There's no way to give you an exact date.

Pregnancies last for nine months. December 27 to September 27 is nine months.

As Wondergirl stated, there is no way to know exact date. Women have different cycles from each other, ovulation will be different, length of pregnancy will be different.

Pregnancies are usually dated from your last menstrual period. Conception most likely, again it is not exact, will occur a week or two after that. With a due date of Sept. 27, it would put your conception to be around the end of December/early January.

If this is a matter of who the father might be, DNA testing will be the only way to know for sure if you were with more than one man within a few weeks period.