From AMS Glossary
The theorem states that an equation for a physical system that can be written f(Q1, Q2, . . . , Qm) = 0 can also be written as g(π1, π2, . . . , πm - n) = 0 where Qi are m dimensional parameters, numbers, and variables; πi are m - n nondimensional quantities; and n is the number of fundamental dimensional units.