Here are some size recommendations for different species: For smaller birds, like budgies, canaries, and finches, a cage that is at least 18 inches wide by 18 inches deep and 18 inches tall is good.

Notes on Cage Birds (Second series); or, Practical Hints on the Management of British and Foreign Cage Birds, Hybrids, and Canaries. Edited by W. T. Greene. Pp. xii + 340. (London: L. Upcott Gill ...