**Dimensional Analysis** is a technique for studying dimensions of physical quantities. It can also be used for other purposes as well, some of these other purposes are as following: –

- Reducing physical properties of derived SI units into those of the more fundamental SI base units
- Assist in converting quantities expressed in
**non-SI units**to**SI units** - Verfiying correctness of an equation in terms of
**dimensional**and**unitary consistency** - Determining dimension and unit of a
**variable**in an equation

A **Dimension Symbol** is represented as a capital letter enclosed in square brackets. For example – The dimension for time is [T], for mass it’s [M]. Below is a table containing Dimensional Symbols of SI Base units.

Table of Contents

## Dimension Symbols of SI Base Physical Quantities

Physical Quantity | Dimension Symbol |
---|---|

Time | [T] |

Length | [L] |

Mass | [M] |

Luminous Intensity | [J] |

Thermodynamic Temperature | |

Electric Current | [I] |

Amount of Substance | [N] |

## Dimensional Equations

For an equation describing some physical situation to be true, it need to have same dimensions on both sides of the equation. For instance – The velocity equation to be true on both sides of the equation and need to have same dimensions.

## Dimensional Symbols for Derived SI Units

Physical Quantity | SI Unit | Dimensional Symbol |
---|---|---|

Plane Angle | radian | |

Solid Angle | steradian | |

Frequency | hertz | |

Force | newton | |

Pressure | pascal | |

Energy | joule | |

Power | watt | |

Electric Charge | coulomb | |

Potential Difference | volt | |

Capacitance | farad | |

Electrical Resistance | ohm | |

Magnetic Flux | weber | |

Magnetic Flux Denstiy | tesla | |

Inductance | henry | |

Luminous Flux | lumen | |

illuminance | lux | |

Activity | bequerel | |

Area | square metre | |

Volume | cubic metre | |

Speed/Velocity | metre per second | |

Acceleration | metre per socond squared | |

Wavenumber | reciprocal metre | |

Density, Mass Density | kilogram per cubic metre | |

Specific Volume | cubic metre per kilogram | |

Current Density | ampere per square metre | |

Magnetic Field Strength | ampere per metre | |

Concentration of amount of substance | mole per cubic metre | |

Luminance | candela per square metre | |

Rate of Cooling | kelvin per second |