Formal apology letter conveys your sincerest and heartfelt apologies to the reader in the formal and a professional tone. Through this letter sender expresses a thought of guilt for a mistake, insincere or an unethical act and says sorry to the reader. A sample letter is given below for reference.

Sample Formal Apology Letter

Mr. James Anderson
Professor  of Mechanics
University of Nottingham

24th May,2014

Subject:  Formal apology letter.
Respected Sir,

I am writing this letter to express my sincerest apologies to you in reference to the insincere behaviour that I showed up in the class yesterday. I genuinely feel very sad on my part to display an act of disrespect towards you in the class.

While returning home, I deeply realized my actions and words which I said in the class at that time and the thought makes me feel really guilty. I would like to sincerely apologize from the deepest core of my heart for behaving so recklessly in the heat of the moment. I assure you that I will pace up with my academics and tune favourably with all the lectures, assignments, tests and practical performances. I am writing this letter and beg for your forgiveness. Please give me last chance to be a better student and person.

I once again apologise for such an unethical and disobedient behaviour but I promise you that I will abide by the rules, norms and conduct that are expected in the classroom.

Thanking you for your consideration.
Yours obedient,
Michael Wills

Student- 2nd Semester