A method of manipulating unit measures algebraically to determine the proper units for a quantity computed algebraically. For example, velocity has units of the form length over time (e.g., meters per second [ m/sec ]), and acceleration has units of velocity over time; so it follows that acceleration has units ( m/sec)/sec = m/(sec2).

A method of determining possible relationships between meteorological variables based on their dimensions. A systematic method called Buckingham Pi theory can be used to find such relationships. The results are often expressed as dimensionless groups, called Pi groups. While Buckingham Pi theory helps to identify the appropriate dimensionless groups, it cannot indicate the relationships between the groups. Such relationships must be found empirically, based on field or laboratory measurements of the dimensionless groups. When the empirical data are plotted on graphs of one dimensionless group versus another, often data from many disparate meteorological conditions will result in one common curve, yielding a similarity relationship that may be universal. Dimensional analysis has been used extensively and successfully in studies of the atmospheric boundary layer, where turbulence precludes other more precise descriptions of the flow because exact solutions of the equations of motion are impossible to find due to the closure problem. Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology, 347â€“404.

Dimensional analysis is a conceptual tool often applied in physics, chemistry, and engineering to understand physical situations involving a mix of different kinds of physical quantities. It is routinely used by physical scientists and engineers to check the plausibility of derived equations and computations. It is also used to form reasonable hypotheses about complex physical situations that can be tested by experiment or by more developed theories of the phenomena.