For 1 bird, the bare minimum for width is at least 1.5x their wingspan (this is the legal limit is some countries); ideally the minimum is 2x their wingspan (a more humane limit). Say we list the parakeet's (am assuming budgie) wingspan as 12 inches. 'Legal' minimum would be 18 inches; humane minimum would be 24 inches. This is for 1 single budgie.
Now considering you want to house multiple birds, that limit of 1.5x and 2x is no longer valid. You would be looking at more than 3x the individual wingspan. One place recommends 39 inches long, 20 inches wide and 32 inches high for two budgies that don't spend a lot of time in the cage - they explicitly say to get a larger cage if the birds will not be spending the majority of their time outside of the cage.
Now that's if you want to follow what veterinary schools, parrot books, and rescue organisations recommend. Ultimately it's your decision.
Around here, experience says to get a cage for your worst day. If things go south in your life (medical emergency, housing problems, family matters), what cage is ok for your birds to stay in for 48 hours plus with no outside time? If you go with the bare minimum, that's for you to sort out.