The columnar - to - equiaxed transition (CET) was investigated in Al-Cu alloys (Al-1wt.%Cu, Al-4.5wt.%Cu, Al-15wt.%Cu and Al-33.2wt.%Cu) solidified directionally upward from a chill face. The CET occurs when the temperature gradient in the melt ahead of the columnar front reaches minimum and critical values. Two dimensionless numbers (Ω and Π numbers) that can relate the system parameters (cooling rate, local solidification time and liquidus temperature of the alloy) were defined. The Ω number which shows a linear relationship with the local solidification time and the Π number, that for the Al-rich region in the Al-Cu system, strongly depend on the macrostructure. These results are important to correlate the experimental values of physical quantities, which are relevant to describe the solidification process.