Although they are not powerful enough to break your finger, parrot bites are going to hurt, and the area will probably be tender for a while and take time to recover. However, how badly a parrot bite will hurt mainly depends on the following factors.
Factors for the Severity of a Bite
The Size of the Parrot
Without underestimating small parrots like budgies and their smaller beaks, some species like macaws and cockatoo are renowned for their reasonably large beaks and are associated with the most powerful bites.
How Threatened They Feel
Just like humans, parrots can control how much force to exert into their bite. How badly the bite will hurt depends on the situation and how vulnerable the parrot is feeling.
Not comfortable with what you are doing
Certain parakeet species like budgies are serious birds and will use a quick and relatively gentle bite. It is not very painful, but uncomfortable enough to get your attention.
Reasons for Biting
Most parrots have reasons for attacking, and these reasons need to be understood. Here are the significant reasons why a parrot could be biting.
Parrots may develop a fear of humans if they are not adequately socialized. They may end up biting their owners out of fear, or they are frightened by something, thus influencing them to attack.
Stress, hormonal changes during breeding seasons, territoriality, are some of the causes of attacks. These factors influence parrots to behave aggressively or defensively.
Also, parrots use their beaks for multiple functions: preening, climbing, eating. It is, therefore, always important to evaluate whether or not your parrot is biting or it is merely using its beak just like other hookbills.