Today half of my tooth broke off but it was realy random. i touched it and it just cracked off. is that normal for it break without any injury/impact?

Not normal: Your tooth may have been previously fractured by a bow, perhaps years ago, or from chewing ice, hard candy, etc. Can also be do to cavity undermining support for the enamel. Please see your Dentist immediately for restoration.

See DDS: See the dentist, there was either decay or a fracture evident, which you did not know about. See the dentist to have your dentition checked, so there are no more surprises.