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How does conception actually occur? How does it relate to ovulation?

Ovulation occurs just about two weeks after the first day of your period. If all conditions are perfect, that's when conception happens. Usually one of your ovaries (and on rare occasions, both) will release an egg about 12 to 16 days after your cycle begins. The egg travels through the fallopian tube on its journey towards the uterus. The egg will only survive about 24 hours, so it needs to meet up with the sperm during that time in order for you to become pregnant. Each ejaculation is comprised of anywhere from 30 to 300 million squiggly sperm cells, which live up to 72 hours in the woman's body. But remember, it takes only one to fertilise the egg.

However, those millions of little squiggly swimmers do encounter some major obstacles along the way to fertilise that little egg. It's a long and hazardous journey for the sperm to meet up with that one little egg. The vagina itself is a hostile, acid environment that's tough on a sperm, not to mention the cervical mucus-cervix which forms a pretty effective road block all by itself, although it does thin out on your cycle's most fertile days. Then the sperm must continue on through the uterus and to the fallopian tube. And if the sperm and egg do happen to meet, the sperm must burrow into the egg's outer layer. Once the genetic material combines, you have an embryo. The embryo travels the remainder of the way down into the uterus and implants itself in the uterine wall and voilà! You're pregnant. 

Your doctor calculates your due date by counting 40 weeks from the start of your last menstrual period. Why the two bonus weeks of pregnancy? Your doctor can't be certain of the date when you last ovulated, but you can be sure of the last date your cycle started, so the count begins with that date.
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More questions

The best timing for pregnancy testing is once you miss your period.
Ectopic pregnancies are fertilized eggs which implant themselves outside of the uterus. They must be terminated and can indicate future fertility issues.
Ovulation is the period during which you can conceive. Tracking ovulation can be tricky, but you can increase your chances of conceiving through math, prediction kits, or simple scientific observation.
Implantation bleeding is not a common experience, but some women do report small amounts of blood with or without cramping roughly a week or less before their anticipated period.
Pregnancy tests are only as good as the execution. Read all instructions to avoid getting inaccurate results on a home pregnancy test.
The best over the counter kits measure luteinizing hormone (LH).
There are many things that you can do to increase your chances of getting pregnant.
How STD’s can affect your pregnancy, your baby and how you should deal with them during pregnancy.
Taking care of your body before and during pregnancy
Ovulation occurs just about two weeks after the first day of your period.