The *principle of dimensional homogeneity* states that all terms summed to yield an equation modelling a system must have the same dimensions.
**Theorem**
An equation *dimensionally homogenous* iff it can be written the form $f(\pi_{1},\pi_{2},\dots)=0$where $f$ is some function and $\pi_{1},\pi_{2},\dots$ are dimensionless products of variables and constants appearing in the original equation.
See [[Dimensional Analysis]].