Dimensional analysis: Difference between revisions

In [[engineering]] and [[science]], '''dimensional analysis''' is the analysis of the relationships between different [[Physical quantity|physical quantities]] by identifying their [[base quantity|base quantities]] (such as [[length]], [[mass]], [[time]], and [[electric current]]) and [[units of measurement]] (such as metersmetres and grams) and tracking these dimensions as calculations or comparisons are performed. The term dimensional analysis is also used to refer to [[conversion of units]] from one dimensional unit to another, which can be used to evaluate scientific formulae.

'''''Commensurable''''' physical quantities are of the same [[Kind of quantity|kind]] and have the same dimension, and can be directly compared to each other, even if they are expressed in differing units of measurement; e.g., metersmetres and feet, gallonsgrams and literspounds, seconds and years. ''Incommensurable'' physical quantities are of different kinds and have different dimensions, and can not be directly compared to each other, no matter what units they are expressed in, e.g. metres and grams, seconds and grams, metres and seconds. For example, asking whether a gram is larger than an hour is meaningless.