Dimensional analysis: Difference between revisions

'''''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., metres and feet, grams and pounds, seconds and years. ''Incommensurable'' physical [[Quantity|quantities]] are of different [[Kind of quantity|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.

Any physically meaningful [[equation]], or [[inequality (mathematics)|inequality]], ''must'' have the same dimensions on its left and right sides, a property known as ''dimensional homogeneity''. Checking for dimensional homogeneity is a common application of dimensional analysis, serving as a plausibility check on [[Formal proof|derived]] equations and [[Computation|computations]]. It also serves as a guide and constraint in deriving equations that may describe a physical [[system]] in the absence of a more rigorous derivation.