Dimensional Analysis
An analytical method used to verify equation consistency and establish mathematical relationships between physical quantities by examining fundamental dimensions.
Governing formula
[M]^a [L]^b [T]^c
SI unit
Dimensionless
In depth
Dimensional homogeneity requires every additive term in a physical equation to have identical fundamental dimensions (M, L, T, I, Θ, N, J). Buckingham π theorem uses dimensional analysis to reduce complex physical problems into dimensionless parameters.
Examples in the real world
Checking that kinetic energy (½mv²) has dimensions [M L² T⁻²], matching work (F·d = [M L T⁻²][L] = [M L² T⁻²]).