Nothing is exact, and the only thing ultrasound can tell is an EDD-estimated due date. Nothing (unless you're undergoing fertility treatments and/or charting BBT) can tell you when you ovulated or when conception occured.
I assume paternity is called into question, as generally these questions are not otherwise asked. If this is the case, you need DNA testing done when the child is born.
A lot depends on when the ultrasound was. An ultrasound at 7 weeks pregnant (i.e., about 5 weeks after conception) will measure the embryo crown to rump, and the estimates at that stage are pretty accurate. When I did IVF, we knew exactly when the egg became an embryo, and when the ultrasonographer measured at 5 weeks 1 day after the embryo began, she said "I get 7 weeks 1 day." (In other words, she was spot on, if you add the two weeks to track back to the first day of the last period.) I would trust an early ultrasound.
But if your ultrasound(s) were later in the pregnancy, all babies grow at different rates, so you cannot count on them for dating conception.
As Clysta says, if you are wondering who is the father, a DNA test is the only real way to know.
They are pretty accurate but like they have said above, the only way to be really sure is to take a DNA test.
I have the same problem, I had an early ultrasound and they told me I was 8weeks + 5 days pregnant so worked out everything based on this, then when I had my first real scan last week they said I was 15 weeks exactly, which was nearly 2 weeks off what I thought!
I've been trying to work out dates of conception but finding it impossible, as my periods arent the most regular!
Conception calculator says my LMP was the 16th June which it wasnt - i'm usually due around the very end of the month - to the very start of the month.