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Whether or not you can get pregnant during your period really depends on when you ovulate and how long your period lasts.

Keep in mind that sperm can live in the female reproductive tract for up to five days after intercourse.

Here's a scenario where you could get pregnant from sex during your period:
You have sex on cycle day six while you still have your period. You ovulate on cycle day ten. The sperm released on cycle day six when you had your period could still be capable of fertilizing your egg.

So, yes, in this and similar scenarios, you could get pregnant from the sex you had during your period.