# Pi theorem

From Glossary of Meteorology

## Pi theorem

The theorem states that an equation for a physical system that can be written

*f*(*Q*_{1},*Q*_{2}, . . . ,*Q*_{m}) = 0 can also be written as*g*(*π*_{1},*π*_{2}, . . . ,*π*_{m - n}) = 0 where*Q*_{i}are*m*dimensional parameters, numbers, and variables; π_{i}are*m*-*n*nondimensional quantities; and*n*is the number of fundamental dimensional units.