The origins of dimensional analysis have been disputed by historians. The first written application of dimensional analysis has been credited to François Daviet, a student of Lagrange, in a 1799 article at the Turin Academy of Science.
This led to the conclusion that meaningful laws must be homogeneous equations in their various units of measurement, a result which was eventually later formalized in the Buckingham π theorem.
Simeon Poisson also treated the same problem of the parallelogram law by Daviet, in his treatise of 1811 and 1833 (vol I, p. 39). In the second edition of 1833, Poisson explicitly introduces the term dimension instead of the Daviet homogeneity.
In 1822, the important Napoleonic scientist Joseph Fourier made the first credited important contributions based on the idea that physical laws like Newton's second law| should be independent of the units employed to measure the physical variables.
James Clerk Maxwell played a major role in establishing modern use of dimensional analysis by distinguishing mass, length, and time as fundamental units, while referring to other units as derived. Although Maxwell defined length, time and mass to be "the three fundamental units", he also noted that gravitational mass can be derived from length and time by assuming a form of Newtons law of universal gravitation in which the gravitational constant  is taken as unity, thereby defining . By assuming a form of Coulombs law in which the Coulomb constant k is taken as unity, Maxwell then determined that the dimensions of an electrostatic unit of charge were , which, after substituting his  equation for mass, results in charge having the same dimensions as mass, viz. .
Dimensional analysis is also used to derive relationships between the physical quantities that are involved in a particular phenomenon that one wishes to understand and characterize.  It was used for the first time in this way in 1872 by Lord Rayleigh, who was trying to understand why the sky is blue.  Rayleigh first published the technique in his 1877 book The Theory of Sound.
The original meaning of the word dimension, in Fouriers Theorie de la Chaleur', was the numerical value of the exponents of the base units. For example, acceleration was considered to have the dimension 1 with respect to the unit of length, and the dimension −2 with respect to the unit of time. This was slightly changed by Maxwell, who said the dimensions of acceleration are TL, instead of just the exponents.