The Estimated Date of Confinement (EDC) or due date (EDD) is usually calculated from the date of the last menstrual period (LMP). With someone who has irregular periods or doesn't know the date of her LMP, it's a challenge to determine when conception occurred.
if the doctor says "the calculated date of your menses is...let's say 1 of April"...
The doctor doesn't calculate the date of the last menstrual period. The doctor doesn't need that particular piece of information if it's not available.
In that case, the treating physician must obtain what's referred to as an "ultrasound for dates". This is important mostly to know not how the baby is doing - that's available on a regular ultrasound - but for exactly how old the baby is, because towards the end of the pregnancy, the physician needs to do special tests if the pregnancy is not progressing as it should. To know what should be happening, we need to know how old the fetus is exactly. Then the doctor will give the patient her estimated due date (EDD), not the estimated date of her last period.
In other words, the doctor doesn't need to estimate LMP, only EDD, so he/she will say, "Your baby's due date is (date based on fetal age)".
Confirming the correct dates of your pregnancy. Some women are uncertain of their last menstrual period (LMP) or have irregular menstrual cycles, making it difficult for their doctor to correctly estimate when the baby is due. Establishing accurate dates can be important, especially if there are concerns about your baby later in the pregnancy (for example, if the baby is not growing well). An ultrasound in the first trimester can give an accurate estimated date of confinement (EDC) to within 3-5 days. Generally speaking, the earlier in your pregnancy the ultrasound is performed, the more accurate it will be at estimating your baby’s due date (technical factors such as the quality of the ultrasound image and the expertise of the sonographer will affect this accuracy).
For example, if a baby is not born by it's due date, the physician must start ordering non-stress tests. Since it's actually more dangerous for the baby to be born late, the physician must consider inducing labor, something that isn't in anyone's best interests if it's not necessary. So, the ultrasound for dates.
The link on the bottom of this post discusses hoe the estimated due date (EDD) is calculated. An excerpt:
Determining the first day of the LMP traditionally is the first step in establishing the EDD. By convention, the EDD is 280 days after the first day of the LMP. Because this practice assumes a regular menstrual cycle of 28 days, with ovulation occurring on the 14th day after the beginning of the menstrual cycle, this practice does not account for inaccurate recall of the LMP, irregularities in cycle length, or variability in the timing of ovulation.
If there is question of paternity, there are tests for that. But it doesn't matter if the doctor picked up signs of ovuation. What matters is if the man and woman had sex and made a baby.
Method for Estimating Due Date