Dimensional Formula

In mathematics, dimensions were the measurements of an object’s and region’s or space’s size and even distance in one direction. It is also the measurement of something’s length, width, or height.

Types of Dimensions

• Zero Dimensional

A point is a zero-dimensional object as it has no length, breadth, or height. This has no dimensions. It merely mentions the place.

• One Dimensional

A one-dimensional object is a line segment drawn on a surface which only has length but no breadth.

• Two Dimensional 

In geometry, two-dimensional shapes and objects were flat planar figures with two dimensions: length and width. Two-dimensional (or 2-D) shapes also had no thickness, and they can only be assessed in two directions.

• Three dimensional

Solid figures, objects, or shapes with three dimensions — length, breadth, and height – were three-dimensional shapes within geometry. Three-dimensional shapes contain thickness and depth versus two-dimensional forms.

Dimensional Equations and Dimensional Formulas

A dimensional equation relates fundamental and derived units in terms of dimensions. The fundamental mechanical units were the metre, kilogramme, kelvin, mole, and candela, with length, mass, time, temperature, or electric current being the three base dimensions. The dimensional formula of different values is used to build a link between the variables in almost every dimensional equation. A dimensional equation can be described as follows:

Area dimensional formula (equation):

Area = length × breadth

= length × length

= [L] × [L]

= [L]2

Area(A) dimensional formula (equation) 

= [L2 M0T0]

Dimensional Formula Application

The dimensional formula is useful in the following situations:

• For any specified quantity, convert from one unit system to the next.
• It is a mathematical expression representing a single quantity in terms of the fundamental units.
• The dimensional formula helps in the calculation of relationships among physical quantities.
• It is a mathematical expression that expresses a single value in terms of the fundamental units.