Develop the appropriate, academic tone for the letter. While you are not writing an essay for the professor, you still are essentially composing an argument paper with which you want the professor to agree with your point of view. An academic tone essentially gives your professor an informed argument about why you need more time before taking the exam. Write in complete sentences. Do not use Internet shorthand or emoticons.
State the purpose of your email in the subject line, if a shortage of time requires an email. Provide your class name and section number in the subject line of the email if the class is particularly large. For example: Extension Requested/Shelley Smith/Computer Science 101 MWF 9-9:50.
Compose a note that is brief, yet informative. Deliver the note in person if at all possible; if the letter must be sent as a email, still keep the tone as academic and professional as possible.
Begin the letter with the appropriate greeting, such as "Dear Professor Miller." Open the letter with a formal statement of intent, including your name and the class you attend: "My name is Shelley Smith from your Computer Science 101 class. I am writing to request an extension on my final exam."
Inform the professor, from the beginning, why you are requesting the extension. If it is because of a medical problem or a death in the family, the professor could request documentation. If the extension is requested because of mental health, such as stress, make the reason clear. However, try to stay academic in your tone, rather than becoming melodramatic, when requesting more time to prepare.
Provide a completion date that you can fulfill the assignment. If the exam is on a Monday, request that your new date of taking the exam be within the week, at the most. Do not tell the professor that is when you will be taking the exam; rather, politely request a date that you know you can meet, still providing your best work.
Conclude the note with a salutation such as "Sincerely" or "Thank you for your time." Sign your full name, including the class section and time. Be sure to include an email address for the professor to respond if you have delivered a handwritten note.