What is the difference between 究竟 and 到底 ？ So， a teacher explained to me that 究竟 is a more formal way of saying 到底. However, I'm still curious are there any other usage differences between the two? Is 究竟  only used in examples that are relatively “夸张” 
Ex。 你究竟为什么要离开我。
1) "究竟" is more formal than "到底". In everyday spoken Chinese, "究竟" is rarely used. It is used almost only in drama and written Chinese.

2) Well, I would say that the magnitude of "究竟" is equal to that of "到底". They are all equivalent to "on the earth".