Budgies are only sexually dimorphic, meaning you can tell their sex by looking at them, after 8 to 12 months of age. You can estimate their age by observing their feathers and eyes, and once they are older than 12 months, you can determine their sex by looking at the skin colour surrounding their nostrils. There are a few exceptions for some specially bred varieties of budgies, but determining their sex is still possible.
Estimate the age of your budgie by looking at its cap feathers. Some of these cap feathers running from its beak, across the top of its head and to its neck will look like black and white stripes. If there is a large white area closest to its beak, your budgie has already moulted once, meaning he is at least 3 to 4 months old. If you have a lutino/albino or a recessive pied budgie, you will not be able to determine its age this way as its feather markings are abnormal.
Look at your budgie's eyes to further estimate its age. Entirely dark eyes indicate a budgie that is less than 4 months old. Dark grey irises mean your budgie is likely 4 to 6 months old. By 6 to 8 months of age, your budgie's irises will be medium grey. Once your budgie is 8 months or older his eyes will be very light in colour. Some varieties are exceptions, including lutino/albino, lacewing, fallow, recessive pied and dark-eyed centre.
Look at your budgie's cere, which is where its nostrils are located just above its beak. In young birds, this patch of skin is typically either bright pink or violet. In budgies older than 12 months, this colour will vary for males or females. Male budgies will maintain the violet or pink colour from their youth if they are recessive pied, lutino/albino, dark-eyed clear, lacewing or fallow. The cere colour will change to blue or purplish-blue for all other males. All adult female budgies will have a white/light-blue, tan or brown cere.