Different ways to Apologize to people for different situations.
Informal: Sorry! I broke the window.
Formal: That's my fault, I'll fix it.
Informal
Sorry.
British
American
Sorry about that.
British
American
I'm so sorry.
British
American
I'm sorry for...
British
American
I'm sorry that...
British
American
Formal
I'm really sorry.
British
American
That's my fault / It was my fault.
British
American
How careless of me.
British
American
Please excuse my ignorance.
British
American
Please accept our apologies.
British
American