Atticus is very calm, even mellow.  His children think it is because he is old, but it has more to do with his attitude toward people.  He believes that everyone should be treated with respect.  What makes him unusual is that this idea extends to children, poor people, outcasts and people of all races.

Atticus tries to raise his children to be good people.  He treats them with "exaggerated courtesy" and more like adults than children.  This is likely due to his attitudes toward people in general, and the fact that he raised them without a mother.  He chose Calpurnia to be not just a cook and housekeeper, but rather his partner in raising his children.

Atticus is never mean or loud.  He threatens constantly to beat Scout and Jem, but it is revealed that he has never laid a hand on either of them.  He tells Jack that he has gotten away with threats instead, but based on Jem’s attitude it is clear that his children are more afraid of losing his respect and letting him down.

Atticus is soft-spoken, but when he talks everyone listens.  His manner at trial is polite and shrewd, but also unnervingly calm.  When he is polite and gentle to Mayella, she assumes he is making fun of her.  He treats the jury just as respectfully, and they return that respect by taking longer than usual to convict Tom.