In an adult bird, this is fairly easy – the males have a blue cere (the area just above the beak, where the nostrils are) and the females have a white or brown cere, sometimes tinged with blue around the top and/or the nostrils.
The problem is with determining young birds or some of the fancy coloured budgies. Baby male budgies have a pink or purple or a combination of pink and purple cere. Baby female budgies have a white, pink or blue or a combination of white, pink and blue cere (which can sometimes look purple). Usually the young male's cere is a little darker than the young female's cere if they are the same colour.
Thanks to Louis Garwood for the use of these pictures.
One of the first pairs of budgies that I got – and I got them from a store – might have been K-Mart of another like that (I didn't even know then that people bred budgies in their homes and a breeder would be a better place to get them). Anyway, the clerk helped me pick out a male and a female. The male had a blue cere and the female had a very light pink cere. It turned out that I did actually have a male and a female, but the one that the clerk and I both thought was a female was the male and the one we thought was a male was the female.
A breeder who has been breeding budgies for awhile usually learns to be able to tell the subtle differences in the colours of the ceres when his birds are young and is really the best person to help you find the sex of budgie that you are looking for. Even the breeder is never always right because it is very difficult to tell with some of the babies, especially some the fancy coloured ones, when both sexes seem to have mostly pink ceres.
If you want help to decide if you have a male or female budgie, see if you can get a good clear picture of your bird's head and post it in the forum.
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