Both verbs can be translated as to know, but they have different meanings.
Use conocer when you mean "being familiar" or "being acquainted" with a thing, a place or a person.
Examples:
I know Juan. (Meaning I’m acquainted with Juan).
Conozco a Juan. (We have to use the personal a).
I know the rules. (Meaning I’m acquainted with the rules).
Conozco las reglas.
Use saber for skills (as in how to do something)
Examples:
I don’t know how to swim. (Meaning I can’t swim).
No sé nadar.
I know how to play the piano. (Meaning I can play the piano.)
Yo sé tocar el piano.
Use saber for “information:”
Examples:
I know that Peter lives in Viena.
Sé que Peter vive en Viena.
I know that you don’t know her.
Yo sé que tú no la conoces.
If you read the examples above, you’ll notice some structural differences: conocer usually takes a thing/place/person as a direct object (conozco [algo/a alguien]), while saber usually takes either verbs, for skills (nadar, tocar el piano) or subordinate clauses connected by que, which have a subject and a verb ([que] Peter vive en Viena, [que] tú no la conoces), for “information.”
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