Here is what my new book says minimum cage dimensions: 36" long by 24 inches wide by 24 inches high Parakeets need to live in large cages because they are strong fliers and need to exercise their wings The above was from the book. Hope this helps
that was for grass parakeets very simalar to budgies but I just found the budgie page now this is for 1 bird minimum cage dimensions 12 inches long by 14 inches wide by 12 inches high. To tell you the truth I think that is way to small we bought the first cage it was that size Tiki was not in it long before I bought a bigger cage.
according to a previous post by superkeets or another person the minimum for one bird is 18x 18 x18. if you let your birds out you might be able to get by with a 16x 16x 16 but nothing smaller that that...and most people on this site recommend a cage wider than it is tall so you could use the space for more toys..