I know it's important to take a birth control pill every day at the same time to have the greatest chance at preventing pregnancy leading up to sex, but is it as important to be as precise with the time AFTER the sex has occurred?

You don’t really have to take your pill at the same time every day, just every day is enough.  It may not be the best practice to take one at night than another in the morning.  You should try to keep some regularity. 

The birth control pill works by preventing the release of an egg during ovulation.  If you take a pill everyday that will happen.  When you have sex doesn’t matter at all since you won’t have an egg to fertilize, if you’ve been taking your pill everyday.

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