professionals looking to strengthen their knowledge of unit analysis and dimensional consistency
Derived SI units with Special Names
| Physical Quantity | SI Unit | Symbol |
| Frequency | hertz | Hz |
| Energy | joule | J |
| Force | newton | N |
| Power | watt | W |
| Pressure | pascal | Pa |
| Electric charge or quantity of electricity | coulomb | C |
| Electric potential difference and emf | volt | V |
| Electric resistance | ohm | \(\begin{array}{l}\Omega\end{array} \) |
| Electric conductance | siemen | S |
| Electric capacitance | farad | F |
| Magnetic flux | weber | Wb |
| Inductance | henry | H |
| Magnetic flux density | tesla | T |
| Illumination | lux | Lx |
| Luminous flux | lumen | Lm |
Dimensional Formulas for Important Physical Quantities
| Physical Quantity | Unit | Dimensional Formula |
| Acceleration or acceleration due to gravity | msโ2 | LTโ2 |
| Angle (arc/radius) | rad | MoLoTo |
| Angular displacement | rad | MoloTo |
| Angular frequency (angular displacement/time) | radsโ1 | Tโ1 |
| Angular impulse (torque x time) | Nms | ML2Tโ1 |
| Angular momentum (Iฯ) | kgm2sโ1 | ML2Tโ1 |
| Angular velocity (angle/time) | radsโ1 | Tโ1 |
| Area (length x breadth) | m2 | L2 |
| Boltzmannโs constant | JKโ1 | ML2Tโ2ฮธโ1 |
| Bulk modulus \(\begin{array}{l}\left(\Delta P.\frac{V}{\Delta V} \right)\end{array} \) | Nmโ2, Pa | M1Lโ1Tโ2 |
| Calorific value | Jkgโ1 | L2Tโ2 |
| Coefficient of linear or areal or volume expansion | oCโ1 or Kโ1 | ฮธโ1 |
| Coefficient of surface tension (force/length) | Nmโ1 or Jmโ2 | MTโ2 |
| Coefficient of thermal conductivity | Wmโ1Kโ1 | MLTโ3ฮธโ1 |
| Coefficient of viscosity \(\begin{array}{l}\left(F=\eta A\frac{dv}{dx} \right)\end{array} \) | poise | MLโ1Tโ1 |
| Compressibility (1/bulk modulus) | Paโ1, m2Nโ2 | Mโ1LT2 |
| Density (mass/volume) | kgmโ3 | MLโ3 |
| Displacement, wavelength, focal length | m | L |
| Electric capacitance (charge/potential) | CVโ1, farad | Mโ1Lโ2T4I2 |
| Electric conductance (1/resistance) | Ohmโ1 or mho or siemen | Mโ1Lโ2T3I2 |
| Electric conductivity (1/resistivity) | siemen/metre or Smโ1 | Mโ1Lโ3T3I2 |
| 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) | NCโ1, Vmโ1 | MLTโ3Iโ1 |
| Electric resistance \(\begin{array}{l}\left(\frac{potential\ difference}{current} \right)\end{array} \) | ohm | ML2Tโ3Iโ2 |
| Emf (or) electric potential (work/charge) | volt | ML2Tโ3Iโ1 |
| Energy (capacity to do work) | joule | ML2Tโ2 |
| Energy density \(\begin{array}{l}\left(\frac{energy}{volume} \right)\end{array} \) | Jmโ3 | MLโ1Tโ2 |
| Entropy \(\begin{array}{l}\left(\Delta S=\Delta Q/T \right)\end{array} \) | Jฮธโ1 | ML2Tโ2ฮธโ1 |
| Force (mass x acceleration) | newton (N) | MLTโ2 |
| Force constant or spring constant (force/extension) | Nmโ1 | MTโ2 |
| Frequency (1/period) | Hz | Tโ1 |
| Gravitational potential (work/mass) | Jkgโ1 | L2Tโ2 |
| Heat (energy) | J or calorie | ML2Tโ2 |
| Illumination (Illuminance) | lux (lumen/metre2) | MTโ3 |
| Impulse (force x time) | Ns or kgmsโ1 | MLTโ1 |
| Inductance (L) \(\begin{array}{l}\left(energy =\frac{1}{2}L{{I}^{2}} \right)\end{array} \) or coefficient of self-induction | henry (H) | ML2Tโ2Iโ2 |
| Intensity of gravitational field (F/m) | Nkgโ1 | L1Tโ2 |
| Intensity of magnetization (I) | Amโ1 | Lโ1I |
| Jouleโs constant or mechanical equivalent of heat | Jcalโ1 | MoLoTo |
| Latent heat (Q = mL) | Jkgโ1 | MoL2Tโ2 |
