Expanding on what Clysta said (which I agree with)...Conception typically isn't calculated until the fertilized egg implants into the uterus. Conception rarely occurs on the exact same day as intercourse...there is usually a window of a few days. Once the sperm fertilizes the egg it takes a day or so for it to travel down the fallopian tube and into the uterus and burrow into the lining. Once that occurs it triggers your body to start producing the pregnancy hormone. Being 3 days off from the day of intercourse is about as accurate as you will get and not at all uncommon. Congrats on the pregnancy :)
Sperm can last 5 days on average in the female body, and 7 in perfect conditions. Ultrasounds are fairly accurate, but are not 100% when it comes to determining when conception occurs. I've only gone full term once, and didn't track when we were sexually active so I can't say this has happened to me personally.