Sexing Parrots & Parakeets: How Do You Tell if a Budgie is Male or Female?

Many parakeet owners start with one bird, and then decide that it would be nice to get their pet a mate, either for companionship, or possibly with the intention of breeding their birds. The best scenario is a compatible mate of the opposite sex, but firstly you need to know the sex of your bird. So, how do you tell if a budgie is male or female?