| Linear density (mass per unit length) | kgmโ1 | MLโ1 |
| Luminous flux | lumen or (Jsโ1) | ML2Tโ3 |
| Magnetic dipole moment | Am2 | L2I |
| Magnetic flux (magnetic induction x area) | weber (Wb) | ML2Tโ2Iโ1 |
| Magnetic induction (F = Bil) | NIโ1mโ1 or T | MTโ2Iโ1 |
| Magnetic pole strength (unit: ampereโmeter) | Am | LI |
| Modulus of elasticity (stress/strain) | Nmโ2, Pa | MLโ1Tโ2 |
| Moment of inertia (mass x radius2) | kgm2 | ML2 |
| Momentum (mass x velocity) | kgmsโ1 | MLTโ1 |
| Permeability of free space \(\begin{array}{l}\left(\mu_o = \frac{4\pi Fd^{2}}{m_1m_2} \right)\end{array} \) | Hmโ1 or NAโ2 | MLTโ2Iโ2 |
| Permittivity of free space \(\begin{array}{l}\left({{\varepsilon }_{o}}=\frac{{{Q}_{1}}{{Q}_{2}}}{4\pi F{{d}^{2}}} \right)\end{array} \) | Fmโ1 or C2Nโ1mโ2 | Mโ1Lโ3T4I2 |
| Planckโs constant (energy/frequency) | Js | ML2Tโ1 |
| Poissonโs ratio (lateral strain/longitudinal strain) | โโ | MoLoTo |
| Power (work/time) | Jsโ1 or watt (W) | ML2Tโ3 |
| Pressure (force/area) | Nmโ2 or Pa | MLโ1Tโ2 |
| Pressure coefficient or volume coefficient | oCโ1 or ฮธโ1 | ฮธโ1 |
| Pressure head | m | MoLTo |
| Radioactivity | disintegrations per second | MoLoTโ1 |
| Ratio of specific heats | โโ | MoLoTo |
| Refractive index | โโ | MoLoTo |
| Resistivity or specific resistance | \(\begin{array}{l}\Omega\end{array} \) โm | ML3Tโ3Iโ2 |
| Specific conductance or conductivity (1/specific resistance) | siemen/metre or Smโ1 | Mโ1Lโ3T3I2 |
| Specific entropy (1/entropy) | KJโ1 | Mโ1Lโ2T2ฮธ |
| Specific gravity (density of the substance/density of water) | โโ | MoLoTo |
| Specific heat (Q = mst) | Jkgโ1ฮธโ1 | MoL2Tโ2ฮธโ1 |
| Specific volume (1/density) | m3kgโ1 | Mโ1L3 |
| Speed (distance/time) | msโ1 | LTโ1 |
| Stefanโs constant \(\begin{array}{l}\left( \frac{heat\ energy}{area\ x\ time\ x\ temperatur{{e}^{4}}} \right)\end{array} \) . | Wmโ2ฮธโ4 | MLoTโ3ฮธโ4 |
| Strain (change in dimension/original dimension) | โโ | MoLoTo |
| Stress (restoring force/area) | Nmโ2 or Pa | MLโ1Tโ2 |
| Surface energy density (energy/area) | Jmโ2 | MTโ2 |
| Temperature | oC or ฮธ | MoLoToฮธ |
| Temperature gradient \(\begin{array}{l}\left(\frac{change\text{ in temperature}}{\text{distance}} \right)\end{array} \) | oCmโ1 or ฮธmโ1 | MoLโ1Toฮธ |
| Thermal capacity (mass x specific heat) | Jฮธโ1 | ML2Tโ2ฮธโ1 |
| Time period | second | T |
| Torque or moment of force (force x distance) | Nm | ML2Tโ2 |
| Universal gas constant (work/temperature) | Jmolโ1ฮธโ1 | ML2Tโ2ฮธโ1 |
| Universal gravitational constant \(\begin{array}{l}\left(F = G.\frac{{{m}_{1}}{{m}_{2}}}{{{d}^{2}}} \right)\end{array} \) | Nm2kgโ2 | Mโ1L3Tโ2 |
| Velocity (displacement/time) | msโ1 | LTโ1 |
| Velocity gradient (dv/dx) | sโ1 | Tโ1 |
| Volume (length x breadth x height) | m3 | L3 |
| Water equivalent | kg | MLoTo |
| Work (force x displacement) | J | ML2Tโ2 |
Quantities Having the Same Dimensional Formula
- Impulse and momentum.
- Work, torque, the moment of force, energy.
- Angular momentum, Planckโs constant, rotational impulse.
- Stress, pressure, modulus of elasticity, energy density.
- Force constant, surface tension, surface energy.
- Angular velocity, frequency, velocity gradient.
- Gravitational potential, latent heat.
- Thermal capacity, entropy, universal gas constant and Boltzmannโs constant.
- Force, thrust.
- Power, luminous flux.
