The 7 SI base units can be used to derive all other SI units called SI derived units.
The following table shows some commonly used SI derived units.
| Qunatity | Symbol | SI Unit Name | SI Unit | Conversion to Base Units | Remarks |
|---|---|---|---|---|---|
| Area | \(A\) | - | \(\text{m}^2\) | \(\text{m}^2\) | - |
| Volume | \(V\) | - | \(\text{m}^3\) | \(\text{m}^3\) | - |
| Force | \(F\) | Newton | \(\text{N}\) | \(\text{kg} \cdot \text{m/s}^2\) | - |
| Weight | \(w\) | Newton | \(\text{N}\) | \(\text{kg} \cdot \text{m/s}^2\) | - |
| Work | \(W\) | Joule | \(\text{J}\) or \(\text{N}\cdot\text{m}\) | \(\text{kg} \cdot \text{m}^2/\text{s}^2\) | - |
| Kinetic Energy | \(K\) | Joule | \(\text{J}\) or \(\text{N}\cdot\text{m}\) | \(\text{kg} \cdot \text{m}^2/\text{s}^2\) | - |
| Potential Energy | \(U\) | Joule | \(\text{J}\) or \(\text{N}\cdot\text{m}\) | \(\text{kg} \cdot \text{m}^2/\text{s}^2\) | - |
| Energy | \(E\) | Joule | \(\text{J}\) or \(\text{N}\cdot\text{m}\) | \(\text{kg} \cdot \text{m}^2/\text{s}^2\) | - |
| Power | \(P\) | Watt | \(\text{W}\) or \(\text{J/s}\) | \(\text{kg} \cdot \text{m}^2/\text{s}^3\) | - |
| Impulse | \(J\) | - | \(\text{N}\cdot\text{s}\) | \(\text{kg} \cdot \text{m/s}\) | - |
| Momentum (Linear) | \(p\) | - | \(\text{kg} \cdot \text{m/s}\) | \(\text{kg} \cdot \text{m/s}\) | - |
| Angular Momentum | \(L\) | - | \(\text{kg} \cdot \text{m}^2/{s}\) | \(\text{kg} \cdot \text{m}^2/{s}\) | - |
| Moment of Inertia | \(I\) | - | \(\text{kg} \cdot \text{m}^2\) | \(\text{kg} \cdot \text{m}^2\) | - |
| Torque | \(\tau\) | - | \(\text{N} \cdot \text{m}\) | \(\text{kg} \cdot \text{m}^2/\text{s}^2\) | The SI unit of torque is not Joule(\(\text{J}\)) even though we used Newton-meter as Joule for work and energy. Torque is not the work or energy. |
| Pressure | \(p\) | Pascal | \(\text{Pa}\) or \(\text{N}/\text{m}^2\) | \(\text{kg}/(\text{m} \cdot \text{s}^2)\) | - |
| Stress | - | Pascal | \(\text{Pa}\) or \(\text{N}/\text{m}^2\) | \(\text{kg}/(\text{m} \cdot \text{s}^2)\) | - |
| Density | \(\rho\) | - | \(\text{kg}/\text{m}^3\) | \(\text{kg}/\text{m}^3\) | - |
| Frequency | \(f\) | Hertz | \(\text{Hz}\) | \(\text{s}^{-1}\) | - |
| Heat | \(Q\) | Joule | \(\text{J}\) | \(\text{kg} \cdot \text{m}^2/\text{s}^2\) | - |
| Heat Current | \(H\) | Watt | \(\text{W}\) or \(\text{J/s}\) | \(\text{kg} \cdot \text{m}^2/\text{s}^3\) | - |
| Entropy | \(S\) | - | \(\text{J/K}\) | \((\text{kg} \cdot \text{m}^2)/(\text{K} \cdot \text{s}^2)\) | - |
| Electric Charge | \(q\) or \(Q\) | Coulomb | \(\text{C}\) | \(\text{A} \cdot \text{s}\) | - |
| Electric Flux | \(\Phi\) | - | \(\text{N} \cdot \text{m}^2 / \text{C}\) | \((\text{kg}\cdot\text{m}^3)/(\text{A}\cdot\text{s}^3)\) | - |
| Electric Potential or Potential Difference | \(V\) | Volt | \(\text{J} / \text{C}\) | \((\text{kg}\cdot\text{m}^2)/(\text{A}\cdot\text{s}^3)\) | - |
| Emf | \(\mathcal{E}\) | Volt | \(\text{J} / \text{C}\) | \((\text{kg}\cdot\text{m}^2)/(\text{A}\cdot\text{s}^3)\) | - |
| Electric Field | \(E\) | - | \(\text{N} / \text{C}\) or \(\text{V} /\text{m}\) | \((\text{kg}\cdot\text{m})/(\text{A}\cdot\text{s}^3)\) | - |
| Capacitance | \(C\) | Farad | \(\text{F}\) or \(\text{C} /\text{V}\) | \((\text{A}^2\cdot\text{s}^4)/(\text{kg}\cdot\text{m}^2)\) | - |
| Resistance | \(R\) | Ohm | \(\Omega\) or \(\text{V} /\text{A}\) | \((\text{kg}\cdot\text{m}^2)/(\text{A}^2\cdot\text{s}^3)\) | - |
| Magnetic Field | \(B\) | Tesla | \(\text{T}\) or \(\text{N} /\text{A}\cdot\text{m}\) | \(\text{kg}/(\text{A}\cdot\text{s}^2)\) | - |
| Magnetic Flux | \(\Phi_B\) | Weber | \(\text{Wb}\) or \(\text{T}\cdot\text{m}^2\) | \(\text{kg}\cdot\text{m}^2/(\text{A}\cdot\text{s}^2)\) | - |
| Magnetic Dipole Moment | \(\mu\) | - | \(\text{A}\cdot\text{m}^2\) | \(\text{A}\cdot\text{m}^2\) | - |
| Inductance | \(L\) | Henry | \(\text{H}\) or \(\text{Wb}/\text{A}\) or \(\text{V}\cdot\text{s}/\text{A}\) or \(\Omega \cdot\text{s}\) | \((\text{kg}\cdot\text{m}^2)/(\text{A}^2\cdot\text{s}^2)\) | - |
| Reactance | \(X\) | Ohm | \(\Omega\) | \((\text{kg}\cdot\text{m}^2)/(\text{A}^2\cdot\text{s}^3)\) | - |
| Impedance | \(Z\) | Ohm | \(\Omega\) | \((\text{kg}\cdot\text{m}^2)/(\text{A}^2\cdot\text{s}^3)\) | - |
These SI base units and all SI derived units from those SI base units are used to measure all physical quantities in Physics.
The 7 SI base units and all derived units from those SI base units are collectively called SI units.
You can further increase or decrease size of these units using unit prefixes. We also need to convert one form of unit to another form, more generally from other types of units to the SI units. While doing so, we carry the units and cancel them as needed. A good habit in calculations in Physics is to carry them in the calculation and cancel them as needed. It will help to keep track of whether the calculation is going in the right direction or not.
