I watched a video on essential Japanese phrases and saw this sentence しりませんでした which translates to “I didn’t know that.” I’d like to know exactly what context this phrase is used in, and whether it’s formal or informal (I’m guessing that it’s at least semi-formal, but I want to make sure to avoid misunderstanding in the future.) I would also like to know what the informal form of this phrase is.
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Casual would be しらなかった
While it is formal it can be impolite to say. There’s a distinction between 分からない and 知らない where the latter can suggest something like “how am I supposed to know?” or “I don’t care about that.”
Your understanding is basicly correct,it’s formal and also semiformal.「しりませんでした」includes’until now’and also somewhat a little unpredictable emotion.equivarant saying is「しらなかったです」
There is no informal variant for this phrase,when it’s usedin talking between family members or your friends,「しらなかった」is usual form.
知る（しる）means “know”.
For positive situations, Japanese actually say the equivalent of “(I) am knowing”, which is 知っている ／ 知ってる informally or 知っています formally.
The negative “(I) don’t know” is 知らない informally or 知りません formally.
The past negative “(I) didn’t know” is 知らなかった informally or 知りませんでした formally.
Generally, unless you know someone very well, it’s best to use the formal forms (at least at the very ends of sentences).